Orbit Determination (OD) Error Analysis Results for the Triana Sun-Earth L1 Libration Point Mission and for the Fourier Kelvin Stellar Interferometer (FKSI) Sun-Earth L2 Libration Point Mission Concept

NASA Technical Reports Server (NTRS)

Marr, Greg C.

2003-01-01

The Triana spacecraft was designed to be launched by the Space Shuttle. The nominal Triana mission orbit will be a Sun-Earth L1 libration point orbit. Using the NASA Goddard Space Flight Center's Orbit Determination Error Analysis System (ODEAS), orbit determination (OD) error analysis results are presented for all phases of the Triana mission from the first correction maneuver through approximately launch plus 6 months. Results are also presented for the science data collection phase of the Fourier Kelvin Stellar Interferometer Sun-Earth L2 libration point mission concept with momentum unloading thrust perturbations during the tracking arc. The Triana analysis includes extensive analysis of an initial short arc orbit determination solution and results using both Deep Space Network (DSN) and commercial Universal Space Network (USN) statistics. These results could be utilized in support of future Sun-Earth libration point missions.

The end-of-life disposal of satellites in libration-point orbits using solar radiation pressure

NASA Astrophysics Data System (ADS)

Soldini, Stefania; Colombo, Camilla; Walker, Scott

2016-04-01

This paper proposes an end-of-life propellant-free disposal strategy for libration-point orbits which uses solar radiation pressure to restrict the evolution of the spacecraft motion. The spacecraft is initially disposed into the unstable manifold leaving the libration-point orbit, before a reflective sun-pointing surface is deployed to enhance the effect of solar radiation pressure. Therefore, the consequent increase in energy prevents the spacecraft's return to Earth. Three European Space Agency missions are selected as test case scenarios: Herschel, SOHO and Gaia. Guidelines for the end-of-life disposal of future libration-point orbit missions are proposed and a preliminary study on the effect of the Earth's orbital eccentricity on the disposal strategy is shown for the Gaia mission.

Conceptual Design of a Synoptic Interplanetary Monitor Platform at L sub 1 (SIMPL).

DTIC Science & Technology

1985-11-01

solar events. -159- . . . .. . 105 II1II" -I .5 year mission at Earth-Sun- libration point plus transfer orbit eDashed line is approximate true dose as...Design .. ...................................... 27 4.1 The L Libration Point .......................... 27 4.2 L Orbit Options...34) to provide power, attitude control, communications, and other support to maintain the instruments in a halo orbit around the L libration point ; 4. a

Higher order approximation to the Hill problem dynamics about the libration points

NASA Astrophysics Data System (ADS)

Lara, Martin; Pérez, Iván L.; López, Rosario

2018-06-01

An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture all the relevant periodic orbits originated from the libration points within a reasonable accuracy, the normalization is approached in complex variables. The validity of the solution extends to energy values considerably far away from that of the libration points and, therefore, can be used in the computation of Halo orbits as an alternative to the classical Lindstedt-Poincaré approach. Furthermore, the theory correctly predicts the existence of the two-lane bridge of periodic orbits linking the families of planar and vertical Lyapunov orbits.

Integration of Libration Point Orbit Dynamics into a Universal 3-D Autonomous Formation Flying Algorithm

NASA Technical Reports Server (NTRS)

Folta, David; Bauer, Frank H. (Technical Monitor)

2001-01-01

The autonomous formation flying control algorithm developed by the Goddard Space Flight Center (GSFC) for the New Millennium Program (NMP) Earth Observing-1 (EO-1) mission is investigated for applicability to libration point orbit formations. In the EO-1 formation-flying algorithm, control is accomplished via linearization about a reference transfer orbit with a state transition matrix (STM) computed from state inputs. The effect of libration point orbit dynamics on this algorithm architecture is explored via computation of STMs using the flight proven code, a monodromy matrix developed from a N-body model of a libration orbit, and a standard STM developed from the gravitational and coriolis effects as measured at the libration point. A comparison of formation flying Delta-Vs calculated from these methods is made to a standard linear quadratic regulator (LQR) method. The universal 3-D approach is optimal in the sense that it can be accommodated as an open-loop or closed-loop control using only state information.

Flights between a neighborhoods of unstable libration points of Sun-Earth system

NASA Astrophysics Data System (ADS)

Surkova, Valerya; Shmyrov, Vasily

2018-05-01

In this paper we study the problem of constructing impulse flights between neighborhoods of unstable collinear libration points of the Sun-Earth system [1]. Such maneuvering in near-Earth space may prove to be in demand in modern space navigation. For example, such a maneuvering was done by the space vehicle GENESIS. Three test points are chosen for the implementation of the impulse control, in order to move to a neighborhood of the libration point L2. It is shown that the earlier on the exit from the vicinity of the libration point L1 impulse control was realized, the sooner the neighborhood L2 was achieved. Separated from this problem, the problem of optimal control in the neighborhood of L2 was considered and a form of stabilizing control is presented.

Human Exploration Missions Study: Space Surveillance Telescope Transfer to and Station at a Halo Orbit at the Earth-Sun Libration Point L2

NASA Technical Reports Server (NTRS)

Dauro, Vincent A., Sr.

2001-01-01

This study was undertaken to determine mission profile and delta velocity requirements to place a telescope at the Earth-Sun libration point L2. The program, Integrated Mission Program (IMP), was selected to be used in the investigation. A description of IMP and its capabilities may be found in the Addenda. The Addenda also contains the libration halo equations, constants and other parameters. Comments regarding the chaotic nature of numerical integration near the libration points are also attached in the Addenda. A basic two stage S/C with a simple mission profile was selected. This profile is shown.

Two-craft Coulomb formation study about circular orbits and libration points

NASA Astrophysics Data System (ADS)

Inampudi, Ravi Kishore

This dissertation investigates the dynamics and control of a two-craft Coulomb formation in circular orbits and at libration points; it addresses relative equilibria, stability and optimal reconfigurations of such formations. The relative equilibria of a two-craft tether formation connected by line-of-sight elastic forces moving in circular orbits and at libration points are investigated. In circular Earth orbits and Earth-Moon libration points, the radial, along-track, and orbit normal great circle equilibria conditions are found. An example of modeling the tether force using Coulomb force is discussed. Furthermore, the non-great-circle equilibria conditions for a two-spacecraft tether structure in circular Earth orbit and at collinear libration points are developed. Then the linearized dynamics and stability analysis of a 2-craft Coulomb formation at Earth-Moon libration points are studied. For orbit-radial equilibrium, Coulomb forces control the relative distance between the two satellites. The gravity gradient torques on the formation due to the two planets help stabilize the formation. Similar analysis is performed for along-track and orbit-normal relative equilibrium configurations. Where necessary, the craft use a hybrid thrusting-electrostatic actuation system. The two-craft dynamics at the libration points provide a general framework with circular Earth orbit dynamics forming a special case. In the presence of differential solar drag perturbations, a Lyapunov feedback controller is designed to stabilize a radial equilibrium, two-craft Coulomb formation at collinear libration points. The second part of the thesis investigates optimal reconfigurations of two-craft Coulomb formations in circular Earth orbits by applying nonlinear optimal control techniques. The objective of these reconfigurations is to maneuver the two-craft formation between two charged equilibria configurations. The reconfiguration of spacecraft is posed as an optimization problem using the calculus of variations approach. The optimality criteria are minimum time, minimum acceleration of the separation distance, minimum Coulomb and electric propulsion fuel usage, and minimum electrical power consumption. The continuous time problem is discretized using a pseudospectral method, and the resulting finite dimensional problem is solved using a sequential quadratic programming algorithm. The software package, DIDO, implements this approach. This second part illustrates how pseudospectral methods significantly simplify the solution-finding process.

Mission design for a halo orbiter of the earth

NASA Technical Reports Server (NTRS)

Farquhar, R. W.; Muhonen, D. P.; Richardson, D. L.

1976-01-01

The International Sun-Earth Explorer (ISEE) scientific satellite to be stationed in 1978 in the vicinity of the sun-earth interior libration point to continuously monitor the space between the sun and the earth, including the distant geomagnetic tail is described. Orbit selection considerations for the ISEE-C are discussed along with stationkeeping requirements and fuel-optimal trajectories. Due to the alignment of the interior libration point with the sun as viewed from the earth, it will be necessary to place the satellite into a 'halo orbit' around the libration point, in order to eliminate solar interference with down-link telemetry. Parametric data for transfer trajectories between an earth parking orbit (altitude about 185 km) and a libration-point orbit are presented. It is shown that the insertion magnitude required for placing a satellite into an acceptable halo orbit is rather modest.

Stochastic analysis of the control of the movement of the spacecraft in the vicinity of the colinear libration point by means of the forces of luminous pressure

NASA Technical Reports Server (NTRS)

Lukyanov, S. S.

1983-01-01

This paper is dedicated to the possible investigation of the utilization of the solar radiation pressure for the spacecraft motion control in the vicinity of collinear libration point of planar restricted ring problem of three bodies. The control is realized by changing the solar sail area at its permanent orientation. In this problem the influence of the trajectory errors and the errors of the execution control is accounted. It is worked out, the estimation method of the solar sail sizes, which are necessary for spacecraft keeping in the vicinity of collinear libration point during the certain time with given probability. The main control parameters were calculated for some examples in case of libration points of the Sun-Earth and Earth-Moon systems.

Effect of electromagnetic field on Kordylewski clouds formation

NASA Astrophysics Data System (ADS)

Salnikova, Tatiana; Stepanov, Sergey

2018-05-01

In previous papers the authors suggest a clarification of the phenomenon of appearance-disappearance of Kordylewski clouds - accumulation of cosmic dust mass in the vicinity of the triangle libration points of the Earth-Moon system. Under gravi-tational and light perturbation of the Sun the triangle libration points aren't the points of relative equilibrium. However, there exist the stable periodic motion of the particles, surrounding every of the triangle libration points. Due to this fact we can consider a probabilistic model of the dust clouds formation. These clouds move along the periodical orbits in small vicinity of the point of periodical orbit. To continue this research we suggest a mathematical model to investigate also the electromagnetic influences, arising under consideration of the charged dust particles in the vicinity of the triangle libration points of the Earth-Moon system. In this model we take under consideration the self-unduced force field within the set of charged particles, the probability distribution density evolves according to the Vlasov equation.

The Inherent Limitations of Spacepower: Fact or Fiction?

DTIC Science & Technology

1995-01-01

advantageously to affect near-earth space, as well as the Earth, itself. These are termed the libration points . Collins writes: The five so-called libration ... Libration points allow for little or no energy expense for station keeping, while operating from atop the "gravity well" allows for high potential energy...navigation, communica- tions, earth resources, lift orbit transfer , and tracking and control systems. Integrating many aspects of these systems to serve both

Optimization of Insertion Cost for Transfer Trajectories to Libration Point Orbits

NASA Technical Reports Server (NTRS)

Howell, K. C.; Wilson, R. S.; Lo, M. W.

1999-01-01

The objective of this work is the development of efficient techniques to optimize the cost associated with transfer trajectories to libration point orbits in the Sun-Earth-Moon four body problem, that may include lunar gravity assists. Initially, dynamical systems theory is used to determine invariant manifolds associated with the desired libration point orbit. These manifolds are employed to produce an initial approximation to the transfer trajectory. Specific trajectory requirements such as, transfer injection constraints, inclusion of phasing loops, and targeting of a specified state on the manifold are then incorporated into the design of the transfer trajectory. A two level differential corrections process is used to produce a fully continuous trajectory that satisfies the design constraints, and includes appropriate lunar and solar gravitational models. Based on this methodology, and using the manifold structure from dynamical systems theory, a technique is presented to optimize the cost associated with insertion onto a specified libration point orbit.

On the use of a sunward libration-point-orbiting spacecraft as an interplanetary magnetic field monitor for magnetospheric studies

NASA Technical Reports Server (NTRS)

Kelly, T. J.; Crooker, N. U.; Siscoe, G. L.; Russell, C. T.; Smith, E. J.

1986-01-01

In order to test the accuracy of using magnetometer data from a spacecraft orbiting the sunward libration point to determine the orientation of the interplanetary magnetic field (IMF), the angle between the IMF at ISEE 3, when it was positioned around the libration point, and at ISEE 1, orbiting the earth, has been calculated for a data set of 1-hour periods covering four months. For each period, a 10-minute average of ISEE 1 data is compared with 10-minute averages of ISEE 3 data at successively lagged intervals. It is concluded that the IMF orientation at a libration-point-orbiting spacecraft, lagged by the time required for the solar wind to convect to the earth, is a convenient predictor of IMF orientation near the earth, to within about 20-degree accuracy.

Use of libration-point orbits for space observatories

NASA Technical Reports Server (NTRS)

Farquhar, Robert W.; Dunham, David W.

1990-01-01

The sun-earth libration points, L1 and L2, are located 1.5 million kilometers from the earth toward and away from the sun. Halo orbits about these points have significant advantages for space observatories in terms of viewing geometry, thermal and radiation environment, and delta-V expediture.

Time-free transfers between libration-point orbits in the elliptic restricted problem

NASA Astrophysics Data System (ADS)

Howell, K. C.; Hiday-Johnston, L. A.

This work is part of a larger research effort directed toward the formulation of a strategy to design optimal time-free impulsive transfers between three-dimensional libration-point orbits in the vicinity of the interior LI libration point of the Sun-Earth/Moon barycenter system. Inferior transfers that move a spacecraft from a large halo orbit to a smaller halo orbit are considered here. Primer vector theory is applied to non-optimal impulsive trajectories in the elliptic restricted three-body problem in order to establish whether the implementation of a coast in the initial orbit, a coast in the final orbit, or dual coasts accomplishes a reduction in fuel expenditure. The addition of interior impulses is also considered. Results indicate that a substantial savings in fuel can be achieved by the allowance for coastal periods on the specified libration-point orbits. The resulting time-free inferior transfers are compared to time-free superior transfers between halo orbits of equal z-amplitude separation.

Time-free transfers between libration-point orbits in the elliptic restricted problem

NASA Astrophysics Data System (ADS)

Howell, K. C.; Hiday, L. A.

1992-08-01

This work is directed toward the formulation of a strategy to design optimal time-free impulsive transfers between 3D libration-point orbits in the vicinity of the interior L1 libration point of the sun-earth/moon barycenter system. Inferior transfers that move a spacecraft from a large halo orbit to a smaller halo orbit are considered here. Primer vector theory is applied to nonoptimal impulsive trajectories in the elliptic restricted three-body problem in order to establish whether the implementation of a coast in the initial orbit, a coast in the final orbit, or dual coasts accomplishes a reduction in fuel expenditure. The addition of interior impulses is also considered. Results indicate that a substantial savings in fuel can be achieved by the allowance for coastal periods on the specified libration-point orbits. The resulting time-free inferior transfers are compared to time-free superior transfers between halo orbits of equal z-amplitude separation.

Applying Dynamical Systems Theory to Optimize Libration Point Orbit Stationkeeping Maneuvers for WIND

NASA Technical Reports Server (NTRS)

Brown, Jonathan M.; Petersen, Jeremy D.

2014-01-01

NASA's WIND mission has been operating in a large amplitude Lissajous orbit in the vicinity of the interior libration point of the Sun-Earth/Moon system since 2004. Regular stationkeeping maneuvers are required to maintain the orbit due to the instability around the collinear libration points. Historically these stationkeeping maneuvers have been performed by applying an incremental change in velocity, or (delta)v along the spacecraft-Sun vector as projected into the ecliptic plane. Previous studies have shown that the magnitude of libration point stationkeeping maneuvers can be minimized by applying the (delta)v in the direction of the local stable manifold found using dynamical systems theory. This paper presents the analysis of this new maneuver strategy which shows that the magnitude of stationkeeping maneuvers can be decreased by 5 to 25 percent, depending on the location in the orbit where the maneuver is performed. The implementation of the optimized maneuver method into operations is discussed and results are presented for the first two optimized stationkeeping maneuvers executed by WIND.

Transfers between libration-point orbits in the elliptic restricted problem

NASA Astrophysics Data System (ADS)

Hiday, L. A.; Howell, K. C.

The present time-fixed impulsive transfers between 3D libration point orbits in the vicinity of the interior L(1) libration point of the sun-earth-moon barycenter system are 'optimal' in that the total characteristic velocity required for implementation of the transfer exhibits a local minimum. The conditions necessary for a time-fixed, two-impulse transfer trajectory to be optimal are stated in terms of the primer vector, and the conditions necessary for satisfying the local optimality of a transfer trajectory containing additional impulses are addressed by requiring continuity of the Hamiltonian and the derivative of the primer vector at all interior impulses.

Preliminary Design Considerations for Access and Operations in Earth-Moon L1/L2 Orbits

NASA Technical Reports Server (NTRS)

Folta, David C.; Pavlak, Thomas A.; Haapala, Amanda F.; Howell, Kathleen C.

2013-01-01

Within the context of manned spaceflight activities, Earth-Moon libration point orbits could support lunar surface operations and serve as staging areas for future missions to near-Earth asteroids and Mars. This investigation examines preliminary design considerations including Earth-Moon L1/L2 libration point orbit selection, transfers, and stationkeeping costs associated with maintaining a spacecraft in the vicinity of L1 or L2 for a specified duration. Existing tools in multi-body trajectory design, dynamical systems theory, and orbit maintenance are leveraged in this analysis to explore end-to-end concepts for manned missions to Earth-Moon libration points.

On the restricted four-body problem with the effect of small perturbations in the Coriolis and centrifugal forces

NASA Astrophysics Data System (ADS)

Suraj, Md Sanam; Aggarwal, Rajiv; Arora, Monika

2017-09-01

We have studied the restricted four-body problem (R4BP) with the effect of the small perturbation in the Coriolis and centrifugal forces on the libration points and zero velocity curves (ZVCs). Further, we have supposed that all the primaries are set in an equilateral triangle configuration, moving in the circular orbits around their common centre of mass. We have observed that the effect of the small perturbation in centrifugal force has a substantial effect on the location of libration points but a small perturbation in the Coriolis force has no impact on the location of libration points. But the stability of the libration points is highly influenced by the effect of the small perturbation in the Coriolis force. It is observed that as the Coriolis parameter increases, the libration points become stable. Further, it is found that the effect of the small perturbation in the centrifugal force has a substantial influence on the regions of possible motion. Also, when the effect of small perturbation in the centrifugal force increases the forbidden region decreases; here the motion is not possible for the infinitesimal mass. It is observed when the value of the Jacobian constant decreases, the regions of possible motion increase. In addition, we have also discussed how small perturbations in the Coriolis and centrifugal forces influence the Newton-Raphson basins of convergence.

Lunar libration point flight dynamics study

NASA Technical Reports Server (NTRS)

1969-01-01

Two satellite concepts, Halo and Hummingbird, for a lunar libration point satellite to be used as a tracking and communications link with the far side of the moon were evaluated. Study areas included flight dynamics, communications, attitude control, propulsion, and system integration. Both concepts were proved feasible, but Halo was shown to be the better concept.

Orbit Determination Issues for Libration Point Orbits

NASA Technical Reports Server (NTRS)

Beckman, Mark; Bauer, Frank (Technical Monitor)

2002-01-01

Libration point mission designers require knowledge of orbital accuracy for a variety of analyses including station keeping control strategies, transfer trajectory design, and formation and constellation control. Past publications have detailed orbit determination (OD) results from individual libration point missions. This paper collects both published and unpublished results from four previous libration point missions (ISEE (International Sun-Earth Explorer) -3, SOHO (Solar and Heliospheric Observatory), ACE (Advanced Composition Explorer) and MAP (Microwave Anisotropy Probe)) supported by Goddard Space Flight Center's Guidance, Navigation & Control Center. The results of those missions are presented along with OD issues specific to each mission. All past missions have been limited to ground based tracking through NASA ground sites using standard range and Doppler measurement types. Advanced technology is enabling other OD options including onboard navigation using seaboard attitude sensors and the use of the Very Long Baseline Interferometry (VLBI) measurement Delta Differenced One-Way Range (DDOR). Both options potentially enable missions to reduce coherent dedicated tracking passes while maintaining orbital accuracy. With the increased projected loading of the DSN (Deep Space Network), missions must find alternatives to the standard OD scenario.

Design of optimal impulse transfers from the Sun-Earth libration point to asteroid

NASA Astrophysics Data System (ADS)

Wang, Yamin; Qiao, Dong; Cui, Pingyuan

2015-07-01

The lunar probe, Chang'E-2, is the first one to successfully achieve both the transfer to Sun-Earth libration point orbit and the flyby of near-Earth asteroid Toutatis. This paper, taking the Chang'E-2's asteroid flyby mission as an example, provides a method to design low-energy transfers from the libration point orbit to an asteroid. The method includes the analysis of transfer families and the design of optimal impulse transfers. Firstly, the one-impulse transfers are constructed by correcting the initial guesses, which are obtained by perturbing in the direction of unstable eigenvector. Secondly, the optimality of one-impulse transfers is analyzed and the optimal impulse transfers are built by using the primer vector theory. After optimization, the transfer families, including the slow and the fast transfers, are refined to be continuous and lower-cost transfers. The method proposed in this paper can be also used for designing transfers from an arbitrary Sun-Earth libration point orbit to a near-Earth asteroid in the Sun-Earth-Moon system.

The research of the coupled orbital-attitude controlled motion of celestial body in the neighborhood of the collinear libration point L1

NASA Astrophysics Data System (ADS)

Shmyrov, A.; Shmyrov, V.; Shymanchuk, D.

2017-10-01

This article considers the motion of a celestial body within the restricted three-body problem of the Sun-Earth system. The equations of controlled coupled attitude-orbit motion in the neighborhood of collinear libration point L1 are investigated. The translational orbital motion of a celestial body is described using Hill's equations of circular restricted three-body problem of the Sun-Earth system. Rotational orbital motion is described using Euler's dynamic equations and quaternion kinematic equation. We investigate the problem of stability of celestial body rotational orbital motion in relative equilibrium positions and stabilization of celestial body rotational orbital motion with proposed control laws in the neighborhood of collinear libration point L1. To study stabilization problem, Lyapunov function is constructed in the form of the sum of the kinetic energy and special "kinematic function" of the Rodriguez-Hamiltonian parameters. Numerical modeling of the controlled rotational motion of a celestial body at libration point L1 is carried out. The numerical characteristics of the control parameters and rotational motion are given.

Access to Mars from Earth-Moon Libration Point Orbits:. [Manifold and Direct Options

NASA Technical Reports Server (NTRS)

Kakoi, Masaki; Howell, Kathleen C.; Folta, David

2014-01-01

This investigation is focused specifically on transfers from Earth-Moon L(sub 1)/L(sub 2) libration point orbits to Mars. Initially, the analysis is based in the circular restricted three-body problem to utilize the framework of the invariant manifolds. Various departure scenarios are compared, including arcs that leverage manifolds associated with the Sun-Earth L(sub 2) orbits as well as non-manifold trajectories. For the manifold options, ballistic transfers from Earth-Moon L(sub 2) libration point orbits to Sun-Earth L(sub 1)/L(sub 2) halo orbits are first computed. This autonomous procedure applies to both departure and arrival between the Earth-Moon and Sun-Earth systems. Departure times in the lunar cycle, amplitudes and types of libration point orbits, manifold selection, and the orientation/location of the surface of section all contribute to produce a variety of options. As the destination planet, the ephemeris position for Mars is employed throughout the analysis. The complete transfer is transitioned to the ephemeris model after the initial design phase. Results for multiple departure/arrival scenarios are compared.

Formation Flying With Decentralized Control in Libration Point Orbits

NASA Technical Reports Server (NTRS)

Folta, David; Carpenter, J. Russell; Wagner, Christoph

2000-01-01

A decentralized control framework is investigated for applicability of formation flying control in libration orbits. The decentralized approach, being non-hierarchical, processes only direct measurement data, in parallel with the other spacecraft. Control is accomplished via linearization about a reference libration orbit with standard control using a Linear Quadratic Regulator (LQR) or the GSFC control algorithm. Both are linearized about the current state estimate as with the extended Kalman filter. Based on this preliminary work, the decentralized approach appears to be feasible for upcoming libration missions using distributed spacecraft.

Trajectory Design Strategies for the NGST L2 Libration Point Mission

NASA Technical Reports Server (NTRS)

Folta, David; Cooley, Steven; Howell, Kathleen; Bauer, Frank H.

2001-01-01

The Origins' Next Generation Space Telescope (NGST) trajectory design is addressed in light of improved methods for attaining constrained orbit parameters and their control at the exterior collinear libration point, L2. The use of a dynamical systems approach, state-space equations for initial libration orbit control, and optimization to achieve constrained orbit parameters are emphasized. The NGST trajectory design encompasses a direct transfer and orbit maintenance under a constant acceleration. A dynamical systems approach can be used to provide a biased orbit and stationkeeping maintenance method that incorporates the constraint of a single axis correction scheme.

Long Term Missions at the Sun-Earth Libration Point L1: ACE, SOHO, and WIND

NASA Technical Reports Server (NTRS)

Roberts, Craig E.

2011-01-01

Three heliophysics missions - the Solar Heliospheric Observatory (SOHO), the Advanced Composition Explorer (ACE), and the Global Geoscience WIND - have been orbiting the Sun-Earth interior libration point L1 continuously since 1996, 1997, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center Flight Dynamics Facility. While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND prior to 2004 flew a remarkable 10-year deep-space trajectory that featured 38 targeted lunar flybys. The L1 orbits and the mission histories of the three spacecraft are briefly reviewed, and the station-keeping techniques and orbit maneuver experience are discussed.

Earth-Moon Libration Point Orbit Stationkeeping: Theory, Modeling and Operations

NASA Technical Reports Server (NTRS)

Folta, David C.; Pavlak, Thomas A.; Haapala, Amanda F.; Howell, Kathleen C.; Woodard, Mark A.

2013-01-01

Collinear Earth-Moon libration points have emerged as locations with immediate applications. These libration point orbits are inherently unstable and must be maintained regularly which constrains operations and maneuver locations. Stationkeeping is challenging due to relatively short time scales for divergence effects of large orbital eccentricity of the secondary body, and third-body perturbations. Using the Acceleration Reconnection and Turbulence and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) mission orbit as a platform, the fundamental behavior of the trajectories is explored using Poincare maps in the circular restricted three-body problem. Operational stationkeeping results obtained using the Optimal Continuation Strategy are presented and compared to orbit stability information generated from mode analysis based in dynamical systems theory.

ARTEMIS: The First Mission to the Lunar Libration Orbits

NASA Technical Reports Server (NTRS)

Woodward, Mark; Folta, David; Woodfork, Dennis

2009-01-01

The ARTEMIS mission will be the first to navigate to and perform stationkeeping operations around the Earth-Moon L1 and L2 Lagrangian points. The NASA Goddard Space Flight Center (GSFC) has previous mission experience flying in the Sun-Earth L1 (SOHO, ACE, WIND, ISEE-3) and L2 regimes (WMAP) and have maintained these spacecraft in libration point orbits by performing regular orbit stationkeeping maneuvers. The ARTEMIS mission will build on these experiences, but stationkeeping in Earth-Moon libration orbits presents new challenges since the libration point orbit period is on the order of two weeks rather than six months. As a result, stationkeeping maneuvers to maintain the Lissajous orbit will need to be performed frequently, and the orbit determination solutions between maneuvers will need to be quite accurate. The ARTEMIS mission is a collaborative effort between NASA GSFC, the University of California at Berkeley (UCB), and the Jet Propulsion Laboratory (JPL). The ARTEMIS mission is part of the THEMIS extended mission. ARTEMIS comprises two of the five THEMIS spacecraft that will be maneuvered from near-Earth orbits into lunar libration orbits using a sequence of designed orbital maneuvers and Moon & Earth gravity assists. In July 2009, a series of orbit-raising maneuvers began the proper orbit phasing of the two spacecraft for the first lunar flybys. Over subsequent months, additional propulsive maneuvers and gravity assists will be performed to move each spacecraft though the Sun-Earth weak stability regions and eventually into Earth-Moon libration point orbits. We will present the overall orbit designs for the two ARTEMIS spacecraft and provide analysis results of the 3/4-body dynamics, and the sensitivities of the trajectory design to both · maneuver errors and orbit determination errors. We will present results from the. initial orbit-raising maneuvers.

Lunar Navigation with Libration Point Orbiters and GPS

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2004-01-01

NASA is currently studying a Vision for Space Exploration based on spiral development of robotic and piloted missions to the moon and Mars, but research into how to perform such missions has continued ever since the first era of lunar exploration. One area of study that a number of researchers have pursued is libration point navigation and communication relay concepts. These concepts would appear to support many of NASA's current requirements for navigation and communications coverage for human and robotic spacecraft operating in lunar space and beyond. In trading libration point concepts against other options, designers must consider issues such as the number of spacecraft, required to provide coverage, insertion and stationkeeping costs, power and data rate requirements, frequency allocations, and many others. The libration points, along with a typical cis-lunar trajectory, are equilibrium locations for an infinitesimal mass in the rotating coordinate system that follows the motion of two massive bodies in circular orbits with respect to their common barycenter. There are three co-linear points along the line connecting the massive bodies: between the bodies, beyond the secondary body, and beyond the primary body. The relative distances of these points along the line connecting the bodies depend on the mass ratios. There are also two points that form equilateral triangles with the massive bodies. Ideally, motion in the neighborhood of the co-linear points is unstable, while motion near the equilibrium points is stable. However, in the real world, the motions are highly perturbed so that a satellite will require stationkeeping maneuvers.

Transfers between libration-point orbits in the elliptic restricted problem

NASA Astrophysics Data System (ADS)

Hiday-Johnston, L. A.; Howell, K. C.

1994-04-01

A strategy is formulated to design optimal time-fixed impulsive transfers between three-dimensional libration-point orbits in the vicinity of the interior L1 libration point of the Sun-Earth/Moon barycenter system. The adjoint equation in terms of rotating coordinates in the elliptic restricted three-body problem is shown to be of a distinctly different form from that obtained in the analysis of trajectories in the two-body problem. Also, the necessary conditions for a time-fixed two-impulse transfer to be optimal are stated in terms of the primer vector. Primer vector theory is then extended to nonoptimal impulsive trajectories in order to establish a criterion whereby the addition of an interior impulse reduces total fuel expenditure. The necessary conditions for the local optimality of a transfer containing additional impulses are satisfied by requiring continuity of the Hamiltonian and the derivative of the primer vector at all interior impulses. Determination of location, orientation, and magnitude of each additional impulse is accomplished by the unconstrained minimization of the cost function using a multivariable search method. Results indicate that substantial savings in fuel can be achieved by the addition of interior impulsive maneuvers on transfers between libration-point orbits.

Human Exploration of Earth's Neighborhood and Mars

NASA Technical Reports Server (NTRS)

Condon, Gerald

2003-01-01

The presentation examines Mars landing scenarios, Earth to Moon transfers comparing direct vs. via libration points. Lunar transfer/orbit diagrams, comparison of opposition class and conjunction class missions, and artificial gravity for human exploration missions. Slides related to Mars landing scenarios include: mission scenario; direct entry landing locations; 2005 opportunity - Type 1; Earth-mars superior conjunction; Lander latitude accessibility; Low thrust - Earth return phase; SEP Earth return sequence; Missions - 200, 2007, 2009; and Mission map. Slides related to Earth to Moon transfers (direct vs. via libration points (L1, L2) include libration point missions, expeditionary vs. evolutionary, Earth-Moon L1 - gateway for lunar surface operations, and Lunar mission libration point vs. lunar orbit rendezvous (LOR). Slides related to lunar transfer/orbit diagrams include: trans-lunar trajectory from ISS parking orbit, trans-Earth trajectories, parking orbit considerations, and landing latitude restrictions. Slides related to comparison of opposition class (short-stay) and conjunction class (long-stay) missions for human exploration of Mars include: Mars mission planning, Earth-Mars orbital characteristics, delta-V variations, and Mars mission duration comparison. Slides related to artificial gravity for human exploration missions include: current configuration, NEP thruster location trades, minor axis rotation, and example load paths.

Stationkeeping of Lissajous Trajectories in the Earth-Moon System with Applications to ARTEMIS

NASA Technical Reports Server (NTRS)

Folta, D. C.; Pavlak, T. A.; Howell, K. C.; Woodard, M. A.; Woodfork, D. W.

2010-01-01

In the last few decades, several missions have successfully exploited trajectories near the.Sun-Earth L1 and L2 libration points. Recently, the collinear libration points in the Earth-Moon system have emerged as locations with immediate application. Most libration point orbits, in any system, are inherently unstable. and must be controlled. To this end, several stationkeeping strategies are considered for application to ARTEMIS. Two approaches are examined to investigate the stationkeeping problem in this regime and the specific options. available for ARTEMIS given the mission and vehicle constraints. (I) A baseline orbit-targeting approach controls the vehicle to remain near a nominal trajectory; a related global optimum search method searches all possible maneuver angles to determine an optimal angle and magnitude; and (2) an orbit continuation method, with various formulations determines maneuver locations and minimizes costs. Initial results indicate that consistent stationkeeping costs can be achieved with both approaches and the costs are reasonable. These methods are then applied to Lissajous trajectories representing a baseline ARTEMIS libration orbit trajectory.

L1 libration point manned space habitat

NASA Technical Reports Server (NTRS)

Luttges, Marvin; Johnson, Steve; Banks, Gary; Johnson, Richard; Meyer, Christian; Pepin, Scott; Macelroy, Robert

1989-01-01

Second generation stations or Manned Space Habitats (MSHs) are discussed for an Earth-Moon libration point and in lunar orbit. The conceptual design of such a station is outlined. Systems and subsystems described reflect anticipation of moderate technology growth. The evolution of the L1 environments is discussed, several selected subsystems are outlined, and how the L1 MSH will complete some of its activities is described.

A note on libration point orbits, temporary capture and low-energy transfers

NASA Astrophysics Data System (ADS)

Fantino, E.; Gómez, G.; Masdemont, J. J.; Ren, Y.

2010-11-01

In the circular restricted three-body problem (CR3BP) the weak stability boundary (WSB) is defined as a boundary set in the phase space between stable and unstable motion relative to the second primary. At a given energy level, the boundaries of such region are provided by the stable manifolds of the central objects of the L1 and L2 libration points, i.e., the two planar Lyapunov orbits. Besides, the unstable manifolds of libration point orbits (LPOs) around L1 and L2 have been identified as responsible for the weak or temporary capture around the second primary of the system. These two issues suggest the existence of natural dynamical channels between the Earth's vicinity and the Sun-Earth libration points L1 and L2. Furthermore, it has been shown that the Sun-Earth L2 central unstable manifolds can be linked, through an heteroclinic connection, to the central stable manifolds of the L2 point in the Earth-Moon three-body problem. This concept has been applied to the design of low energy transfers (LETs) from the Earth to the Moon. In this contribution we consider all the above three issues, i.e., weak stability boundaries, temporary capture and low energy transfers, and we discuss the role played by the invariant manifolds of LPOs in each of them. The study is made in the planar approximation.

User and technical documentation

NASA Astrophysics Data System (ADS)

1988-09-01

The program LIBRATE calculates velocities for trajectories from low earth orbit (LEO) to four of the five libration points (L2, L3, L4, and L5), and from low lunar orbit (LLO) to libration points L1 and L2. The flight to be analyzed departs from a circular orbit of any altitude and inclination about the Earth or Moon and finishes in a circular orbit about the Earth at the desired libration point within a specified flight time. This program produces a matrix of the delta V's needed to complete the desired flight. The user specifies the departure orbit, and the maximum flight time. A matrix is then developed with 10 inclinations, ranging from 0 to 90 degrees, forming the columns, and 19 possible flight times, ranging from the flight time (input) to 36 hours less than the input value, in decrements of 2 hours, forming the rows. This matrix is presented in three different reports including the total delta V's, and both of the delta V components discussed. The input required from the user to define the flight is discussed. The contents of the three reports that are produced as outputs are also described. The instructions are also included which are needed to execute the program.

Solar Warning Architecture for Manned Missions to Mars

DTIC Science & Technology

2011-06-01

public discussions of manned missions to return to the Moon, explore near-earth asteroids , and even visit Mars, a deep-space solar weather warning...mission planning, and libration points. In addition, the limited previous analysis on this problem was mined for information. 2.2 Radiation Effects...behind the Earth, on its orbital path. These two libration points are stable along all 3 axes, leading some to theorize there may be asteroids or

Proceedings from the 2nd International Symposium on Formation Flying Missions and Technologies

NASA Technical Reports Server (NTRS)

2004-01-01

Topics discussed include: The Stellar Imager (SI) "Vision Mission"; First Formation Flying Demonstration Mission Including on Flight Nulling; Formation Flying X-ray Telescope in L2 Orbit; SPECS: The Kilometer-baseline Far-IR Interferometer in NASA's Space Science Roadmap Presentation; A Tight Formation for Along-track SAR Interferometry; Realization of the Solar Power Satellite using the Formation Flying Solar Reflector; SIMBOL-X : Formation Flying for High-Energy Astrophysics; High Precision Optical Metrology for DARWIN; Close Formation Flight of Micro-Satellites for SAR Interferometry; Station-Keeping Requirements for Astronomical Imaging with Constellations of Free-Flying Collectors; Closed-Loop Control of Formation Flying Satellites; Formation Control for the MAXIM Mission; Precision Formation Keeping at L2 Using the Autonomous Formation Flying Sensor; Robust Control of Multiple Spacecraft Formation Flying; Virtual Rigid Body (VRB) Satellite Formation Control: Stable Mode-Switching and Cross-Coupling; Electromagnetic Formation Flight (EMFF) System Design, Mission Capabilities, and Testbed Development; Navigation Algorithms for Formation Flying Missions; Use of Formation Flying Small Satellites Incorporating OISL's in a Tandem Cluster Mission; Semimajor Axis Estimation Strategies; Relative Attitude Determination of Earth Orbiting Formations Using GPS Receivers; Analysis of Formation Flying in Eccentric Orbits Using Linearized Equations of Relative Motion; Conservative Analytical Collision Probabilities for Orbital Formation Flying; Equations of Motion and Stability of Two Spacecraft in Formation at the Earth/Moon Triangular Libration Points; Formations Near the Libration Points: Design Strategies Using Natural and Non-Natural Ares; An Overview of the Formation and Attitude Control System for the Terrestrial Planet Finder Formation Flying Interferometer; GVE-Based Dynamics and Control for Formation Flying Spacecraft; GNC System Design for a New Concept of X-Ray Distributed Telescope; GNC System for the Deployment and Fine Control of the DARWIN Free-Flying Interferometer; Formation Algorithm and Simulation Testbed; and PLATFORM: A Formation Flying, RvD and Robotic Validation Test-bench.

Transport and Capture of Comets

NASA Astrophysics Data System (ADS)

Ross, S. D.; Koon, W. S.; Lo, M. W.; Marsden, J. E.

2001-11-01

The dynamics of comets and other solar system objects which have a three-body energy close to that of the collinear libration points are known to exhibit a complicated array of behaviors such as rapid transition between the interior and exterior Hill's regions, temporary capture, and collision. The invariant manifold structures of the collinear libration points for the restricted three-body problem, which exist for a range of energies, provide the framework for understanding these transport phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold "tubes" associated to libration point orbits are the phase space conduits transporting material to and from the smaller primary body (e.g., Jupiter), and between primary bodies for separate three-body systems (e.g., Saturn and Jupiter). This point of view has worked well in describing the planar circular restricted three-body problem. The current work seeks to extend the results to three degrees of freedom. This work was supported by the National Science Foundation Grant No. KDI/ATM-9873133 under a contract with the Jet Propulsion Laboratory, NASA.

Design of the stabilizing control of the orbital motion in the vicinity of the collinear libration point L1 using the analytical representation of the invariant manifold

NASA Astrophysics Data System (ADS)

Maliavkin, G. P.; Shmyrov, A. S.; Shmyrov, V. A.

2018-05-01

Vicinities of collinear libration points of the Sun-Earth system are currently quite attractive for the space navigation. Today, various projects on placing of spacecrafts observing the Sun in the L1 libration point and telescopes in L2 have been implemented (e.g. spacecrafts "WIND", "SOHO", "Herschel", "Planck"). Collinear libration points being unstable leads to the problem of stabilization of a spacecraft's motion. Laws of stabilizing motion control in vicinity of L1 point can be constructed using the analytical representation of a stable invariant manifold. Efficiency of these control laws depends on the precision of the representation. Within the model of Hill's approximation of the circular restricted three-body problem in the rotating geocentric coordinate system one can obtain the analytical representation of an invariant manifold filled with bounded trajectories in a form of series in terms of powers of the phase variables. Approximate representations of the orders from the first to the fourth inclusive can be used to construct four laws of stabilizing feedback motion control under which trajectories approach the manifold. By virtue of numerical simulation the comparison can be made: how the precision of the representation of the invariant manifold influences the efficiency of the control, expressed by energy consumptions (characteristic velocity). It shows that using approximations of higher orders in constructing the control laws can significantly reduce the energy consumptions on implementing the control compared to the linear approximation.

Time and Energy, Exploring Trajectory Options Between Nodes in Earth-Moon Space

NASA Technical Reports Server (NTRS)

Martinez, Roland; Condon, Gerald; Williams, Jacob

2012-01-01

The Global Exploration Roadmap (GER) was released by the International Space Exploration Coordination Group (ISECG) in September of 2011. It describes mission scenarios that begin with the International Space Station and utilize it to demonstrate necessary technologies and capabilities prior to deployment of systems into Earth-Moon space. Deployment of these systems is an intermediate step in preparation for more complex deep space missions to near-Earth asteroids and eventually Mars. In one of the scenarios described in the GER, "Asteroid Next", there are activities that occur in Earth-Moon space at one of the Earth-Moon Lagrange (libration) points. In this regard, the authors examine the possible role of an intermediate staging point in an effort to illuminate potential trajectory options for conducting missions in Earth-Moon space of increasing duration, ultimately leading to deep space missions. This paper will describe several options for transits between Low Earth Orbit (LEO) and the libration points, transits between libration points, and transits between the libration points and interplanetary trajectories. The solution space provided will be constrained by selected orbital mechanics design techniques and physical characteristics of hardware to be used in both crewed missions and uncrewed missions. The relationships between time and energy required to transfer hardware between these locations will provide a better understanding of the potential trade-offs mission planners could consider in the development of capabilities, individual missions, and mission series in the context of the ISECG GER.

On the photo-gravitational restricted four-body problem with variable mass

NASA Astrophysics Data System (ADS)

Mittal, Amit; Agarwal, Rajiv; Suraj, Md Sanam; Arora, Monika

2018-05-01

This paper deals with the photo-gravitational restricted four-body problem (PR4BP) with variable mass. Following the procedure given by Gascheau (C. R. 16:393-394, 1843) and Routh (Proc. Lond. Math. Soc. 6:86-97, 1875), the conditions of linear stability of Lagrange triangle solution in the PR4BP are determined. The three radiating primaries having masses m1, m2 and m3 in an equilateral triangle with m2=m3 will be stable as long as they satisfy the linear stability condition of the Lagrangian triangle solution. We have derived the equations of motion of the mentioned problem and observed that there exist eight libration points for a fixed value of parameters γ (m at time t/m at initial time, 0<γ≤1 ), α (the proportionality constant in Jeans' law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), 0≤α≤2.2), the mass parameter μ=0.005 and radiation parameters qi, (0< qi≤1, i=1, 2, 3). All the libration points are non-collinear if q2≠ q3. It has been observed that the collinear and out-of-plane libration points also exist for q2=q3. In all the cases, each libration point is found to be unstable. Further, zero velocity curves (ZVCs) and Newton-Raphson basins of attraction are also discussed.

Libration Point Navigation Concepts Supporting Exploration Vision

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell; Folta, David C.; Moreau, Michael C.; Gramling, Cheryl J.

2004-01-01

Farquhar described several libration point navigation concepts that would appear to support NASA s current exploration vision. One concept is a Lunar Relay Satellite operating in the vicinity of Earth-Moon L2, providing Earth-to-lunar far-side and long- range surface-to-surface navigation and communications capability. Reference [ 1] lists several advantages of such a system in comparison to a lunar orbiting relay satellite constellation. Among these are one or two vs. many satellites for coverage, simplified acquisition and tracking due to very low relative motion, much longer contact times, and simpler antenna pointing. An obvious additional advantage of such a system is that uninterrupted links to Earth avoid performing critical maneuvers "in the blind." Another concept described is the use of Earth-Moon L1 for lunar orbit rendezvous, rather than low lunar orbit as was done for Apollo. This rendezvous technique would avoid large plane change and high fuel cost associated with high latitude landing sites and long stay times. Earth-Moon L1 also offers unconstrained launch windows from the lunar surface. Farquhar claims this technique requires only slightly higher fuel cost than low lunar orbit rendezvous for short-stay equatorial landings. Farquhar also describes an Interplanetary Transportation System that would use libration points as terminals for an interplanetary shuttle. This approach would offer increased operational flexibility in terms of launch windows, rendezvous, aborts, etc. in comparison to elliptical orbit transfers. More recently, other works including Folta[3] and Howell[4] have shown that patching together unstable trajectories departing Earth-Moon libration points with stable trajectories approaching planetary libration points may also offer lower overall fuel costs than elliptical orbit transfers. Another concept Farquhar described was a Deep Space Relay at Earth-Moon IA and/or L5 that would serve as a high data rate optical navigation and communications relay satellite. The advantages in comparison to a geosynchronous relay are minimal Earth occultation, distance from large noise sources on Earth, easier pointing due to smaller relative velocity, and a large baseline for interferometry if both L4 and L5 are used.

Librations and Interior Structure of the Galilean Satellites

NASA Astrophysics Data System (ADS)

van Hoolst, T.; Baland, R.; Karatekin, O.; Rambaux, N.

2009-12-01

We investigate the influence of the interior structure of the Galilean satellites on their rotation variations (or librations). Since the Galilean satellites are significantly aspherical due to rotation and static tides, Jupiter exerts a gravitational torque on them. In a circular orbit, the long axis of a satellite would always point towards Jupiter and the gravitational torque would be zero. However, the eccentric orbits of the Galilean satellites lead to misalignment of the long axis with the direction to Jupiter and result in non-zero gravitational torques that tend to modify the rotation of the satellites. Since the torque varies with the orbital phase, the main libration period is equal to the orbital period. In a first-order approximation, the libration amplitude is usually calculated by assuming that the satellite reacts rigidly to the gravitational torque. The corresponding amplitudes, expressed as a shift at the surface of the orientation of the long axis with respect to that for the mean rotation rate, decrease with increasing distance from Jupiter from a few hundred meters for Io to about ten meter for Callisto. Internal liquid layers, such as a subsurface ocean, can lead to differential rotation of the solid and liquid layers and to differences of the libration of surface with respect to that for a rigid libration. Here, we present a method to determine the influence of gravitational and pressure interactions between internal layers on the libration of the Galilean satellites. For Io, we show that the liquid core has only a small effect on the surface librations. For Europa, Ganymede and Callisto, the presence of a subsurface ocean can significantly increase the libration amplitude. We also study the effect of the possible existence of two liquid layers in Ganymede and Europa: a subsurface ocean and a liquid core. We quantify the sensitivity of the libration amplitude to the internal structure and assess expected improvements in the interior structure of the Galilean satellites from future libration observations with the joint NASA/ESA Europa Jupiter System Mission.

Servicing and Deployment of National Resources in Sun-Earth Libration Point Orbits

NASA Technical Reports Server (NTRS)

Folta, David C.; Beckman, Mark; Mar, Greg C.; Mesarch, Michael; Cooley, Steven; Leete, Steven J.

2002-01-01

Spacecraft travel between the Sun-Earth system, the Earth-Moon system, and beyond has received extensive attention recently. The existence of a connection between unstable regions enables mission designers to envision scenarios of multiple spacecraft traveling cheaply from system to system, rendezvousing, servicing, and refueling along the way. This paper presents examples of transfers between the Sun-Earth and Earth-Moon systems using a true ephemeris and perturbation model. It shows the (Delta)V costs associated with these transfers, including the costs to reach the staging region from the Earth. It explores both impulsive and low thrust transfer trajectories. Additionally, analysis that looks specifically at the use of nuclear power in libration point orbits and the issues associated with them such as inadvertent Earth return is addressed. Statistical analysis of Earth returns and the design of biased orbits to prevent any possible return are discussed. Lastly, the idea of rendezvous between spacecraft in libration point orbits using impulsive maneuvers is addressed.

On the use of a sunward-libration-point orbiting spacecraft as an IMF monitor for magnetospheric studies

NASA Technical Reports Server (NTRS)

Kelly, T. J.; Crooker, N. U.; Siscoe, G. L.; Russell, C. T.; Smith, E. J.

1984-01-01

Magnetospheric studies often require knowledge of the orientation of the IMF. In order to test the accuracy of using magnetometer data from a spacecraft orbiting the sunward libration point for this purpose, the angle between the IMF at ISEE 3, when it was positioned around the libration point, and at ISEE 1, orbiting Earth, has been calculated for a data set of two-hour periods covering four months. For each period, a ten-minute average of ISEE 1 data is compared with ten-minute averages of ISEE 3 data at successively lagged intervals. At the lag time equal to the time required for the solar wind to convect from ISEE 3 to ISEE 1, the median angle between the IMF orientation at the two spacecraft is 20 deg, and 80% of the cases have angles less than 38 deg. The results for the angles projected on the y-z plane are essentially the same.

Direct and indirect capture of near-Earth asteroids in the Earth-Moon system

NASA Astrophysics Data System (ADS)

Tan, Minghu; McInnes, Colin; Ceriotti, Matteo

2017-09-01

Near-Earth asteroids have attracted attention for both scientific and commercial mission applications. Due to the fact that the Earth-Moon L1 and L2 points are candidates for gateway stations for lunar exploration, and an ideal location for space science, capturing asteroids and inserting them into periodic orbits around these points is of significant interest for the future. In this paper, we define a new type of lunar asteroid capture, termed direct capture. In this capture strategy, the candidate asteroid leaves its heliocentric orbit after an initial impulse, with its dynamics modeled using the Sun-Earth-Moon restricted four-body problem until its insertion, with a second impulse, onto the L2 stable manifold in the Earth-Moon circular restricted three-body problem. A Lambert arc in the Sun-asteroid two-body problem is used as an initial guess and a differential corrector used to generate the transfer trajectory from the asteroid's initial obit to the stable manifold associated with Earth-Moon L2 point. Results show that the direct asteroid capture strategy needs a shorter flight time compared to an indirect asteroid capture, which couples capture in the Sun-Earth circular restricted three-body problem and subsequent transfer to the Earth-Moon circular restricted three-body problem. Finally, the direct and indirect asteroid capture strategies are also applied to consider capture of asteroids at the triangular libration points in the Earth-Moon system.

Invariant Manifolds, the Spatial Three-Body Problem and Space Mission Design

NASA Technical Reports Server (NTRS)

Gomez, G.; Koon, W. S.; Lo, Martin W.; Marsden, J. E.; Masdemont, J.; Ross, S. D.

2001-01-01

The invariant manifold structures of the collinear libration points for the spatial restricted three-body problem provide the framework for understanding complex dynamical phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold 'tubes' associated to libration point orbits are the phase space structures that provide a conduit for orbits between primary bodies for separate three-body systems. These invariant manifold tubes can be used to construct new spacecraft trajectories, such as 'Petit Grand Tour' of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. The current work extends the results to the spatial case.

Spacecraft formation keeping near the libration points of the Sun-Earth/Moon system

NASA Astrophysics Data System (ADS)

Marchand, Belinda G.

Multi-spacecraft formations, evolving near the vicinity of the libration points of the Sun-Earth/Moon system, have drawn increased interest for a variety of applications. This is particularly true for space based interferometry missions such as Terrestrial Planet Finder (TPF) and the Micro Arcsecond X-Ray Imaging Mission (MAXIM). Recent studies in formation flight have focused, primarily, on the control of formations that evolve in the immediate vicinity of the Earth. However, the unique dynamical structure near the libration points requires that the effectiveness and feasibility of these methods be re-examined. The present study is divided into two main topics. First, a dynamical systems approach is employed to develop a better understanding of the natural uncontrolled formation dynamics in this region of space. The focus is formations that evolve near halo orbits and Lissajous trajectories, near the L1 and L2 libration points of the Sun-Earth/Moon system. This leads to the development of a Floquet controller designed to simplify the process of identifying naturally existing formations as well as the associated stable manifolds for deployment. The initial analysis is presented in the Circular Restricted Three-Body Problem, but the results are later transitioned into the more complete Ephemeris model. The next subject of interest in this investigation is non-natural formations. That is, formations that are not consistent with the natural dynamical flow near the libration points. Mathematically, precise formation keeping of a given nominal configuration requires continuous control. Hence, a detailed analysis is presented to contrast the effectiveness and issues associated with linear optimal control and feedback linearization methods. Of course, continuous operation of the thrusters, may not represent a feasible option for a particular mission. If discrete formation keeping is implemented, however, the formation keeping goal will be subject to increased tracking errors relative to the nominal path. With this in mind, the final phase of the analysis presented here is centered on discrete formation keeping. The initial analysis is devoted to both linear state and radial targeters. The results from these two methodologies are later employed as a starting solution for an optimal impulsive control algorithm.

Lunar flyby transfers between libration point orbits

NASA Astrophysics Data System (ADS)

Qi, Yi; Xu, Shijie; Qi, Rui

2017-06-01

Lunar flyby or lunar gravity assist is a classical technique to change the energy and trajectory of space vehicle in space mission. In this paper, lunar flyby transfers between Sun-Earth/Moon libration point orbits with different energies are investigated in the Sun-Earth-Moon restricted four-body problem. Distinguished by behaviours before and after lunar flyby, classification of lunar flyby orbits is defined and studied. Research indicates that junction point of special regions of four types of lunar flyby orbits denotes the perilune of lunar flyby transfer between libration point orbits. Based on those special perilunes, retrograde and prograde lunar flyby transfers are discussed in detail, respectively. The mean energy level transition distribution is proposed and applied to analyse the influence of phase angle and eccentricity on lunar flyby transfers. The phase space is divided into normal and chaotic intervals based on the topology pattern of transfers. A continuation strategy of lunar flyby transfer in the bicircular model is presented. Numerical examples show that compared with the single-impulse transfers based on patched invariant manifolds, lunar flyby transfers are more energy efficient. Finally, lunar flyby transfers are further extended to the realistic models.

Resonance and Capture of Jupiter Comets

NASA Astrophysics Data System (ADS)

Koon, W. S.; Lo, M. W.; Marsden, J. E.; Ross, S. D.

A number of Jupiter family comets such as Oterma and Gehrels 3 make a rapid transition from heliocentric orbits outside the orbit of Jupiter to heliocentric orbits inside the orbit of Jupiter and vice versa. During this transition, the comet can be captured temporarily by Jupiter for one to several orbits around Jupiter. The interior heliocentric orbit is typically close to the 3:2 resonance while the exterior heliocentric orbit is near the 2:3 resonance. An important feature of the dynamics of these comets is that during the transition, the orbit passes close to the libration points L_1 and L_2, two of the equilibrium points for the restricted three-body problem for the Sun-Jupiter system. Studying the libration point invariant manifold structures for L_1 and L_2 is a starting point for understanding the capture and resonance transition of these comets. For example, the recently discovered heteroclinic connection between pairs of unstable periodic orbits (one around the L_1 and the other around L_2) implies a complicated dynamics for comets in a certain energy range. Furthermore, the stable and unstable invariant manifold `tubes' associated to libration point periodic orbits, of which the heteroclinic connections are a part, are phase space conduits transporting material to and from Jupiter and between the interior and exterior of Jupiter's orbit.

Early Mission Maneuver Operations for the Deep Space Climate Observatory Sun-Earth L1 Libration Point Mission

NASA Technical Reports Server (NTRS)

Roberts, Craig; Case, Sara; Reagoso, John; Webster, Cassandra

2015-01-01

The Deep Space Climate Observatory mission launched on February 11, 2015, and inserted onto a transfer trajectory toward a Lissajous orbit around the Sun-Earth L1 libration point. This paper presents an overview of the baseline transfer orbit and early mission maneuver operations leading up to the start of nominal science orbit operations. In particular, the analysis and performance of the spacecraft insertion, mid-course correction maneuvers, and the deep-space Lissajous orbit insertion maneuvers are discussed, com-paring the baseline orbit with actual mission results and highlighting mission and operations constraints..

Stationkeeping Approach for the Microwave Anisotropy Probe (MAP)

NASA Technical Reports Server (NTRS)

Rohrbaugh, Dave; Schiff, Conrad

2002-01-01

The Microwave Anisotropy Probe was successfully launched on June 30, 2001 and placed into a Lissajous orbit about the L2 Sun-Earth-Moon libration point. However, the L2 libration point is unstable which necessitates occasional stationkeeping maneuvers in order to maintain the spacecraft s Lissajous orbit. Analyses were performed in order to develop a feasible L2 stationkeeping strategy for the MAP mission. The resulting strategy meets the allotted fuel budget, allowing for enough fuel to handle additional he1 taxes, while meeting the attitude requirements for the maneuvers. Results from the first two stationkeeping maneuvers are included.

The Propeller and the Frog

NASA Astrophysics Data System (ADS)

Pan, Margaret; Chiang, Eugene

2010-10-01

"Propellers" in planetary rings are disturbances in ring material excited by moonlets that open only partial gaps. We describe a new type of co-orbital resonance that can explain the observed non-Keplerian motions of propellers. The resonance is between the moonlet underlying the propeller and co-orbiting ring particles downstream of the moonlet where the gap closes. The moonlet librates within the gap about an equilibrium point established by co-orbiting material and stabilized by the Coriolis force. In the limit of small libration amplitude, the libration period scales linearly with the gap azimuthal width and inversely as the square root of the co-orbital mass. The new resonance recalls but is distinct from conventional horseshoe and tadpole orbits; we call it the "frog" resonance, after the relevant term in equine hoof anatomy. For a ring surface density and gap geometry appropriate for the propeller Blériot in Saturn's A ring, our theory predicts a libration period of ~4 years, similar to the ~3.7 year period over which Blériot's orbital longitude is observed to vary. These librations should be subtracted from the longitude data before any inferences about moonlet migration are made.

THE PROPELLER AND THE FROG

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Margaret; Chiang, Eugene, E-mail: mpan@astro.berkeley.ed

2010-10-20

'Propellers' in planetary rings are disturbances in ring material excited by moonlets that open only partial gaps. We describe a new type of co-orbital resonance that can explain the observed non-Keplerian motions of propellers. The resonance is between the moonlet underlying the propeller and co-orbiting ring particles downstream of the moonlet where the gap closes. The moonlet librates within the gap about an equilibrium point established by co-orbiting material and stabilized by the Coriolis force. In the limit of small libration amplitude, the libration period scales linearly with the gap azimuthal width and inversely as the square root of themore » co-orbital mass. The new resonance recalls but is distinct from conventional horseshoe and tadpole orbits; we call it the 'frog' resonance, after the relevant term in equine hoof anatomy. For a ring surface density and gap geometry appropriate for the propeller Bleriot in Saturn's A ring, our theory predicts a libration period of {approx}4 years, similar to the {approx}3.7 year period over which Bleriot's orbital longitude is observed to vary. These librations should be subtracted from the longitude data before any inferences about moonlet migration are made.« less

ADRC for spacecraft attitude and position synchronization in libration point orbits

NASA Astrophysics Data System (ADS)

Gao, Chen; Yuan, Jianping; Zhao, Yakun

2018-04-01

This paper addresses the problem of spacecraft attitude and position synchronization in libration point orbits between a leader and a follower. Using dual quaternion, the dimensionless relative coupled dynamical model is derived considering computation efficiency and accuracy. Then a model-independent dimensionless cascade pose-feedback active disturbance rejection controller is designed to spacecraft attitude and position tracking control problems considering parameter uncertainties and external disturbances. Numerical simulations for the final approach phase in spacecraft rendezvous and docking and formation flying are done, and the results show high-precision tracking errors and satisfactory convergent rates under bounded control torque and force which validate the proposed approach.

Four-body trajectory optimization

NASA Technical Reports Server (NTRS)

Pu, C. L.; Edelbaum, T. N.

1973-01-01

A collection of typical three-body trajectories from the L1 libration point on the sun-earth line to the earth is presented. These trajectories in the sun-earth system are grouped into four distinct families which differ in transfer time and delta V requirements. Curves showing the variations of delta V with respect to transfer time, and typical two and three-impulse primer vector histories, are included. The development of a four-body trajectory optimization program to compute fuel optimal trajectories between the earth and a point in the sun-earth-moon system are also discussed. Methods for generating fuel optimal two-impulse trajectories which originate at the earth or a point in space, and fuel optimal three-impulse trajectories between two points in space, are presented. A brief qualitative comparison of these methods is given. An example of a four-body two-impulse transfer from the Li libration point to the earth is included.

Anti-sway control of tethered satellite systems using attitude control of the main satellite

NASA Astrophysics Data System (ADS)

Yousefian, Peyman; Salarieh, Hassan

2015-06-01

In this study a new method is introduced to suppress libration of a tethered satellite system (TSS). It benefits from coupling between satellites and tether libration dynamics. The control concept uses the main satellite attitude maneuvers to suppress librational motion of the tether, and the main satellite's actuators for attitude control are used as the only actuation in the system. The study considers planar motion of a two body TSS system in a circular orbit and it is assumed that the tether's motion will not change it. Governing dynamic equations of motion are derived using the extended Lagrange method. Controllability of the system around the equilibrium state is studied and a linear LQG controller is designed to regulate libration of the system. Tether tension and satellite attitude are assumed as only measurable outputs of the system. The Extended Kalman Filter (EKF) is used to estimate states of the system to be used as feedback to the controller. The designed controller and observer are implemented to the nonlinear plant and simulations demonstrate that the controller lead to reduction of the tether libration propoerly. By the way, because the controller is linear, it is applicable only at low amplitudes in the vicinity of equilibrium point. To reach global stability, a nonlinear controller is demanded.

Low-Latency Lunar Surface Telerobotics from Earth-Moon Libration Points

NASA Technical Reports Server (NTRS)

Lester, Daniel; Thronson, Harley

2011-01-01

Concepts for a long-duration habitat at Earth-Moon LI or L2 have been advanced for a number of purposes. We propose here that such a facility could also have an important role for low-latency telerobotic control of lunar surface equipment, both for lunar science and development. With distances of about 60,000 km from the lunar surface, such sites offer light-time limited two-way control latencies of order 400 ms, making telerobotic control for those sites close to real time as perceived by a human operator. We point out that even for transcontinental teleoperated surgical procedures, which require operational precision and highly dexterous manipulation, control latencies of this order are considered adequate. Terrestrial telerobots that are used routinely for mining and manufacturing also involve control latencies of order several hundred milliseconds. For this reason, an Earth-Moon LI or L2 control node could build on the technology and experience base of commercially proven terrestrial ventures. A lunar libration-point telerobotic node could demonstrate exploration strategies that would eventually be used on Mars, and many other less hospitable destinations in the solar system. Libration-point telepresence for the Moon contrasts with lunar telerobotic control from the Earth, for which two-way control latencies are at least six times longer. For control latencies that long, telerobotic control efforts are of the "move-and-wait" variety, which is cognitively inferior to near real-time control.

Adaptive surrogate model based multi-objective transfer trajectory optimization between different libration points

NASA Astrophysics Data System (ADS)

Peng, Haijun; Wang, Wei

2016-10-01

An adaptive surrogate model-based multi-objective optimization strategy that combines the benefits of invariant manifolds and low-thrust control toward developing a low-computational-cost transfer trajectory between libration orbits around the L1 and L2 libration points in the Sun-Earth system has been proposed in this paper. A new structure for a multi-objective transfer trajectory optimization model that divides the transfer trajectory into several segments and gives the dominations for invariant manifolds and low-thrust control in different segments has been established. To reduce the computational cost of multi-objective transfer trajectory optimization, a mixed sampling strategy-based adaptive surrogate model has been proposed. Numerical simulations show that the results obtained from the adaptive surrogate-based multi-objective optimization are in agreement with the results obtained using direct multi-objective optimization methods, and the computational workload of the adaptive surrogate-based multi-objective optimization is only approximately 10% of that of direct multi-objective optimization. Furthermore, the generating efficiency of the Pareto points of the adaptive surrogate-based multi-objective optimization is approximately 8 times that of the direct multi-objective optimization. Therefore, the proposed adaptive surrogate-based multi-objective optimization provides obvious advantages over direct multi-objective optimization methods.

Orbit Determination Error Analysis Results for the Triana Sun-Earth L2 Libration Point Mission

NASA Technical Reports Server (NTRS)

Marr, G.

2003-01-01

Using the NASA Goddard Space Flight Center's Orbit Determination Error Analysis System (ODEAS), orbit determination error analysis results are presented for all phases of the Triana Sun-Earth L1 libration point mission and for the science data collection phase of a future Sun-Earth L2 libration point mission. The Triana spacecraft was nominally to be released by the Space Shuttle in a low Earth orbit, and this analysis focuses on that scenario. From the release orbit a transfer trajectory insertion (TTI) maneuver performed using a solid stage would increase the velocity be approximately 3.1 km/sec sending Triana on a direct trajectory to its mission orbit. The Triana mission orbit is a Sun-Earth L1 Lissajous orbit with a Sun-Earth-vehicle (SEV) angle between 4.0 and 15.0 degrees, which would be achieved after a Lissajous orbit insertion (LOI) maneuver at approximately launch plus 6 months. Because Triana was to be launched by the Space Shuttle, TTI could potentially occur over a 16 orbit range from low Earth orbit. This analysis was performed assuming TTI was performed from a low Earth orbit with an inclination of 28.5 degrees and assuming support from a combination of three Deep Space Network (DSN) stations, Goldstone, Canberra, and Madrid and four commercial Universal Space Network (USN) stations, Alaska, Hawaii, Perth, and Santiago. These ground stations would provide coherent two-way range and range rate tracking data usable for orbit determination. Larger range and range rate errors were assumed for the USN stations. Nominally, DSN support would end at TTI+144 hours assuming there were no USN problems. Post-TTI coverage for a range of TTI longitudes for a given nominal trajectory case were analyzed. The orbit determination error analysis after the first correction maneuver would be generally applicable to any libration point mission utilizing a direct trajectory.

Halo-orbit and lunar-swingby missions of the 1990's

NASA Technical Reports Server (NTRS)

Farquhar, Robert W.

1990-01-01

A significant number of spacecraft are planning to use halo orbits and lunar-swingby trajectories in the next decade. Four spacecraft will be placed into halo orbits around the earth's sunward libration point, while two others will be stationed near the sun-earth L2 libration point in the distant geomagnetic tail. Six spacecraft, including two of the aforementioned halo orbiters, will make use of lunar-swingby maneuvers to fulfill their mission objectives. Thus, a total of ten spacecraft, five from the Soviet Union, two from Japan, two from the United States, and one from the European Space Agency, will employ halo orbits and/or lunar-swingby trajectories in the 1990's. Pertinent facts are presented for each of these missions.

Solar radiation pressure application for orbital motion stabilization near the Sun-Earth collinear libration point

NASA Astrophysics Data System (ADS)

Polyakhova, Elena; Shmyrov, Alexander; Shmyrov, Vasily

2018-05-01

Orbital maneuvering in a neighborhood of the collinear libration point L1 of Sun-Earth system has specific properties, primarily associated with the instability L1. For a long stay in this area of space the stabilization problem of orbital motion requires a solution. Numerical experiments have shown that for stabilization of motion it is requires very small control influence in comparison with the gravitational forces. On the other hand, the stabilization time is quite long - months, and possibly years. This makes it highly desirable to use solar pressure forces. In this paper we illustrate the solar sail possibilities for solving of stabilization problem in a neighborhood L1 with use of the model example.

Formations Near the Libration Points: Design Strategies Using Natural and Non-Natural Arcs

NASA Technical Reports Server (NTRS)

Howell, K. C.; Marchand, B. G.

2004-01-01

Space based observatory and interferometry missions, such as Terrestrial Planet Finder (TPF), Stellar Imager, and MAXIM, have sparked great interest in multi-spacecraft formation flight in the vicinity of the Sun-Earth/Moon (SEM) libration points. The initial phase of this research considered the formation keeping problem from the perspective of continuous control as applied to non-natural formations. In the present study, closer inspection of the flow, corresponding to the stable and center manifolds near the reference orbit, reveals some interesting natural relative motions as well as some discrete control strategies for deployment. A hybrid control strategy is also employed that combines both the natural formation dynamics with non-natural motions via input feedback linearization techniques.

Numerical investigation of the dynamical environment of 65803 Didymos

NASA Astrophysics Data System (ADS)

Dell'Elce, L.; Baresi, N.; Naidu, S. P.; Benner, L. A. M.; Scheeres, D. J.

2017-03-01

The Asteroid Impact & Deflection Assessment (AIDA) mission is planning to visit the Didymos binary system in 2022 in order to perform the first demonstration ever of the kinetic impact technique. Binary asteroids are an ideal target for this since the deflection of the secondary body can be accurately measured by a satellite orbiting in the system. However, these binaries offer an extremely rich dynamical environment whose accurate investigation through analytical approaches is challenging at best and requires a significant number of restrictive assumptions. For this reason, a numerical investigation of the dynamical environment in the vicinity of the Didymos system is offered in this paper. After computing various families of periodic orbits, their robustness is assessed in a high-fidelity environment consisting of the perturbed restricted full three-body problem. The results of this study suggest that several nominally stable trajectories, including the triangular libration points, should not be considered as safe as a state vector perturbation may cause the spacecraft to drift from the nominal orbit and possibly impact one of the primary bodies within a few days. Nonetheless, there exist two safe solutions, namely terminator and interior retrograde orbits. The first one is adequate for observation purposes of the entire system and for communications. The second one is more suitable to perform close investigations of the primary body.

Stability of libration points in the restricted four-body problem with variable mass

NASA Astrophysics Data System (ADS)

Mittal, Amit; Aggarwal, Rajiv; Suraj, Md. Sanam; Bisht, Virender Singh

2016-10-01

We have investigated the stability of the Lagrangian solutions for the restricted four-body problem with variable mass. It has been assumed that the three primaries with masses m1, m2 and m3 form an equilateral triangle, wherein m2=m3. According to Jeans' law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), the infinitesimal body varies its mass m with time. The space-time transformations of Meshcherskii (Studies on the Mechanics of Bodies of Variable Mass, GITTL, Moscow, 1949) are used by taking the values of the parameters q=1/2, k=0, n=1. The equations of motion of the infinitesimal body with variable mass have been determined. The equations of motion of the current problem differ from the ones of the restricted four-body problem with constant mass. There exist eight libration points, out of which two are collinear with the primary m1 and the rest are non-collinear for a fixed value of parameters γ (m {at time} t/m {at initial time}, 0<γ≤1 ), α (the proportionality constant in Jeans' law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), 0≤α≤2.2) and μ=0.019 (the mass parameter). All the libration points are found to be unstable. The zero velocity surfaces (ZVS) are also drawn and regions of motion are discussed.

Earth to Moon Transfer: Direct vs Via Libration Points (L1, L2)

NASA Technical Reports Server (NTRS)

Condon, Gerald L.; Wilson, Samuel W.

2004-01-01

For some three decades, the Apollo-style mission has served as a proven baseline technique for transporting flight crews to the Moon and back with expendable hardware. This approach provides an optimal design for expeditionary missions, emphasizing operational flexibility in terms of safely returning the crew in the event of a hardware failure. However, its application is limited essentially to low-latitude lunar sites, and it leaves much to be desired as a model for exploratory and evolutionary programs that employ reusable space-based hardware. This study compares the performance requirements for a lunar orbit rendezvous mission type with one using the cislunar libration point (L1) as a stopover and staging point for access to arbitrary sites on the lunar surface. For selected constraints and mission objectives, it contrasts the relative uniformity of performance cost when the L1 staging point is used with the wide variation of cost for the Apollo-style lunar orbit rendezvous.

Tides in a body librating about a spin-orbit resonance: generalisation of the Darwin-Kaula theory

NASA Astrophysics Data System (ADS)

Frouard, Julien; Efroimsky, Michael

2017-09-01

The Darwin-Kaula theory of bodily tides is intended for celestial bodies rotating without libration. We demonstrate that this theory, in its customary form, is inapplicable to a librating body. Specifically, in the presence of libration in longitude, the actual spectrum of Fourier tidal modes differs from the conventional spectrum rendered by the Darwin-Kaula theory for a nonlibrating celestial object. This necessitates derivation of formulae for the tidal torque and the tidal heating rate, that are applicable under libration. We derive the tidal spectrum for longitudinal forced libration with one and two main frequencies, generalisation to more main frequencies being straightforward. (By main frequencies we understand those emerging due to the triaxiality of the librating body.) Separately, we consider a case of free libration at one frequency (once again, generalisation to more frequencies being straightforward). We also calculate the tidal torque. This torque provides correction to the triaxiality-caused physical libration. Our theory is not self-consistent: we assume that the tidal torque is much smaller than the permanent-triaxiality-caused torque, so the additional libration due to tides is much weaker than the main libration due to the permanent triaxiality. Finally, we calculate the tidal dissipation rate in a body experiencing forced libration at the main mode, or free libration at one frequency, or superimposed forced and free librations.

Librations and obliquity of Mercury from the BepiColombo laser altimetry, radio science and camera experiments

NASA Astrophysics Data System (ADS)

Pfyffer, G.; van Hoolst, T.; Dehant, V. M.

2010-12-01

Through its anomalously high uncompressed density implying a metal fraction of 60% or more by mass, Mercury represents an extreme outcome of planetary formation in the inner solar system. The space missions MESSENGER and BepiColombo are expected to advance largely our knowledge of the structure, formation, and evolution of Mercury. In particular, insight into Mercury's deep interior will be obtained from observations of the obliquity, the 88-day forced libration, the planetary induced librations and the degree-two coefficients of the gravity field of Mercury. We report here on aspects of the observational strategy of ESA’s BepiColombo mission to determine the libration amplitude and obliquity, taking into account the space as well as the ground segment of the experiment. Repeated photographic measurements of selected target positions on the surface of Mercury are central to the strategy to determine the obliquity and libration in the frame of the BepiColombo mission, but a significant constraint is posed by the fact that the planetary surface can only be photographed under very strict illumination conditions. We therefore study the possibility to use the information embedded in the groundtrack crossings (crosstracks) of the BepiColombo laser altimeter (BELA) in addition to the primary photographic data in order to estimate the librations and obliquity of Mercury. An advantage of the laser altimetry data is that it does not depend on the solar incidence angle on the surface nor on the presence of specific surface features as required for the camera data in the camera rotation experiment. Both laser and photographic measurements were simulated in a realistic set-up in order to estimate the accuracy of the reconstruction of the orientation and rotational motion of the planet as a function of the amount of measurements made, the number of different targets and crosstrack points considered and their locations on the surface of the planet. Such an analysis requires the use of an accurate model of the rotation of Mercury, which takes into account longitudinal librations additional to the main 88 day libration due to planetary perturbations on Mercury's orbit. Our simulations show that the achievable level of accuracy on the libration amplitude and obliquity will only be sufficient to constrain the size and physical state of the core of Mercury if certain conditions are satisfied. If the orbiter follows the ESA baseline mission scenario, and at least 25 landmarks are imaged at least twice over the mission duration (360 days), the annual libration amplitude and obliquity can be determined with sufficient accuracy. Also the Jupiter induced libration amplitude can pose an additional constraint on the interior of the planet. We will discuss the relative contributions of the different methods will enable us to determine the optimum combinations of the observations with consequences for the mission planning and the instrument performances.

PPF Dependent Fixed Point Results for Triangular α c-Admissible Mappings

PubMed Central

Ćirić, Ljubomir; Alsulami, Saud M.; Salimi, Peyman

2014-01-01

We introduce the concept of triangular α c-admissible mappings (pair of mappings) with respect to η c nonself-mappings and establish the existence of PPF dependent fixed (coincidence) point theorems for contraction mappings involving triangular α c-admissible mappings (pair of mappings) with respect to η c nonself-mappings in Razumikhin class. Several interesting consequences of our theorems are also given. PMID:24672352

TYCHO: Demonstrator and operational satellite mission to Earth-Moon-Libration point EML-4 for communication relay provision as a service

NASA Astrophysics Data System (ADS)

Hornig, Andreas; Homeister, Maren

2015-03-01

In the current wake of mission plans to the Moon and to Earth-Moon Libration points (EML) by several agencies and organizations, TYCHO identifies the key role of telecommunication provision for the future path of lunar exploration. It demonstrates an interesting extension to existing communication methods to the Moon and beyond by combining innovative technology with a next frontier location and the commercial space communication sector. It is evident that all communication systems will rely on direct communication to Earth ground stations. In case of EML-2 missions around HALO orbits or bases on the far side of the Moon, it has to be extended by communication links via relay stations. The innovative approach is that TYCHO provides this relay communication to those out-of-sight lunar missions as a service. TYCHO will establish a new infrastructure for future missions and even create a new market for add-on relay services. The TMA-0 satellite is TYCHO's first phase and a proposed demonstrator mission to the Earth-Moon Libration point EML-4. It demonstrates relay services needed for automated exploratory and manned missions (Moon bases) on the rim (>90°E and >90°W) and far side surface, to lunar orbits and even to EML-2 halo orbits (satellites and space stations). Its main advantage is the permanent availability of communication coverage. This will provide full access to scientific and telemetry data and furthermore to crucial medical monitoring and safety. The communication subsystem is a platform for conventional communication but also a test-bed for optical communication with high data-rate LASER links to serve the future needs of manned bases and periodic burst data-transfer from lunar poles. The operational TMA-1 satellite is a stand-alone mission integrated into existing space communication networks to provide open communication service to external lunar missions. Therefore the long-time stable libration points EML-4 and -5 are selected to guarantee an operation time of up to 10 years. It also enables measurements of the libration point environment with the scientific payloads. This includes sensors for space dust, solar and cosmic radiation activity for satellite lifetime estimation and lunar crew protection by providing early-warning systems. The paper describes the mission concept and the pre-design of the demonstrator satellite according to the operational mission requirements, advantages and benefits of this service. The concept was awarded with the Space Generation Advisory Council and OHB Scholarship in 2011 and the concept study is conducted at the Institute of Space Systems (IRS) [1] of the University of Stuttgart and OHB-System, Bremen [2].

Using Cassini CIRS Data to Constrain Enceladus' Libration State

NASA Technical Reports Server (NTRS)

Hurford, T. A.; Helfenstein, P.; Spencer, J. R.; Nimmo, F.

2009-01-01

Given the non-spherical shape of Enceladus, the satellite may experience gravitational torques that will cause it to physically librate as it orbits Saturn. Physical Libration would produce a diurnal oscillation in the longitude of Enceladus' tidal bulge, which could have a profound effect on the diurnal stresses experienced by the surface of the satellite. Although Cassini ISS has placed an observational upper limit on Enceladus' libration amplitude, small amplitude librations may have geologically significant consequences. For example, a physical libration will affect heat production. along the tiger stripes as produced by tidal shear heating. We have modeled the expected power en-litted along the tiger stripes for various types of physical libration and have quantified which types of physical libration best reproduce the observed power flux as detailed in Cassini CIRS data. We find that including a physical libration does allow better fits to the observations and we have identified regions of the libration phase space that where these fits are optimized. A physical libration has important implications for tidal dissipation within Enceladus and if identified may provide an additional constraint on its interior mass distribution.

Using Cassini CIRS Data to Constrain Enceladus' Libration State

NASA Technical Reports Server (NTRS)

Hurford, T. A.; Helfenstein, P.; Spencer, J. R.; Nimmo, P.

2010-01-01

Given the non-spherical shape of Enceladus, the satellite may experience gravitational torques that will cause it to physically librate as it orbits Saturn. Physical libration would produce a diurnal oscillation in the longitude of Enceladus' tidal bulge, which could have a profound effect on the diurnal stresses experienced by the surface of the satellite. Although Cassini ISS has placed an observational upper limit on Enceladus' libration amplitude, small amplitude librations may have geologically significant consequences. For example, a physical libration will affect heat production along the tiger stripes as produced by tidal shear heating. We have modeled the expected power emitted along the tiger stripes for various types of physical libration and have quantified which types of physical libration best reproduce the observed power f1ux as detailed in Cassini CIRS data. We find that including a physical libration does allow better fits to the observations and we have identified regions of the libration phase space that where these fits are optimized. A physical libration has important implications for tidal dissipation within Ence1adus and if identified may provide an additional constraint on its interior mass distribution.

Stationkeeping of the First Earth-Moon Libration Orbiters: The ARTEMIS Mission

NASA Technical Reports Server (NTRS)

Folta, David; Woodard, Mark; Cosgrove, D.

2011-01-01

Libration point orbits near collinear locations are inherently unstable and must be controlled. For Acceleration Reconnection and Turbulence and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) Earth-Moon Lissajous orbit operations, stationkeeping is challenging because of short time scales, large orbital eccentricity of the secondary, and solar gravitational and radiation pressure perturbations. ARTEMIS is the first NASA mission continuously controlled at both Earth-Moon L1 and L2 locations and uses a balance of optimization, spacecraft implementation and constraints, and multi-body dynamics. Stationkeeping results are compared to pre-mission research including mode directions.

Stability of triangular points in the elliptic restricted three-body problem with oblateness up to zonal harmonic J4 of both primaries

NASA Astrophysics Data System (ADS)

Singh, Jagadish; Tyokyaa, Richard K.

2016-10-01

In this paper, we study the locations and stability of triangular points in the elliptic restricted three-body problem when both primaries are taken as oblate spheroids with oblateness up to J4. The positions of the triangular points are seen to be affected by oblateness of the primaries and the eccentricity of their orbits. The triangular points are conditionally stable for 0<μ<μc0<μ<μc and unstable for μc≤μ≤12μc≤μ≤12, where μcμc is the critical mass parameter depending on the oblateness coefficients J2iJ2i (i =1,2) and the eccentricity of the orbits. We further observe that both coefficients J2 and J4, semi-major axis and the eccentricity have destabilizing tendencies resulting in a decrease in the size of the region of stability with an increase in the parameters involved. Knowing that, in general, the triangular equilibrium points are stable for 0<μ<μc0<μ<μc, in particular systems (Alpha Centauri, X1X1 Bootis, Sirius and Kruger 60) this does not hold and such points are unstable.

Frozen Orbits-Near Constant or Beneficially Varying Orbital Parameters.

DTIC Science & Technology

1986-05-15

89 6.3 Equatorial Near-Circular Orbits ............................... 92 6.4 Stable and Unstable Equilibrium Points ...Angle Libration Period......................................... 78 5-2 Lunar Gravitational Effect on Near-Circular Orbits .................... 80 5-3...6-1 Period of Oscillation about the Stable Equilibrium Point ............... 102 FIGURES Figure 2.1 Orbital Parameters

Collocation of equilibria in gravitational field of triangular body via mass redistribution

NASA Astrophysics Data System (ADS)

Burov, Alexander A.; Guerman, Anna D.; Nikonov, Vasily I.

2018-05-01

We consider a gravitating system with triangular mass distribution that can be used as approximation of gravitational field for small irregular celestial bodies. In such system, the locations of equilibrium points, that is, the points where the gravitational forces are balanced, are analyzed. The goal is to find the mass distribution which provides equilibrium in a pre-assigned location near the triangular system, and to study the stability of this equilibrium.

Cooperative motion in liquids: On librational dynamics of chloroform throughout its normal liquid-phase range

NASA Astrophysics Data System (ADS)

Rothschild, Walter G.; Cavagnat, Raymond M.

1994-03-01

We have extended the Raman spectral accumulations of the ν3 mode (A1, 367 cm-1) of liquid CHCl3-Cl-35 and its simulation in terms of an orientational equilibrium renewal process [W. G. Rothschild, R. M. Cavagnat, and P. Maraval, J. Chem. Phys. 99, 8922 (1993)] to a temperature of 338 K, about the normal boiling point of the system (335 K). The values of the best-fit parameters predict that the orientational motion of liquid chloroform, even at such a relatively high kinetic energy, is described predominantly by libratory states; their lifetime (˜1 ps) is four times longer than that of the free-rotational steps. The character of the orientational motion of the system, when traversing the range of 213 to 338 K from just above its melting to near its boiling point at about atmospheric pressure, reflects the softening of the liquid-cage structure in terms of an increasing dispersion and/or a decreasing value of the mean libration frequency, a lowering of the depth of its potential well, but near-invariance of its lifetime. Simultaneously, there is an approximately twofold increase in the lifetime of the much shorter stages of free-rotational motion. In essence, the system dynamics remain that of an assembly of librators.

Formation Flying Satellite Control Around the L2 Sun-Earth Libration Point

NASA Technical Reports Server (NTRS)

Hamilton, Nicholas H.; Folta, David; Carpenter, Russell; Bauer, Frank (Technical Monitor)

2002-01-01

This paper discusses the development of a linear control algorithm for formations in the vicinity of the L2 sun-Earth libration point. The development of a simplified extended Kalman filter is included as well. Simulations are created for the analysis of the stationkeeping and various formation maneuvers of the Stellar Imager mission. The simulations provide tracking error, estimation error, and control effort results. For formation maneuvering, the formation spacecraft track to within 4 meters of their desired position and within 1.5 millimeters per second of their desired zero velocity. The filter, with few exceptions, keeps the estimation errors within their three-sigma values. Without noise, the controller performs extremely well, with the formation spacecraft tracking to within several micrometers. Each spacecraft uses around 1 to 2 grams of propellant per maneuver, depending on the circumstances.

A Librational Model for the Propeller Blériot in the Saturnian Ring System

NASA Astrophysics Data System (ADS)

Seiler, M.; Sremčević, M.; Seiß, M.; Hoffmann, H.; Spahn, F.

2017-05-01

The reconstruction of the orbital evolution of the propeller structure Blériot orbiting in Saturn’s A ring from recurrent observations in Cassini ISS images yielded a considerable offset motion from the expected Keplerian orbit. This offset motion can be composed by three sinusoidal harmonics with amplitudes and periods of 1845, 152, 58 km and 11.1, 3.7, and 2.2 years, respectively. In this paper we present results from N-body simulations, where we integrated the orbital evolution of a moonlet, which is placed at the radial position of Blériot under the gravitational action of the Saturnian satellites. Our simulations yield that, especially the gravitational interactions with Prometheus, Pandora, and Mimas are forcing the moonlet to librate with the right frequencies, but the libration amplitudes are too small to explain the observations. Thus, further mechanisms are needed to explain the amplitudes of the forced librations—e.g., moonlet-ring interactions. Here, we develop a model, where the moonlet is allowed to be slightly displaced with respect to its created gaps breaking the point symmetry and causing a repulsive force in this way. As a result, the evolution of the moonlet’s longitude can be described by a harmonic oscillator. In the presence of external forcing by the outer moons, the libration amplitudes get the more amplified the closer the forcing frequency is to the eigenfrequency of the disturbed propeller oscillator. Applying our model to Blériot, it is possible to reproduce a libration period of 13 years with an amplitude of about 2000 km.

Effect of catalogues coordinate errors of a star onto determination of the physical libration of the Moon from the observations of stars

NASA Astrophysics Data System (ADS)

Petrova, Natalia; Kocoulin, Valerii; Nefediev, Yurii

2016-07-01

In the Kazan University computer simulation is carried out for observation of lunar physical libration in projects planned installation of measuring equipment on the lunar surface. One such project is the project of ILOM (Japan), in which on the lunar pole an optical telescope with CCD will be equipped. As a result, the determining the selenographic coordinates (x and y) of a star with an accuracy of 1 ms of arc will be achieved. On the basis of the analytical theory of physical libration we developed a technique for solving the inverse problem of the libration. And we have already shown, for example, that the error in determining selenographic coordinates about ɛ seconds does not lead to errors in the determination of the libration angles ρ and Iσ larger than the 1.414ɛ. Libration in longitude is not determined from observations of the polar star (Petrova et al., 2012). The accuracy of the libration in the inverse problem depends on accuracy of the coordinates of the stars - α and δ - taken from the star catalogs. Checking this influence is the task of the present study. To do simulation we have developed that allows to choose the stars, falling in the field of view of the lunar telescope on observation period. Equatorial coordinates of stars were chosen by us from several fundamental catalogs: UCAC2-BSS, Hipparcos, Tycho, FK6 (part I, III) and the Astronomical Almanac. An analysis of these catalogues from the point of view accuracy of coordinates of stars represented in them was performed by Nefediev et al., 2013. The largest error, 20-70 ms, found in the catalogues UCAC2 and Tycho, the others have an error about a millisecond of arc. We simulated the observations with mentioned errors and got the following results. 1. The error in the declination Δδ of the star causes the same order error in libration parameters ρ and Iσ , while the sensitivity of libration to errors in Δα is ten time smaller. Fortunately, due to statistics (30 to 70, depending on the time of observation), this error is reduced by an order, i.e. does not exceed the error of observation selenographic coordinates. 2. The worst thing - errors in coordinates of catalogue causes though a small but constant shift in the ρ and Iσ. So, when Δα, Δδ ˜0.01", then the shift reaches 0.0025". Moreover there is a trend, with a slight, but noticeable slope. 3. Effect of error in declination of a stars is substantially strong than the error in right ascension. Perhaps it is characteristic only for polar observations. For the required accuracy in determination of the physical libration these phenomena must be taken into account when processing the planned observations. Referencies. Nefediev et al., 2013. Uchenye zapiski Kazanskogo universiteta, v. 155, 1, p.188-194. Petrova, N., Abdulmyanov T., Hanada H. Some qualitative manifestations of the physical libration of the Moon by observing stars from the lunar surface. //J. Adv. Space Res., 2012a. V. 50, p. 1702-1711

Continuation of periodic orbits in the Sun-Mercury elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Peng, Hao; Bai, Xiaoli; Xu, Shijie

2017-06-01

Starting from resonant Halo orbits in the Circular Restricted Three-Body Problem (CRTBP), Multi-revolution Elliptic Halo (ME-Halo) orbits around L1 and L2 points in the Sun-Mercury Elliptic Restricted Three-Body Problem (ERTBP) are generated systematically. Three pairs of resonant parameters M5N2, M7N3 and M9N4 are tested. The first pair shows special features and is investigated in detail. Three separated characteristic curves of periodic orbit around each libration point are obtained, showing the eccentricity varies non-monotonically along these curves. The eccentricity of the Sun-Mercury system can be achieved by continuation method in just a few cases. The stability analysis shows that these orbits are all unstable and the complex instability occurs with certain parameters. This paper shows new periodic orbits in both the CRTBP and the ERTBP. Totally four periodic orbits with parameters M5N2 around each libration points are extracted in the Sun-Mercury ERTBP.

Understanding the Sun-Earth Libration Point Orbit Formation Flying Challenges For WFIRST and Starshade

NASA Technical Reports Server (NTRS)

Webster, Cassandra M.; Folta, David C.

2017-01-01

In order to fly an occulter in formation with a telescope at the Sun-Earth L2 (SEL2) Libration Point, one must have a detailed understanding of the dy-namics that govern the restricted three body system. For initial purposes, a linear approximation is satisfactory, but operations will require a high-fidelity modeling tool along with strategic targeting methods in order to be successful. This paper focuses on the challenging dynamics of the transfer trajectories to achieve the relative positioning of two spacecraft to fly in formation at SEL2, in our case, the Wide-Field Infrared Survey Telescope (WFIRST) and a proposed Starshade. By modeling the formation transfers using a high fidelity tool, an accurate V approximation can be made to as-sist with the development of the subsystem design required for a WFIRST and Starshade formation flight mission.

Lunar Gravity-Assist Maneuver As a Way of Reducing the Orbit Amplitude in the Spectrum-Röntgen-Gamma Project

NASA Astrophysics Data System (ADS)

Kovalenko, I. D.; Eismont, N. A.

2018-04-01

Spectrum-Röntgen-Gamma (SRG) is a space observatory designed to observe astrophysical objects in the X-ray range of the electromagnetic spectrum. SRG is planned to be launched in 2019 by a Proton-M launch vehicle with a DM3 upper stage. The spacecraft will be delivered to an orbit around the Sun-Earth collinear libration point L2 located at a distance of 1.5 million km from the Earth. Although the SRG launch scheme has already been determined at present, in this paper we consider an alternative spacecraft transfer scenario using a lunar gravity-assist maneuver. The proposed scenario allows a oneimpulse transfer from a low Earth orbit to a small-amplitude orbit around the libration point to be performed while fulfilling the technical constraints and the scientific requirements of the mission.

Software for C1 interpolation

NASA Technical Reports Server (NTRS)

Lawson, C. L.

1977-01-01

The problem of mathematically defining a smooth surface, passing through a finite set of given points is studied. Literature relating to the problem is briefly reviewed. An algorithm is described that first constructs a triangular grid in the (x,y) domain, and first partial derivatives at the modal points are estimated. Interpolation in the triangular cells using a method that gives C sup.1 continuity overall is examined. Performance of software implementing the algorithm is discussed. Theoretical results are presented that provide valuable guidance in the development of algorithms for constructing triangular grids.

New Worlds Observer Formation Control Design Based on the Dynamics of Relative Motion

NASA Technical Reports Server (NTRS)

Luquette, Richard J.

2008-01-01

The New Worlds Observer (NWO) mission is designed for the direct detection and characterization of extrasolar planets. The NWO mission concept employs a two spacecraft leader-follower formation on a trajectory around the Earth/Moon-Sun L(sub 2) Libration Point. The leader spacecraft is baselined as a 4 meter optical telescope. The follower, Starshade spacecraft, is designed to suppress light from a central body star permitting direct detection of a surrounding exoplanetary system. The current design requires a nominal leader-follower separation range of 72 Megameters. NWO poses many challenges including formation control. NWO cycles between three principal control modes during the nominal mission timeline: science (fine pointing), realignment and transition. This paper examines formation control strategies in the context of dynamics of relative motion for two spacecraft operating in the vicinity of the Earth/Moon-Sun L(sub 2)libration point. The paper presents an overview of the equations of relative motion followed by a discussion of each of the control modes. Discussion and analysis characterize control strategies for each of the mission control modes, including requirements, implementation challenges and project fuel budgets.

Constraints on Titan rotation from Cassini radar

NASA Astrophysics Data System (ADS)

Bills, B. G.; Stiles, B. W.; Kirk, R. L.

2014-12-01

We give an update on efforts to model the rotation of Titan, subject to constraints from Cassini radar observations. The data we are currently using includes 670 tie-points, each of which is a pair of inertial positions of a single surface point, relative to the center of mass of Titan, and the corresponding pair of observation times. The positional accuracy is of order 1 km, in each Cartesian component. A reasonably good fit to the observations is obtained with a simple model which has a fixed spin pole and a rotation rate which is a sum of a constant value and a single sinusoidal oscillation. A better fit is obtained if we insist that Titan should behave as a synchronous rotator, in the dynamical sense of keeping its axis of least inertia oriented toward Saturn. At the level of accuracy required to fit the Cassini radar data, synchronous rotation is notably different than having a uniform rate of rotation. In this case, we need to model time variations in the orbital mean longitude, which is the longitude of periapse, plus the mean anomaly. That angle varies on a wide range of times scales, including Titan's periapse precession period (703 years), Saturn's heliocentric orbital period (29.47 years), perturbations from relatively large satellites Iapetus (79.3 days), and a 4:3 mean motion resonant interaction with Hyperion (640 and 6850 days), and a linear increase at Titan's mean orbital period (15.9455 day). Our rotation model for Titan has 4 free parameters. Two of them specify the orientation of the fixed spin pole, and the other two are the effective free libration period and viscous damping time. Our dynamical model includes a damped forced longitudinal libration, in which gravitational torques attempt to align the axis of least inertia with the instantaneous direction to Saturn. For a rigid tri-axial body, with Titan's moments of inertia, the free oscillation period for longitudinal librations would be 850 days. For a decoupled elastic shell, the effective period is likely somewhat less. Variations in angular position of Saturn, as seen from Titan, with periods shorter than the free libration period, will not be accurately tracked. Thus the short period (one and two cycles per orbit) forced librations will be very small (~50 m), and are, in any event, not well sampled in the data.

On the first ν6 anti-aligned librating asteroid family of Tina

NASA Astrophysics Data System (ADS)

Carruba, V.; Morbidelli, A.

2011-04-01

Asteroid families are groups of bodies identified in the space of proper elements or of frequencies that share a common origin in the collisional break-up of their progenitors. Their dynamical evolution is shaped by the interaction with the local web of mean-motion and secular resonances, and by non-gravitational effects, such as the 'Yarkovsky' and 'Yarkovsky-O'Keefe-Radzievskii-Paddack' (YORP) effects. Thus, obtaining information on their age and original ejection velocity field is generally a difficult task. Recently, two families were found to have a large fraction of members in the non-linear secular resonance z1: the Agnia and Padua families. Conserved quantities of the z1resonance allowed for a more precise determination of their ages and ejection velocity fields. So far, however, no family was known to be in a linear secular resonance, such as the ν6 resonance, although individual asteroids were known to be in ν6 anti-aligned librating states. The ν6 resonance occurs when there is a commensurability between the frequency of precession of the pericentre of an asteroid and that of Saturn. As a consequence, in librating states, the resonant argument oscillates around a stable point. In anti-aligned librating states, the resonant argument oscillates around the stable point at 180°. Here we show that the newly identified Tina family is characterized by having all its members in such a state, making it the only family in the asteroid belt known to be completely embedded in a secular resonance configuration. This rare dynamical configuration limits the maximum eccentricity of Tina members, preventing them from experiencing Martian close encounters and forming a stable island of a new dynamical type. The current dispersion of asteroid resonant elements suggests that the family should be at least 2.5 Myr old, while Monte Carlo simulations including the Yarkovsky and YORP effects suggest that the Tina family should be 170+20-30 Myr old.

Efficient generation of discontinuity-preserving adaptive triangulations from range images.

PubMed

Garcia, Miguel Angel; Sappa, Angel Domingo

2004-10-01

This paper presents an efficient technique for generating adaptive triangular meshes from range images. The algorithm consists of two stages. First, a user-defined number of points is adaptively sampled from the given range image. Those points are chosen by taking into account the surface shapes represented in the range image in such a way that points tend to group in areas of high curvature and to disperse in low-variation regions. This selection process is done through a noniterative, inherently parallel algorithm in order to gain efficiency. Once the image has been subsampled, the second stage applies a two and one half-dimensional Delaunay triangulation to obtain an initial triangular mesh. To favor the preservation of surface and orientation discontinuities (jump and crease edges) present in the original range image, the aforementioned triangular mesh is iteratively modified by applying an efficient edge flipping technique. Results with real range images show accurate triangular approximations of the given range images with low processing times.

The rotation of Io

NASA Astrophysics Data System (ADS)

Henrard, Jacques

2005-11-01

The paper develops, in the framework of Hamiltonian mechanics, a theory of the rotation of Io, considered as a rigid body. The theory includes the perturbation due to Jupiter (considered as an oblate body) and the indirect perturbations due to the other Galilean satellites. In order to describe the orbit of Io around Jupiter, we use the synthetic theory of Lainey [2002, PhD dissertation, Observatoire de Paris], the result of a frequency analysis of a numerically integrated jovian system. The direct effects of the other Galilean satellites are found to be negligible, but their indirect effects are important. Our theory is consistent with the rigid body model and with Lainey's description of the orbit of Io, at least down to 10 rad (0.2 arc-second). Of course the effects of the nonrigidity of Io and of a probable liquid core should be considered. We find a mean obliquity of 7.619×10 rad (157 arc-second) and the period of the three free librations to be 13.25 days (free libration in longitude), 159.39 days (free libration in latitude), and 229.85 days (free wobble). Fourier series are produced describing, in the body frame, the motion of the polar axis of Jupiter, the motion of the unit vector pointing toward Jupiter, and the "motion of the pole" (the motion of the angular momentum with respect to the axis of largest inertia). Free librations (depending on three arbitrary parameters) are also computed.

Diffraction of V-point singularities through triangular apertures.

PubMed

Ram, B S Bhargava; Sharma, Anurag; Senthilkumaran, P

2017-05-01

In this paper we present experimental studies on diffraction of V-point singularities through equilateral and isosceles right triangular apertures. When V-point index, also called Poincare-Hopf index (η), of the optical field is +1, the diffraction disintegrates it into two monstars/lemons. When V-point index η is -1, diffraction produces two stars. The diffraction pattern, unlike phase singularity, is insensitive to polarity of the polarization singularity and the intensity pattern remains invariant. Higher order V-point singularities are generated using Sagnac interferometer and it is observed that the diffraction disintegrates them into lower order C-points.

End of Life Disposal for Three Libration Point Missions through Manipulation of the Jacobi Constant and Zero Velocity Curves

NASA Technical Reports Server (NTRS)

Petersen, Jeremy; Brown, Jonathan

2015-01-01

Flight Dynamics Facility (FDF) located at NASA Goddard Space Flight Center (GSFC) provides the flight dynamics expertise for three Sun-Earth Moon L1 missions. Advanced Composition Explorer (ACE) launched August 1997 Solar and Heliospheric Observatory (SOHO) launched December 1995 Global Geospace Science WIND satellite launched November 1994 entered Lagrange point orbit in 2004.

Two Approaches in the Lunar Libration Theory: Analytical vs. Numerical Methods

NASA Astrophysics Data System (ADS)

Petrova, Natalia; Zagidullin, Arthur; Nefediev, Yurii; Kosulin, Valerii

2016-10-01

Observation of the physical libration of the Moon and the celestial bodies is one of the astronomical methods to remotely evaluate the internal structure of a celestial body without using expensive space experiments. Review of the results obtained due to the physical libration study, is presented in the report.The main emphasis is placed on the description of successful lunar laser ranging for libration determination and on the methods of simulating the physical libration. As a result, estimation of the viscoelastic and dissipative properties of the lunar body, of the lunar core parameters were done. The core's existence was confirmed by the recent reprocessing of seismic data Apollo missions. Attention is paid to the physical interpretation of the phenomenon of free libration and methods of its determination.A significant part of the report is devoted to describing the practical application of the most accurate to date the analytical tables of lunar libration built by comprehensive analytical processing of residual differences obtained when comparing the long-term series of laser observations with numerical ephemeris DE421 [1].In general, the basic outline of the report reflects the effectiveness of two approaches in the libration theory - numerical and analytical solution. It is shown that the two approaches complement each other for the study of the Moon in different aspects: numerical approach provides high accuracy of the theory necessary for adequate treatment of modern high-accurate observations and the analytic approach allows you to see the essence of the various kind manifestations in the lunar rotation, predict and interpret the new effects in observations of physical libration [2].[1] Rambaux, N., J. G. Williams, 2011, The Moon's physical librations and determination of their free modes, Celest. Mech. Dyn. Astron., 109, 85-100.[2] Petrova N., A. Zagidullin, Yu. Nefediev. Analysis of long-periodic variations of lunar libration parameters on the basis of analytical theory / // The Russian-Japanese Workshop, 20-25 October, Tokyo (Mitaka) - Mizusawa, Japan. - 2014.

Inclined asymmetric librations in exterior resonances

NASA Astrophysics Data System (ADS)

Voyatzis, G.; Tsiganis, K.; Antoniadou, K. I.

2018-04-01

Librational motion in Celestial Mechanics is generally associated with the existence of stable resonant configurations and signified by the existence of stable periodic solutions and oscillation of critical (resonant) angles. When such an oscillation takes place around a value different than 0 or π , the libration is called asymmetric. In the context of the planar circular restricted three-body problem, asymmetric librations have been identified for the exterior mean motion resonances (MMRs) 1:2, 1:3, etc., as well as for co-orbital motion (1:1). In exterior MMRs the massless body is the outer one. In this paper, we study asymmetric librations in the three-dimensional space. We employ the computational approach of Markellos (Mon Not R Astron Soc 184:273-281, https://doi.org/10.1093/mnras/184.2.273, 1978) and compute families of asymmetric periodic orbits and their stability. Stable asymmetric periodic orbits are surrounded in phase space by domains of initial conditions which correspond to stable evolution and librating resonant angles. Our computations were focused on the spatial circular restricted three-body model of the Sun-Neptune-TNO system (TNO = trans-Neptunian object). We compare our results with numerical integrations of observed TNOs, which reveal that some of them perform 1:2 resonant, inclined asymmetric librations. For the stable 1:2 TNO librators, we find that their libration seems to be related to the vertically stable planar asymmetric orbits of our model, rather than the three-dimensional ones found in the present study.

Determination of the free lunar libration modes from ephemeris DE430

NASA Astrophysics Data System (ADS)

Yang, Yong-Zhang; Li, Jin-Ling; Ping, Jin-Song; Hanada, Hideo

2017-12-01

The Moon’s physical librations have been extensively studied, and elaborate researches have been developed for the purpose of deriving accurate modes of free librations. Our motivation comes from the Planetary and Lunar Ephemeris DE430 by JPL/NASA, which was created in April 2013, and is reported to be the most accurate lunar ephemeris today using the data from Gravity Recovery and Interior Laboratory (GRAIL). Therefore, the residuals after fitting the model have reduced owing to improvement in the libration models, and the free librations embedded in the Euler angles have also improved. We use Fourier analysis to extract the approximate frequencies from DE430 and then a quadratic interpolation method is used to determine higher accuracy frequencies. With the frequencies, the linear least-squares fitting method is employed to fit the lunar physical librations to DE430. From this analysis we identified the three modes of free physical librations, and estimated the amplitudes as {1.471}\\prime\\prime in longitude, {0.025}\\prime\\prime in latitude and {8.19}\\prime\\prime× {3.31}\\prime\\prime for the wobble, with the respective periods of 1056.16, 8806.9 and 27262.99 d. Since the free librations damp with time, they require recent excitation or a continuous stimulating mechanism in order to sustain.

Trajectory analysis of transfers between L4 and L5 and low lunar orbit

NASA Technical Reports Server (NTRS)

1988-01-01

The flight characteristics and spacecraft performance during missions involving flight between the equilateral libration points and the Moon are discussed. The conclusions drawn will show that a minimum energy trajectory is the most efficient transfer technique for this type of flight.

50 CFR Figures 18a, 18b and 18c to... - Large Frame TED Escape Opening; Minimum Dimensions Using All-Bar Cuts (Triangular Cuts); Large...

Code of Federal Regulations, 2013 CFR

2013-10-01

... Dimensions Using All-Bar Cuts (Triangular Cuts); Large Frame TED Escape Opening; Minimum Dimensions Using All-Bar Cuts and Leading Edge Cut; Large Frame TED Escape Opening; Minimum Dimensions Using All-Points...—Large Frame TED Escape Opening; Minimum Dimensions Using All-Bar Cuts (Triangular Cuts); Large Frame TED...

50 CFR Figures 18a, 18b and 18c to... - Large Frame TED Escape Opening; Minimum Dimensions Using All-Bar Cuts (Triangular Cuts); Large...

Code of Federal Regulations, 2012 CFR

2012-10-01

... Dimensions Using All-Bar Cuts (Triangular Cuts); Large Frame TED Escape Opening; Minimum Dimensions Using All-Bar Cuts and Leading Edge Cut; Large Frame TED Escape Opening; Minimum Dimensions Using All-Points...—Large Frame TED Escape Opening; Minimum Dimensions Using All-Bar Cuts (Triangular Cuts); Large Frame TED...

50 CFR Figures 18a, 18b and 18c to... - Large Frame TED Escape Opening; Minimum Dimensions Using All-Bar Cuts (Triangular Cuts); Large...

Code of Federal Regulations, 2014 CFR

2014-10-01

... Dimensions Using All-Bar Cuts (Triangular Cuts); Large Frame TED Escape Opening; Minimum Dimensions Using All-Bar Cuts and Leading Edge Cut; Large Frame TED Escape Opening; Minimum Dimensions Using All-Points...—Large Frame TED Escape Opening; Minimum Dimensions Using All-Bar Cuts (Triangular Cuts); Large Frame TED...

Geological Implications of a Physical Libration on Enceladus

NASA Technical Reports Server (NTRS)

Hurford, T. A.; Bills, B. G.; Helfenstein, P.; Greenberg, R.; Hoppa, G. V.; Hamilton, D. P.

2008-01-01

Given the non-spherical shape of Enceladus (Thomas et al., 2007), the satellite will experience gravitational torques that will cause it to physically librate as it orbits Saturn. Physical libration would produce a diurnal oscillation in the longitude of Enceladus tidal bulge which, could have a profound effect on the diurnal stresses experienced by the surface of the satellite. Although Cassini ISS has placed an observational upper limit on Enceladus libration amplitude of F < 1.5deg (Porco et al., 2006), smaller amplitudes can still have geologically significant consequences. Here we present the first detailed description of how physical libration affects tidal stresses and how those stresses then might affect geological processes including crack formation and propagation, south polar eruption activity, and tidal heating. Our goal is to provide a framework for testing the hypothesis that geologic features on Enceladus are produced by tidal stresses from diurnal physical and optical librations of the satellite.

On Space Warfare: A Space Power Doctrine

DTIC Science & Technology

1998-06-01

called Panama Theory: that there are strategic places (geostationary orbits , libration points ) in space that have military value similar to the...initial training courses for the orbital analyst career field. In 1969, Lupton was transferred to the Headquarters Strategic Air Command, Directorate...over a point on the equator even though the satellite is moving in a circular orbit through space. This altitude (19,360 nautical miles) is the only

Steady Motions of Rigid Body Satellites in a Central Gravitational Field

DTIC Science & Technology

1993-12-01

been explored for several centuries. Orbiting bodies investigated include point masses, spheres, cylinders, rods, ball-and-socket connected objects...of the satellite model relative to its orbit radius could lead to 5 its treatment as a point mass, doing so would prevent analysis of satellite...8217 librational ’ motion ... and internal elastic forces in the structure balance the orbital dynamic accelerations tending to separate masses orbiting at

Coupling effect of topological states and Chern insulators in two-dimensional triangular lattices

NASA Astrophysics Data System (ADS)

Zhang, Jiayong; Zhao, Bao; Xue, Yang; Zhou, Tong; Yang, Zhongqin

2018-03-01

We investigate topological states of two-dimensional (2D) triangular lattices with multiorbitals. Tight-binding model calculations of a 2D triangular lattice based on px and py orbitals exhibit very interesting doubly degenerate energy points at different positions (Γ and K /K' ) in momentum space, with quadratic non-Dirac and linear Dirac band dispersions, respectively. Counterintuitively, the system shows a global topologically trivial rather than nontrivial state with consideration of spin-orbit coupling due to the "destructive interference effect" between the topological states at the Γ and K /K' points. The topologically nontrivial state can emerge by introducing another set of triangular lattices to the system (bitriangular lattices) due to the breakdown of the interference effect. With first-principles calculations, we predict an intrinsic Chern insulating behavior (quantum anomalous Hall effect) in a family of the 2D triangular lattice metal-organic framework of Co(C21N3H15) (TPyB-Co) from this scheme. Our results provide a different path and theoretical guidance for the search for and design of new 2D topological quantum materials.

An Investigation of Spinup Dynamics of Axial Gyrostats Using Elliptic Integrals and the Method of Averaging

DTIC Science & Technology

1991-01-01

is a gyrostat near one of the five libration points . She identified the equilibria and determined their stability regions. Also, Mavraga- nis [71] has...defines a family of periodic orbits , depending on how close the all-spun motion is to an equilibrium point of the equations of motion for a single...determined by the relationship between the mission orbit and the object the platform is supposed to track. As a limiting case, one might wish to point

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seiler, M.; Seiß, M.; Hoffmann, H.

The reconstruction of the orbital evolution of the propeller structure Blériot orbiting in Saturn’s A ring from recurrent observations in Cassini ISS images yielded a considerable offset motion from the expected Keplerian orbit. This offset motion can be composed by three sinusoidal harmonics with amplitudes and periods of 1845, 152, 58 km and 11.1, 3.7, and 2.2 years, respectively. In this paper we present results from N -body simulations, where we integrated the orbital evolution of a moonlet, which is placed at the radial position of Blériot under the gravitational action of the Saturnian satellites. Our simulations yield that, especiallymore » the gravitational interactions with Prometheus, Pandora, and Mimas are forcing the moonlet to librate with the right frequencies, but the libration amplitudes are too small to explain the observations. Thus, further mechanisms are needed to explain the amplitudes of the forced librations—e.g., moonlet–ring interactions. Here, we develop a model, where the moonlet is allowed to be slightly displaced with respect to its created gaps breaking the point symmetry and causing a repulsive force in this way. As a result, the evolution of the moonlet’s longitude can be described by a harmonic oscillator. In the presence of external forcing by the outer moons, the libration amplitudes get the more amplified the closer the forcing frequency is to the eigenfrequency of the disturbed propeller oscillator. Applying our model to Blériot, it is possible to reproduce a libration period of 13 years with an amplitude of about 2000 km.« less

Stability of triangular lagrangian points in elliptical restricted three body problem under the radiating binary systems

NASA Astrophysics Data System (ADS)

Narayan, A.; Singh, Nutan

2014-10-01

This paper studies the stability of Triangular Lagrangian points in the model of elliptical restricted three body problem, under the assumption that both the primaries are radiating. The model proposed is applicable to the well known binary systems Achird, Luyten, αCen AB, Kruger-60, Xi-Bootis. Conditional stability of the motion around the triangular points exists for 0≤ μ≤ μ ∗, where μ is the mass ratio. The method of averaging due to Grebenikov has been exploited throughout the analysis of stability of the system. The critical mass ratio depends on the combined effects of radiation of both the primaries and eccentricity of this orbit. It is found by adopting the simulation technique that the range of stability decreases as the radiation pressure parameter increases.

A Solar System Survey of Forced Librations in Longitude

NASA Technical Reports Server (NTRS)

Cornstock, Robert L.; Bills, Bruce G.

2003-01-01

Forced librations are periodic rotational rate variations due to gravitational interactions with an orbital partner. We have developed an analytic theory capable of calculating expected amplitudes of forced librations for nonresonant rotators as well as for bodies existing in a spin-orbit resonance. The theory has been applied to 34 solar system bodies, including terrestrial planets, planetary satellites, and the asteroid Eros. Parameters governing libration amplitude are the body s orbital eccentricity, moment difference, and the ratio of its spin rate to its orbital rate. In each case the largest libration amplitude is associated with the forcing frequency 2 (p - 1) n, where n is the orbital mean motion and p is the spin/orbit rate ratio. This dominant frequency is simply semidiurnal as seen from the position of the torquing body. The maximum libration angular amplitude is 1.3 x 10(exp -2) radians for Thebe, and the maximum mean equatorial displacement is 1.4 km for Mimas.

Heteroclinic, Homoclinic Connections Between the Sun-Earth Triangular Points and Quasi-Satellite Orbits for Solar Observations

NASA Technical Reports Server (NTRS)

Llanos, Pedro J.; Hintz, Gerald R.; Lo, Martin W.; Miller, James K.

2013-01-01

Investigation of new orbit geometries exhibits a very attractive behavior for a spacecraft to monitor space weather coming from the Sun. Several orbit transfer mechanisms are analyzed as potential alternatives to monitor solar activity such as a sub-solar orbit or quasi-satellite orbit and short and long heteroclinic and homoclinic connections between the triangular points L(sub 4) and L(sub 5) and the collinear point L(sub 3) of the Circular Restricted Three-Body Problem (CRTBP) in the Sun-Earth system.

An Approach to Optimal Control of Electrodynamic Tethers in a Stochastically Varying Drag Environment

DTIC Science & Technology

2011-05-06

and used to help address some of the complications and drawbacks of chemical propulsion systems. One such technology is electric propulsion, which...in and out of the orbital plane around its equilibrium point. The motion is similar to a swinging pendulum . These librations are due to the

On the dynamical structure of the Trojan group of asteroids

NASA Technical Reports Server (NTRS)

Zagretdinov, R. V.; Williams, I. P.; Yoshikawa, M.

1992-01-01

Using a semi-analytical approach, domains of possible motion for Trojan asteroids were established. It is shown that stable librating motion is possible for both high inclination and high eccentricity. Frequency distributions were also produced for real Trojan asteroids, against differing libration amplitudes and libration periods.

Dissipation in a tidally perturbed body librating in longitude

NASA Astrophysics Data System (ADS)

Efroimsky, Michael

2018-05-01

Internal dissipation in a tidally perturbed librating body differs in several respects from the tidal dissipation in a steadily spinning rotator. First, libration changes the spectral distribution of tidal damping across the tidal modes, as compared to the case of steady spin. This changes both the tidal heating rate and the tidal torque. Second, while a non-librating rotator experiences alternating deformation only due to the potential force exerted on it by the perturber, a librating body is also subject to a toroidal force proportional to the angular acceleration. Third, while the centrifugal force in a steadily spinning body renders only a permanent deformation (which defines the oblateness when the body cools down), in a librating body this force contains two alternating components-one purely radial, another a degree-2 potential force. Both contribute to heating, as well as to the tidal torque and potential (and, thereby, to the orbital evolution). We develop a formalism needed to describe dissipation in a homogeneous terrestrial body performing small-amplitude libration in longitude. This formalism incorporates as its part a linear rheological law defining the response of the rotator's material to forcing. While the developed formalism can work with an arbitrary linear rheology, we consider a simple example of a Maxwell material. We demonstrate that, independent of the rheology, forced libration in longitude can provide a considerable and even leading-and sometimes overwhelming-input in the tidal heating. Based on the observed parameters, this input amounts to 52% in Phobos, 33% in Mimas, 23% in Enceladus, and 96% in Epimetheus. This supports the hypothesis by Makarov and Efroimsky (2014) that the additional tidal damping due to forced libration may have participated in the early heating up of some of the large moons. As one possibility, such a moon could have been chipped by collisions-whereby it acquired a higher permanent triaxiality and, therefore, a higher forced-libration magnitude and, consequently, a higher heating rate. After the moon warms up, its permanent triaxiality decreases, and so does the tidal heating rate.

Convex Hull Aided Registration Method (CHARM).

PubMed

Fan, Jingfan; Yang, Jian; Zhao, Yitian; Ai, Danni; Liu, Yonghuai; Wang, Ge; Wang, Yongtian

2017-09-01

Non-rigid registration finds many applications such as photogrammetry, motion tracking, model retrieval, and object recognition. In this paper we propose a novel convex hull aided registration method (CHARM) to match two point sets subject to a non-rigid transformation. First, two convex hulls are extracted from the source and target respectively. Then, all points of the point sets are projected onto the reference plane through each triangular facet of the hulls. From these projections, invariant features are extracted and matched optimally. The matched feature point pairs are mapped back onto the triangular facets of the convex hulls to remove outliers that are outside any relevant triangular facet. The rigid transformation from the source to the target is robustly estimated by the random sample consensus (RANSAC) scheme through minimizing the distance between the matched feature point pairs. Finally, these feature points are utilized as the control points to achieve non-rigid deformation in the form of thin-plate spline of the entire source point set towards the target one. The experimental results based on both synthetic and real data show that the proposed algorithm outperforms several state-of-the-art ones with respect to sampling, rotational angle, and data noise. In addition, the proposed CHARM algorithm also shows higher computational efficiency compared to these methods.

Research in the Restricted Problems of Three and Four Bodies Final Scientific Report

NASA Technical Reports Server (NTRS)

Richards, Paul B.; Bernstein, Irwin S.; Chai, Winchung A.; Cronin, Jane; Ellis, Jordan; Fine, William E.; Kass, Sheldon; Musa, Samuel A.; Russell, Lawrence H.

1968-01-01

Seven studies have been conducted on research in the existence and nature of solutions of the restricted problems of three and four bodies. The details and results of five of these research investigations have already been published, and the latest two studies will be published shortly. A complete bibliography of publications is included in this report. This research has been primarily qualitative and has yielded new information on the behavior of trajectories near the libration points in the Earth-Moon-Sun and Sun-Jupiter-Saturn systems, and on the existence of periodic trajectories about the libration points of the circular and elliptical restricted four-body models. We have also implemented Birkhoff's normalization process for conservative and nonconservative Hamiltonian systems with equilibrium points. This makes available a technique for analyzing stability properties of certain nonlinear dynamical systems, and we have applied this technique to the circular and elliptical restricted three-body models. A related study was also conducted to determine the feasibility of using cislunar periodic trajectories for various space missions. Preliminary results suggest that this concept is attractive for space flight safety operations in cislunar space. Results of this research will be of interest to mathematicians, particularly those working in ordinary differential equations, dynamical systems and celestial mechanics; to astronomers; and to space guidance and mission analysts.

ON THE DYNAMICS AND TIDAL DISSIPATION RATE OF THE WHITE DWARF IN 4U 1820-30

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prodan, Snezana; Murray, Norman, E-mail: sprodan@cita.utoronto.ca

It has been suggested that the 170 day period in the light curve of the low-mass X-ray binary 4U 1820-30 arises from the presence of a third body with a large inclination to the binary orbit. We show that this long-period motion arises if the system is librating around the stable fixed point in a Kozai resonance. We demonstrate that mass transfer drives the system toward this fixed point and calculate, both analytically and via numerical integrations, that the period of libration is of order 170 days when the mutual inclination is near the Kozai critical value. The non-zero eccentricitymore » of the binary, combined with tidal dissipation, implies that the rate of change of the binary period would be slower than, or even of opposite sign to, that implied by standard mass transfer models. If the 170 day period results from libration, then, contrary to appearances, the orbital period of the inner binary is increasing with time; in that case, (e/0.009){sup 2} Q/k{sub 2} {approx}> 2.5 Multiplication-Sign 10{sup 9}, where k{sub 2} Almost-Equal-To 0.01 is the tidal Love number and e = 0.009 is the fiducial eccentricity of the inner binary. It appears unlikely that the observed negative period derivative results from the smaller than expected (but positive) value of P-dot combined with the previously suggested acceleration of the system in the gravitational field of the host globular cluster NGC 6624. The discrepancy between the observed and the expected period derivative requires further investigation.« less

Interpreting the librations of a synchronous satellite - How their phase assesses Mimas' global ocean

NASA Astrophysics Data System (ADS)

Noyelles, Benoît

2017-01-01

Most of the main planetary satellites of our Solar System are expected to be in synchronous rotation, the departures from the strict synchronicity being a signature of the interior. Librations have been measured for the Moon, Phobos, and some satellites of Saturn. I here revisit the theory of the longitudinal librations in considering that part of the interior is not hydrostatic, i.e. has not been shaped by the rotational and tidal deformations, but is fossil. This consideration affects the rotational behavior. For that, I derive the tensor of inertia of the satellite in splitting these two parts, before proposing an analytical solution that I validate with numerical simulations. I apply this new theory on Mimas and Epimetheus, for which librations have been measured from Cassini data. I show that the large measured libration amplitude of these bodies can be explained by an excess of triaxiality that would not result from the hydrostatic theory. This theory cannot explain the phase shift which has been measured in the diurnal librations of Mimas. This speaks against a solid structure for Mimas, i.e. Mimas could have a global internal ocean.

Modern studies of the Lunar Physical libration at the Kazan University

NASA Astrophysics Data System (ADS)

Petrova, Natalia; Hanada, Hideo; Nefedyev, Yuri; Gusev, Alexander

Main results in investigation of the lunar physical libration in the Kazan University are presented in the report. Modern problems in the lunar spin-dynamics are considered. The accent is done on the fine phenomena of the lunar libration caused by complicated interior structure. Parameters of a free libration are discussed; geometrical interpretation of the chandler-like and free core nutation is given. Over the past 10 years a creative cooperation has been formed between scientists of the Kazan University and the National Astronomical Observatory of Japan (Mizusava). The project ILOM (In situ Lunar Orientation Measurement), planned in the frame of SELENE-2 or -3 missions is aimed at monitoring the physical libration of the Moon. The Russian side has taken over some of the theoretical tasks to ensure the planned observations. One of the important elements of the project is placing of a small optical telescope on the lunar surface with the purpose to detect the lunar physical libration with millisecond accuracy. Computer simulation of the future observations is being done with the purpose of their optimization: effective placement of measuring system on the lunar surface, testing of sensitivity of new observations to various features of the lunar interior structure. The results of the first stage of the simulation are presented in the paper. At this stage the software for the selection of stars and reduction of their coordinates onto the period of observations is developed, the tracks for the selected stars are constructed and analyzed, their sensitivity to the internal characteristics of the lunar body, in the first place, to the selenopotential coefficients, is tested. Inverse problem of lunar physical libration is formulated and solved. It is shown that selenographic coordinates of polar stars are insensitive to longitudinal librations tau(t). Comparing coordinates calculated for two models of a rigid and deformable Moon is carried out and components sensitive to Love number k _{2} are revealed. Analytical theory of physical libration was very convenient tool for modeling the upcoming observations. The main outcome of this collaboration was the understanding of the strategy and tactics of building an improved analytical theory of physical libration. This work was supported by RFBR grant No. 13-02-00792.

Impulsive time-free transfers between halo orbits

NASA Astrophysics Data System (ADS)

Hiday, L. A.; Howell, K. C.

1992-08-01

A methodology is developed to design optimal time-free impulsive transfers between three-dimensional halo orbits in the vicinity of the interior L1 libration point of the sun-earth/moon barycenter system. The transfer trajectories are optimal in the sense that the total characteristics velocity required to implement the transfer exhibits a local minimum. Criteria are established whereby the implementation of a coast in the initial orbit, a coast in the final orbit, or dual coasts accomplishes a reduction in fuel expenditure. The optimality of a reference two-impulse transfer can be determined by examining the slope at the endpoints of a plot of the magnitude of the primer vector on the reference trajectory. If the initial and final slopes of the primer magnitude are zero, the transfer trajectory is optimal; otherwise, the execution of coasts is warranted. The optimal time of flight on the time-free transfer, and consequently, the departure and arrival locations on the halo orbits are determined by the unconstrained minimization of a function of two variables using a multivariable search technique. Results indicate that the cost can be substantially diminished by the allowance for coasts in the initial and final libration-point orbits.

Impulsive Time-Free Transfers Between Halo Orbits

NASA Astrophysics Data System (ADS)

Hiday-Johnston, L. A.; Howell, K. C.

1996-12-01

A methodology is developed to design optimal time-free impulsive transfers between three-dimensional halo orbits in the vicinity of the interior L 1 libration point of the Sun-Earth/Moon barycenter system. The transfer trajectories are optimal in the sense that the total characteristic velocity required to implement the transfer exhibits a local minimum. Criteria are established whereby the implementation of a coast in the initial orbit, a coast in the final orbit, or dual coasts accomplishes a reduction in fuel expenditure. The optimality of a reference two-impulse transfer can be determined by examining the slope at the endpoints of a plot of the magnitude of the primer vector on the reference trajectory. If the initial and final slopes of the primer magnitude are zero, the transfer trajectory is optimal; otherwise, the execution of coasts is warranted. The optimal time of flight on the time-free transfer, and consequently, the departure and arrival locations on the halo orbits are determined by the unconstrained minimization of a function of two variables using a multivariable search technique. Results indicate that the cost can be substantially diminished by the allowance for coasts in the initial and final libration-point orbits.

Design of a Lunar Farside Observatory

NASA Technical Reports Server (NTRS)

1989-01-01

The design of a mantendable lunar farside observatory and science base is presented. A farside observatory will allow high accuracy astronomical observations, as well as the opportunity to perform geological and low gravity studies on the Moon. The requirements of the observatory and its support facilities are determined, and a preliminary timeline for the project development is presented. The primary areas of investigation include observatory equipment, communications, habitation, and surface operations. Each area was investigated to determine the available options, and each option was evaluated to determine the advantages and disadvantages. The options selected for incorporation into the design of the farside base are presented. The observatory equipment deemed most suitable for placement on the lunar farside consist of large optical and radio arrays and seismic equipment. A communications system consisting of a temporary satellite about the L sub 2 libration point and followed by a satellite at the stable L sub 5 libration point was selected. A space station common module was found to be the most practical option for housing the astronauts at the base. Finally, a support system based upon robotic construction vehicles and the use of lunar materials was determined to be a necessary component of the base.

Far-infrared VRT spectroscopy of the water dimer: Characterization of the 20 μm out-of-plane librational vibration.

PubMed

Cole, William T S; Fellers, Ray S; Viant, Mark R; Leforestier, Claude; Saykally, Richard J

2015-10-21

We report the first high-resolution spectra for the out-of-plane librational vibration in the water dimer. Three vibrational subbands comprising a total of 188 transitions have been measured by diode laser spectroscopy near 500 cm(-1) and assigned to (H2O)2 libration-rotation-tunneling eigenstates. The band origin for the Ka = 1 subband is ~524 cm(-1). Librational excitation increases the interchange and bifurcation hydrogen bond rearrangement tunneling splittings by factors of 3-5 and 4-40, respectively. Analysis of the rotational constants obtained from a nonlinear least squares fit indicates that additional external perturbations to the energy levels are likely.

Far-infrared VRT spectroscopy of the water dimer: Characterization of the 20 μm out-of-plane librational vibration

NASA Astrophysics Data System (ADS)

Cole, William T. S.; Fellers, Ray S.; Viant, Mark R.; Leforestier, Claude; Saykally, Richard J.

2015-10-01

We report the first high-resolution spectra for the out-of-plane librational vibration in the water dimer. Three vibrational subbands comprising a total of 188 transitions have been measured by diode laser spectroscopy near 500 cm-1 and assigned to (H2O)2 libration-rotation-tunneling eigenstates. The band origin for the Ka = 1 subband is ˜524 cm-1. Librational excitation increases the interchange and bifurcation hydrogen bond rearrangement tunneling splittings by factors of 3-5 and 4-40, respectively. Analysis of the rotational constants obtained from a nonlinear least squares fit indicates that additional external perturbations to the energy levels are likely.

Librations and tides of icy satellites: model comparison for Enceladus

NASA Astrophysics Data System (ADS)

Trinh, A.; Van Hoolst, T.; Baland, R. M.; Beuthe, M.; Rivoldini, A.; Dehant, V. M. A.

2015-12-01

The latest measurements of the librations of Enceladus suggest that it could have a global subsurface ocean or a non-hydrostatic core (Thomas et al. 2014). Further observations should constrain the properties of the ice shell, and similar insights are expected from future investigation of Europa and Ganymede.Detailed models of the librations and tides are therefore required to properly interpret these measurements in terms of interior structure. Here we compare the `classical', separate tide and libration models (where spherical symmetry is assumed to compute the tides, Van Hoolst et al. 2013) with our combined tide+libration model (Trinh et al. 2013), both extended to account for non-hydrostatic structure.Even with a global ocean, different mechanisms act to prevent Enceladus's shell from moving independently from the rest. Among those, pressure coupling across the flattened boundaries of the ocean requires special care if the shape is not fully relaxed. We discuss how it should be modelled in the classical approach to be consistent with the combined model.

Simulating parameters of lunar physical libration on the basis of its analytical theory

NASA Astrophysics Data System (ADS)

Petrova, N.; Zagidullin, A.; Nefediev, Yu.

2014-04-01

Results of simulating behavior of lunar physical libration parameters are presented. Some features in the speed change of impulse variables are revealed: fast periodic changes in р2 and long periodic changes in р3. A problem of searching for a dynamic explanation of this phenomenon is put. The simulation was performed on the basis of the analytical libration theory [1] in the programming environment VBA.

Experimental study of inertial waves in a spherical shell induced by librations of the inner sphere

NASA Astrophysics Data System (ADS)

Hoff, Michael; Harlander, Uwe; Jahangir, Saad; Egbers, Christoph

2015-04-01

Many planetary bodies do not rotate with a constant velocity but undergo rotations with superposed oscillations called longitudinal librations. This is the case e.g. for the Earth's moon, Mars' moon, Mercury and many other moons of Jupiter and Saturn and some of them have a solid inner core and a molten outer core. It is worth to know the interaction between the libration of the core and the interior of the fluid to understand tidal heating, fluid mixing, and the generation of magnetic fields. Here we present an experimental investigation of inertial waves in a spherical shell. The shell rotates with a mean angular velocity Ω around its vertical axis overlaid by a time periodic oscillation of the inner sphere in the range 0 < ω < 2Ω, in order to excite inertial waves with a known frequency. We want to show the influence of the libration amplitude ɛ on different libration frequencies ω and how efficient libration is, to excite inertial waves in the given frequency range. For low ω and high ɛ instability starts to grow and, beside the excited inertial waves, several low frequency structures can be found. Quantitative PIV analyses of the horizontal plane in the co-rotation frame show clear spiral structures with different wave numbers for high libration amplitudes due to strong shear, similar to differential rotation. Another question, we like to address, is whether high libration amplitudes can also excite very low frequency Rossby wave structures? If the frequency increases, it can be seen from Poincaré plots that large attractor windows for inertial waves appear. We want to show PIV analyses for such flows dominated by wave attractors. It is known that for large excitation frequencies subharmonic parametric instability starts to grow and triads will be excited. Our experimental data show hints for the existence of triads and preliminary results will be discussed.

Fuel-optimal, low-thrust transfers between libration point orbits

NASA Astrophysics Data System (ADS)

Stuart, Jeffrey R.

Mission design requires the efficient management of spacecraft fuel to reduce mission cost, increase payload mass, and extend mission life. High efficiency, low-thrust propulsion devices potentially offer significant propellant reductions. Periodic orbits that exist in a multi-body regime and low-thrust transfers between these orbits can be applied in many potential mission scenarios, including scientific observation and communications missions as well as cargo transport. In light of the recent discovery of water ice in lunar craters, libration point orbits that support human missions within the Earth-Moon region are of particular interest. This investigation considers orbit transfer trajectories generated by a variable specific impulse, low-thrust engine with a primer-vector-based, fuel-optimizing transfer strategy. A multiple shooting procedure with analytical gradients yields rapid solutions and serves as the basis for an investigation into the trade space between flight time and consumption of fuel mass. Path and performance constraints can be included at node points along any thrust arc. Integration of invariant manifolds into the design strategy may also yield improved performance and greater fuel savings. The resultant transfers offer insight into the performance of the variable specific impulse engine and suggest novel implementations of conventional impulsive thrusters. Transfers incorporating invariant manifolds demonstrate the fuel savings and expand the mission design capabilities that are gained by exploiting system symmetry. A number of design applications are generated.

Far-infrared VRT spectroscopy of the water dimer: Characterization of the 20 μm out-of-plane librational vibration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cole, William T. S.; Fellers, Ray S.; Viant, Mark R.

We report the first high-resolution spectra for the out-of-plane librational vibration in the water dimer. Three vibrational subbands comprising a total of 188 transitions have been measured by diode laser spectroscopy near 500 cm{sup −1} and assigned to (H{sub 2}O){sub 2} libration-rotation-tunneling eigenstates. The band origin for the K{sub a} = 1 subband is ~524 cm{sup −1}. Librational excitation increases the interchange and bifurcation hydrogen bond rearrangement tunneling splittings by factors of 3-5 and 4-40, respectively. Analysis of the rotational constants obtained from a nonlinear least squares fit indicates that additional external perturbations to the energy levels are likely.

Prospects for tracking spacecrafts within 2 million Km of Earth with phased array antennas

NASA Technical Reports Server (NTRS)

Amoozegar, F.; Jamnejad, V.; Cesarone, R.

2003-01-01

Recent advances in space technology for Earth observations, global communications, and positioning systems have created heavy traffic at a variety of orbits. These include smart sensors in low Earth orbits (LEO), internet satellites in LEO and GEO orbits, Earth observing satellites in high Earth orbits (HEO), observatory class satellites at Lagrangian libration points, and those heading for deep space.

Optimal transfers between libration-point orbits in the elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Hiday, Lisa Ann

1992-09-01

A strategy is formulated to design optimal impulsive transfers between three-dimensional libration-point orbits in the vicinity of the interior L(1) libration point of the Sun-Earth/Moon barycenter system. Two methods of constructing nominal transfers, for which the fuel cost is to be minimized, are developed; both inferior and superior transfers between two halo orbits are considered. The necessary conditions for an optimal transfer trajectory are stated in terms of the primer vector. The adjoint equation relating reference and perturbed trajectories in this formulation of the elliptic restricted three-body problem is shown to be distinctly different from that obtained in the analysis of trajectories in the two-body problem. Criteria are established whereby the cost on a nominal transfer can be improved by the addition of an interior impulse or by the implementation of coastal arcs in the initial and final orbits. The necessary conditions for the local optimality of a time-fixed transfer trajectory possessing additional impulses are satisfied by requiring continuity of the Hamiltonian and the derivative of the primer vector at all interior impulses. The optimality of a time-free transfer containing coastal arcs is surmised by examination of the slopes at the endpoints of a plot of the magnitude of the primer vector over the duration of the transfer path. If the initial and final slopes of the primer magnitude are zero, the transfer trajectory is optimal; otherwise, the execution of coasts is warranted. The position and timing of each interior impulse applied to a time-fixed transfer as well as the direction and length of coastal periods implemented on a time-free transfer are specified by the unconstrained minimization of the appropriate variation in cost utilizing a multivariable search technique. Although optimal solutions in some instances are elusive, the time-fixed and time-free optimization algorithms prove to be very successful in diminishing costs on nominal transfer trajectories. The inclusion of coastal arcs on time-free superior and inferior transfers results in significant modification of the transfer time of flight caused by shifts in departure and arrival locations on the halo orbits.

Mission Architecture Comparison for Human Lunar Exploration

NASA Technical Reports Server (NTRS)

Geffre, Jim; Robertson, Ed; Lenius, Jon

2006-01-01

The Vision for Space Exploration outlines a bold new national space exploration policy that holds as one of its primary objectives the extension of human presence outward into the Solar System, starting with a return to the Moon in preparation for the future exploration of Mars and beyond. The National Aeronautics and Space Administration is currently engaged in several preliminary analysis efforts in order to develop the requirements necessary for implementing this objective in a manner that is both sustainable and affordable. Such analyses investigate various operational concepts, or mission architectures , by which humans can best travel to the lunar surface, live and work there for increasing lengths of time, and then return to Earth. This paper reports on a trade study conducted in support of NASA s Exploration Systems Mission Directorate investigating the relative merits of three alternative lunar mission architecture strategies. The three architectures use for reference a lunar exploration campaign consisting of multiple 90-day expeditions to the Moon s polar regions, a strategy which was selected for its high perceived scientific and operational value. The first architecture discussed incorporates the lunar orbit rendezvous approach employed by the Apollo lunar exploration program. This concept has been adapted from Apollo to meet the particular demands of a long-stay polar exploration campaign while assuring the safe return of crew to Earth. Lunar orbit rendezvous is also used as the baseline against which the other alternate concepts are measured. The first such alternative, libration point rendezvous, utilizes the unique characteristics of the cislunar libration point instead of a low altitude lunar parking orbit as a rendezvous and staging node. Finally, a mission strategy which does not incorporate rendezvous after the crew ascends from the Moon is also studied. In this mission strategy, the crew returns directly to Earth from the lunar surface, and is thus referred to as direct return. Figures of merit in the areas of safety and mission success, mission effectiveness, extensibility, and affordability are used to evaluate and compare the lunar orbit rendezvous, libration point rendezvous, and direct return architectures, and this paper summarizes the results of those assessments.

Locally optimal transfer trajectories between libration point orbits using invariant manifolds

NASA Astrophysics Data System (ADS)

Davis, Kathryn E.

2009-12-01

Techniques from dynamical systems theory and primer vector theory have been applied to the construction of locally optimal transfer trajectories between libration point orbits. When two libration point orbits have different energies, it has been found that the unstable manifold of the first orbit can be connected to the stable manifold of the second orbit with a bridging trajectory. A bounding sphere centered on the secondary, with a radius less than the radius of the sphere of influence of the secondary, was used to study the stable and unstable manifold trajectories. It was numerically demonstrated that within the bounding sphere, the two-body parameters of the unstable and stable manifold trajectories could be analyzed to locate low transfer costs. It was shown that as the two-body parameters of an unstable manifold trajectory more closely matched the two-body parameters of a stable manifold trajectory, the total DeltaV necessary to complete the transfer decreased. Primer vector theory was successfully applied to a transfer to determine the optimal maneuvers required to create the bridging trajectory that connected the unstable manifold of the first orbit to the stable manifold of the second orbit. Transfer trajectories were constructed between halo orbits in the Sun-Earth and Earth-Moon three-body systems. Multiple solutions were found between the same initial and final orbits, where certain solutions retraced interior portions of the trajectory. All of the trajectories created satisfied the conditions for optimality. The costs of transfers constructed using invariant manifolds were compared to the costs of transfers constructed without the use of invariant manifolds, when data was available. In all cases, the total cost of the transfers were significantly lower when invariant manifolds were used in the transfer construction. In many cases, the transfers that employed invariant manifolds were three to four times more efficient, in terms of fuel expenditure, than the transfer that did not. The decrease in transfer cost was accompanied by an increase in transfer time of flight. Transfers constructed in the Earth-Moon system were shown to be particularly viable for lunar navigation and communication constellations, as excellent coverage of the lunar surface can be achieved during the transfer.

The Future of Human Exploration

NASA Technical Reports Server (NTRS)

Cooke, Doug

2001-01-01

This slide presentation reviews the near term future of human space exploration in terms of possible mission scenarios, propulsion technologies, orbital dynamics that lead to Low-Energy Transfer from Earth-Moon LI to Solar Libration Points and Return Potential Staging Point for Human Mars Missions. It also examines the required evolution of mission architecture, solar electric propulsion concept, vehicle concepts for future Mars missions, and an overview of a Mars Mission, Also in this presentation are pictures of several historic personages and occasions, and a view of a Mars Meteorite (i.e., ALH84001.0)

Three Dimensional Orbital Stability About the Earth-Moon Equilateral Libration Points.

DTIC Science & Technology

1980-12-01

need to be rotated to the ecliptic . If e is the obliquity of the ecliptic , then the transformation matrix for this is: t F e, ’ C]u 11E -12 IF I) I...the use of the above transformation matrix. The frame for the analysis of the problem will be an Earth-centered ecliptic nonrotating rectangular system...The X-axis will point toward the vernal equinox and the Z-axis will be perpendicular to the ecliptic having the XY-plane coincident with the ecliptic

The lunar libration: comparisons between various models - a model fitted to LLR observations

NASA Astrophysics Data System (ADS)

Chapront, J.; Francou, G.

2005-09-01

We consider 4 libration models: 3 numerical models built by JPL (ephemerides for the libration in DE245, DE403 and DE405) and an analytical model improved with numerical complements fitted to recent LLR observations. The analytical solution uses 3 angular variables (ρ1, ρ2, τ) which represent the deviations with respect to Cassini's laws. After having referred the models to a unique reference frame, we study the differences between the models which depend on gravitational and tidal parameters of the Moon, as well as amplitudes and frequencies of the free librations. It appears that the differences vary widely depending of the above quantities. They correspond to a few meters displacement on the lunar surface, reminding that LLR distances are precise to the centimeter level. Taking advantage of the lunar libration theory built by Moons (1984) and improved by Chapront et al. (1999) we are able to establish 4 solutions and to represent their differences by Fourier series after a numerical substitution of the gravitational constants and free libration parameters. The results are confirmed by frequency analyses performed separately. Using DE245 as a basic reference ephemeris, we approximate the differences between the analytical and numerical models with Poisson series. The analytical solution - improved with numerical complements under the form of Poisson series - is valid over several centuries with an internal precision better than 5 centimeters.

Inertial Waves and Steady Flows in a Liquid Filled Librating Cylinder

NASA Astrophysics Data System (ADS)

Subbotin, Stanislav; Dyakova, Veronika

2018-05-01

The fluid flow in a non-uniformly rotating (librating) cylinder about a horizontal axis is experimentally studied. In the absence of librations the fluid performs a solid-body rotation together with the cavity. Librations lead to the appearance of steady zonal flow in the whole cylinder and the intensive steady toroidal flows near the cavity corners. If the frequency of librations is twice lower than the mean rotation rate the inertial waves are excited. The oscillating motion associated with the propagation of inertial wave in the fluid bulk leads to the appearance of an additional steady flow in the Stokes boundary layers on the cavity side wall. In this case the heavy particles of the visualizer are assembled on the side wall into ring structures. The patterns are determined by the structure of steady flow, which in turn depends on the number of reflections of inertial wave beams from the cavity side wall. For some frequencies, inertial waves experience spatial resonance, resulting in inertial modes, which are eigenmodes of the cavity geometry. The resonance of the inertial modes modifies the steady flow structure close to the boundary layer that is manifested in the direct rebuilding of patterns. It is shown that the intensity of zonal flow, as well as the intensity of steady flows excited by inertial waves, is proportional to the square of the amplitude of librations.

Low-temperature matrix effects on orientational motion of Methyl radical trapped in gas solids: Angular tunneling vs. libration

NASA Astrophysics Data System (ADS)

Dmitriev, Yurij A.; Zelenetckii, Ilia A.; Benetis, Nikolas P.

2018-05-01

EPR investigation of the lineshape of matrix -isolated methyl radical, CH3, spectra recorded in solid N2O and CO2 was carried out. Reversible temperature-dependent line width anisotropy was observed in both matrices. This effect is a fingerprint of the extra-slow radical rotation about the in-plane C2 axes. The rotation was found to be anisotropic and closely correlated to the orientational dynamics of the matrix molecules. It was suggested that a recently discovered "hoping precession" effect of matrix molecules in solid CO2 is a common feature of matrices of the linear molecules CO, N2O, and CO2. A new low-temperature matrix effect, referred to as "libration trap", was proposed which accounts for the changing CH3 reorientational motion about the radical C3-axis from rotation to libration. Temperature dependence of the intensity of the EPR satellites produced by these nonrotating-but librating methyls was presented. This allowed for a rough estimation of the rotation hindering potential due to correlation mismatch between the radical and the nearest matrix molecules' librations.

Phobos' gravity field and its influence on its orbit and physical librations

NASA Technical Reports Server (NTRS)

Borderies, N.; Yoder, C. F.

1990-01-01

A model describing the physical libration in longitude and latitude for Phobos is derived. The major effect is the well-known longitude variation with the anomalistic orbital period and amplitude. Several additional meter-sized periodic librations in longitude exist. The latitude variation is dominated by the forced precession of Phobos' figure axis with the precession of Phobos' orbital plane. The contribution of Phobos' topography to its gravity field is estimated using the control network model of Duxbury and Callahan (1989).

Dynamics of the retrograde 1/1 mean motion resonance

NASA Astrophysics Data System (ADS)

Huang, Yukun; Li, Miao; Li, Junfeng; Gong, Shengping

2018-04-01

Mean motion resonances are very common in the solar system. Asteroids in mean motion resonances with giant planets have been studied for centuries. But it was not until recently that asteroids in retrograde mean motion resonances with Jupiter and Saturn were discovered. The newly discovered asteroid, 2015 BZ509 is confirmed to be the first asteroid in retrograde 1:1 mean motion resonance (or retrograde co-orbital resonance) with Jupiter, which gives rise to our interests in its unique resonant dynamics. In this study, we thoroughly investigate the phase-space structure of the retrograde 1:1 resonance within the framework of the circular restricted three-body problem. We begin by constructing a simple integrable approximation for the planar retrograde resonance with the Hamiltonian approach and show that the variables definition of the retrograde resonance is very different to the prograde one. When it comes to the disturbing function, we abandon the classical series expansion approach, whereas numerically carry out the averaging process on the disturbing function in closed form. The phase portrait of the retrograde 1:1 resonance is depicted with the level curves of the averaged Hamiltonian. We find that the topological structure of phase space for the retrograde 1:1 resonance is very different to other resonances, due to the consistent existence of the collision separatrix. And the surprising bifurcation of equilibrium point around 180° (i.e., the apocentric libration center) has never been found in any other mean motion resonances before. We thoroughly analyze the novel apocentric librations and find that close encounter with the planet does not always lead to the disruption of a stable apocentric libration. Afterwards, we examine the Kozai dynamics inside the mean motion resonance with the similar Hamiltonian approach and explain why the exact resonant point does not exist in the 3D retrograde 1:1 resonance model.

Effectiveness of Rotation-free Triangular and Quadrilateral Shell Elements in Sheet-metal Forming Simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brunet, M.; Sabourin, F.

2005-08-05

This paper is concerned with the effectiveness of triangular 3-node shell element without rotational d.o.f. and the extension to a new 4-node quadrilateral shell element called S4 with only 3 translational degrees of freedom per node and one-point integration. The curvatures are computed resorting to the surrounding elements. Extension from rotation-free triangular element to a quadrilateral element requires internal curvatures in order to avoid singular bending stiffness. Two numerical examples with regular and irregular meshes are performed to show the convergence and accuracy. Deep-drawing of a box, spring-back analysis of a U-shape strip sheet and the crash simulation of amore » beam-box complete the demonstration of the bending capabilities of the proposed rotation-free triangular and quadrilateral elements.« less

Applying Strategic Visualization(Registered Trademark) to Lunar and Planetary Mission Design

NASA Technical Reports Server (NTRS)

Frassanito, John R.; Cooke, D. R.

2002-01-01

NASA teams, such as the NASA Exploration Team (NEXT), utilize advanced computational visualization processes to develop mission designs and architectures for lunar and planetary missions. One such process, Strategic Visualization (trademark), is a tool used extensively to help mission designers visualize various design alternatives and present them to other participants of their team. The participants, which may include NASA, industry, and the academic community, are distributed within a virtual network. Consequently, computer animation and other digital techniques provide an efficient means to communicate top-level technical information among team members. Today,Strategic Visualization(trademark) is used extensively both in the mission design process within the technical community, and to communicate the value of space exploration to the general public. Movies and digital images have been generated and shown on nationally broadcast television and the Internet, as well as in magazines and digital media. In our presentation will show excerpts of a computer-generated animation depicting the reference Earth/Moon L1 Libration Point Gateway architecture. The Gateway serves as a staging corridor for human expeditions to the lunar poles and other surface locations. Also shown are crew transfer systems and current reference lunar excursion vehicles as well as the Human and robotic construction of an inflatable telescope array for deployment to the Sun/Earth Libration Point.

Hydrogen bond breaking dynamics in the water pentamer: Terahertz VRT spectroscopy of a 20 μm libration

NASA Astrophysics Data System (ADS)

Cole, William T. S.; Fellers, Raymond S.; Viant, Mark R.; Saykally, Richard J.

2017-01-01

Hydrogen bonds in solid and liquid water are formed and broken via librational vibrations, hence characterizing the details of these motions is vital to understanding these important dynamics. Here we report the measurement and assignment of 875 transitions comprising 6 subbands originating from out-of-plane librational transitions of the water pentamer-d10 near 512 cm-1. The precisely measured (ca. 1 ppm) transitions reveal bifurcation splittings of ˜1884 MHz, a ˜4000× enhancement over ground state splittings and 100× greater than predicted by theory. The pentamer is thus the third water cluster to display greatly enhanced bifurcation tunneling upon single quantum excitation of librational vibrations. From the intensity pattern of the observed transitions, the mechanism of bifurcation is established by comparison with theoretical predictions.

Hydrogen bond breaking dynamics in the water pentamer: Terahertz VRT spectroscopy of a 20 μm libration.

PubMed

Cole, William T S; Fellers, Raymond S; Viant, Mark R; Saykally, Richard J

2017-01-07

Hydrogen bonds in solid and liquid water are formed and broken via librational vibrations, hence characterizing the details of these motions is vital to understanding these important dynamics. Here we report the measurement and assignment of 875 transitions comprising 6 subbands originating from out-of-plane librational transitions of the water pentamer-d 10 near 512 cm -1 . The precisely measured (ca. 1 ppm) transitions reveal bifurcation splittings of ∼1884 MHz, a ∼4000× enhancement over ground state splittings and 100× greater than predicted by theory. The pentamer is thus the third water cluster to display greatly enhanced bifurcation tunneling upon single quantum excitation of librational vibrations. From the intensity pattern of the observed transitions, the mechanism of bifurcation is established by comparison with theoretical predictions.

On the intermolecular vibrational coupling, hydrogen bonding, and librational freedom of water in the hydration shell of mono- and bivalent anions.

PubMed

Ahmed, Mohammed; Namboodiri, V; Singh, Ajay K; Mondal, Jahur A

2014-10-28

The hydration energy of an ion largely resides within the first few layers of water molecules in its hydration shell. Hence, it is important to understand the transformation of water properties, such as hydrogen-bonding, intermolecular vibrational coupling, and librational freedom in the hydration shell of ions. We investigated these properties in the hydration shell of mono- (Cl(-) and I(-)) and bivalent (SO4(2-) and CO3(2-)) anions by using Raman multivariate curve resolution (Raman-MCR) spectroscopy in the OH stretch, HOH bend, and [bend+librational] combination bands of water. Raman-MCR of aqueous Na-salt (NaCl, NaI, Na2SO4, and Na2CO3) solutions provides ion-correlated spectra (IC-spectrum) which predominantly bear the vibrational characteristics of water in the hydration shell of respective anions. Comparison of these IC-spectra with the Raman spectrum of bulk water in different spectral regions reveals that the water is vibrationally decoupled with its neighbors in the hydration shell. Hydrogen-bond strength and librational freedom also vary with the nature of anion: hydrogen-bond strength, for example, decreases as CO3(2-) > SO4(2-) > bulk water ≈ Cl(-) > I(-); and the librational freedom increases as CO3(2-) ≈ SO4(2-) < bulk water < Cl(-) < I(-). It is believed that these structural perturbations influence the dynamics of coherent energy transfer and librational reorientation of water in the hydration shell of anions.

Libration-driven flows in ellipsoidal shells

NASA Astrophysics Data System (ADS)

Lemasquerier, D.; Grannan, A. M.; Vidal, J.; Cébron, D.; Favier, B.; Le Bars, M.; Aurnou, J. M.

2017-09-01

Planets and satellites can undergo physical librations, which consist of forced periodic variations in their rotation rate induced by gravitational interactions with nearby bodies. This mechanical forcing may drive turbulence in interior fluid layers such as subsurface oceans and metallic liquid cores through a libration-driven elliptical instability (LDEI) that refers to the resonance of two inertial modes with the libration-induced base flow. LDEI has been studied in the case of a full ellipsoid. Here we address for the first time the question of the persistence of LDEI in the more geophysically relevant ellipsoidal shell geometries. In the experimental setup, an ellipsoidal container with spherical inner cores of different sizes is filled with water. Direct side view flow visualizations are made in the librating frame using Kalliroscope particles. A Fourier analysis of the light intensity fluctuations extracted from recorded movies shows that the presence of an inner core leads to spatial heterogeneities but does not prevent LDEI. Particle image velocimetry and direct numerical simulations are performed on selected cases to confirm our results. Additionally, our survey at a fixed forcing frequency and variable rotation period (i.e., variable Ekman number, E) shows that the libration amplitude at the instability threshold varies as ˜E0.65. This scaling is explained by a competition between surface and bulk dissipation. When extrapolating to planetary interior conditions, this leads to the E1/2 scaling commonly considered. We argue that Enceladus' subsurface ocean and the core of the exoplanet 55 CnC e should both be unstable to LDEI.

Dynamics of Multibody Systems Near Lagrangian Points

NASA Astrophysics Data System (ADS)

Wong, Brian

This thesis examines the dynamics of a physically connected multi-spacecraft system in the vicinity of the Lagrangian points of a Circular Restricted Three-Body System. The spacecraft system is arranged in a wheel-spoke configuration with smaller and less massive satellites connected to a central hub using truss/beams or tether connectors. The kinematics of the system is first defined, and the kinetic, gravitational potential energy and elastic potential energy of the system are derived. The Assumed Modes Method is used to discretize the continuous variables of the system, and a general set of ordinary differential equations describing the dynamics of the connectors and the central hub are obtained using the Lagrangian method. The flexible body dynamics of the tethered and truss connected systems are examined using numerical simulations. The results show that these systems experienced only small elastic deflections when they are naturally librating or rotating at moderate angular velocities, and these deflections have relatively small effect on the attitude dynamics of the systems. Based on these results, it is determined that the connectors can be modeled as rigid when only the attitude dynamics of the system is of interest. The equations of motion of rigid satellites stationed at the Lagrangian points are linearized, and the stability conditions of the satellite are obtained from the linear equations. The required conditions are shown to be similar to those of geocentric satellites. Study of the linear equations also revealed the resonant conditions of rigid Lagrangian point satellites, when a librational natural frequency of the satellite matches the frequency of its station-keeping orbit leading to large attitude motions. For tethered satellites, the linear analysis shows that the tethers are in stable equilibrium when they lie along a line joining the two primary celestial bodies of the Three-Body System. Numerical simulations are used to study the long term dynamics of two sample rigid bodies when they are in different periodic orbits around a collinear point, and the tether librations of a two-tether system in the same orbits. The results show that the rigid satellites and the tethered system experience greater attitude motions when they are in larger periodic orbits. The dynamics of variable length systems are also studied in order to determine the control cost associated with moving the end bodies in a gapless spiral to cover the area spanned by the system. The control cost is relatively low during tether deployment, and negligible effort is required to maintain the angular velocity of the tethered system after deployment. A set of recommendations for the applications of Lagrangian-point physically-connected systems are presented as well as some future research directions are suggested.

Prospects For Earth-Based Measurements Of Europa's Librations

NASA Astrophysics Data System (ADS)

Margot, Jean-Luc; Campbell, D. B.; Peale, S. J.

2010-10-01

The exploration of Europa is of great interest because it may be hospitable to certain life forms [1]. Several lines of evidence suggest that a subsurface ocean exists beneath an icy shell [2,3], but there is debate about the thickness of the shell [4], which impacts Europa's astrobiological potential. As in the case of Mercury, it may be possible to determine whether an outer shell is decoupled from the interior and to evaluate the shell thickness by measuring the amplitude of forced longitude librations [5,6]. In the simplest configuration of a rigid shell decoupled from a spherically symmetric interior, the libration amplitude is amplified from the nominal value of 18" by C/Cs, where C is the polar moment of inertia of the body and Cs is that of the outer shell that participates in the librations. For a 100-km thick shell, the libration amplitude would reach 200", an estimate that remains valid even in the presence of gravitational coupling between asymmetrical layers [7]. If there are significant departures from rigid behavior, the shell may deform with the ocean underneath and exhibit a libration amplitude of 52" [8]. Europa reaches closest approach in October 2011, offering a once-in-a-decade opportunity to measure spin rate variations by tracking radar speckles, as advocated by Holin [9,10]. Librations of a rigid shell thinner than 100 km would be detectable. We will describe the experimental design and expected sensitivity. References: [1] NRC, Europa Science Strategy, 1999. [2,3] Kivelson et al, Greeley et al, in Jupiter, CUP, 2004. [4] Greenberg, Unmasking Europa, Praxis, 2008. [5] Peale, Nature 262, 1976. [6] Margot et al, Science 316, 2007. [7] van Hoolst et al, Icarus 195, 2008. [8] Goldreich and Mitchell, Icarus, in press. [9] Green, in Radar Astronomy, McGraw-Hill, 1968. [10] Holin, Radiophys. Quant. Elec. 31, 1988.

The long-period librations of large synchronous icy moons

NASA Astrophysics Data System (ADS)

Yseboodt, Marie; Van Hoolst, Tim

2014-11-01

A moon in synchronous rotation has longitudinal librations because of its non-spherical mass distribution and its elliptical orbit around the planet. We study the long-period librations of the Galilean satellites and Titan and include deformation effects and the existence of a subsurface ocean. We take into account the fact that the orbit is not keplerian and has other periodicities than the main period of orbital motion around Jupiter or Saturn due to perturbations by the Sun, other planets and moons. An orbital theory is used to compute the orbital perturbations due to these other bodies. For Titan we also take into account the large atmospheric torque at the semi-annual period of Saturn around the Sun.We numerically evaluate the amplitude and phase of the long-period librations for many interior structure models of the icy moons constrained by the mass, radius and gravity field.

Far-infrared laser vibration-rotation-tunneling spectroscopy of water clusters in the librational band region of liquid water

NASA Astrophysics Data System (ADS)

Keutsch, Frank N.; Fellers, Ray S.; Viant, Mark R.; Saykally, Richard J.

2001-03-01

We report the first high resolution spectrum of a librational vibration for a water cluster. Four parallel bands of (H2O)3 were measured between 510 and 525 cm-1 using diode laser vibration-rotation-tunneling (VRT) spectroscopy. The bands lie in the "librational band" region of liquid water and are assigned to the nondegenerate out of plane librational vibration. The observation of at least three distinct bands within 8 cm-1 originating in the vibrational ground state is explained by a dramatically increased splitting of the rovibrational levels relative to the ground state by bifurcation tunneling and is indicative of a greatly reduced barrier height in the excited state. This tunneling motion is of special significance, as it is the lowest energy pathway for breaking and reforming of hydrogen bonds, a salient aspect of liquid water dynamics.

Solar wind parameters and magnetospheric coupling studies

NASA Technical Reports Server (NTRS)

King, Joseph H.

1986-01-01

This paper presents distributions, means, and standard deviations of the fluxes of solar wind protons, momentum, and energy as observed near earth during the solar quiet and active years 1976 and 1979. Distributions of ratios of energies (Alfven Mach number, plasma beta) and distributions of interplanetary magnetic field orientations are also given. Finally, the uncertainties associated with the use of the libration point orbiting ISEE-3 spacecraft as a solar wind monitor are discussed.

CARE AND FEEDING OF FROGS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Margaret; Chiang, Eugene, E-mail: mpan@astro.berkeley.edu

2012-01-15

'Propellers' are features in Saturn's A ring associated with moonlets that open partial gaps. They exhibit non-Keplerian motion (Tiscareno et al.); the longitude residuals of the best-observed propeller, 'Bleriot', appear consistent with a sinusoid of period {approx}4 years. Pan and Chiang proposed that propeller moonlets librate in 'frog resonances' with co-orbiting ring material. By analogy with the restricted three-body problem, they treated the co-orbital material as stationary in the rotating frame and neglected non-co-orbital material. Here we use simple numerical experiments to extend the frog model, including feedback due to the gap's motion, and drag associated with the Lindblad diskmore » torques that cause Type I migration. Because the moonlet creates the gap, we expect the gap centroid to track the moonlet, but only after a time delay t{sub delay}, the time for a ring particle to travel from conjunction with the moonlet to the end of the gap. We find that frog librations can persist only if t{sub delay} exceeds the frog libration period P{sub lib}, and if damping from Lindblad torques balances driving from co-orbital torques. If t{sub delay} << Pl{sub ib}, then the libration amplitude damps to zero. In the case of Bleriot, the frog resonance model can reproduce the observed libration period P{sub lib} {approx_equal} 4 yr. However, our simple feedback prescription suggests that Bleriot's t{sub delay} {approx} 0.01P{sub lib}, which is inconsistent with the observed libration amplitude of 260 km. We urge more accurate treatments of feedback to test the assumptions of our toy models.« less

Numerical-Diagonalization Study of Magnetization Process of Frustrated Spin-1/2 Heisenberg Antiferromagnets in Two Dimensions: —Triangular- and Kagome-Lattice Antiferromagnets—

NASA Astrophysics Data System (ADS)

Nakano, Hiroki; Sakai, Tôru

2018-06-01

The S = 1/2 triangular- and kagome-lattice Heisenberg antiferromagnets are investigated under a magnetic field using the numerical-diagonalization method. A procedure is proposed to extract data points with very small finite-size deviations using the numerical-diagonalization results for capturing the magnetization curve. For the triangular-lattice antiferromagnet, the plateau edges at one-third the height of the saturation and the saturation field are successfully estimated. This study additionally presents results of magnetization process for a 45-site cluster of the kagome-lattice antiferromagnet; the present analysis suggests that the plateau does not open at one-ninth the height of the saturation.

Libration and obliquity of Mercury from the BepiColombo radio science and camera experiments

NASA Astrophysics Data System (ADS)

Pfyffer, G.; van Hoolst, T.; Dehant, V.

2008-12-01

Mercury is the most enigmatic among the terrestrial planets, but the space missions MESSENGER and BepiColombo are expected to advance largely our knowledge of the structure, formation, and evolution of Mercury. In particular, insight into Mercury's deep interior will be obtained from observations of the 88-day forced libration, the obliquity and the degree-two coefficients of the gravity field of Mercury. Of those quantities, the libration is the most difficult to measure and will hence be a limiting factor We report here on aspects of the observational strategy to determine the libration amplitude and obliquity, taking into account the space and ground segment of the experiment. Repeated photographic measurements of selected target positions on the surface of Mercury are central to the strategy to determine the obliquity and libration in the frame of the BepiColombo mission. We simulated these measurements in order to estimate the accuracy of the reconstruction of the orientation and rotational motion of the planet, as a function of the amount of measurements made, the number of different targets considered and their locations on the surface of the planet. From this study, we determine criteria for the distribution and number of target positions to maximize the accuracy on the orientation and rotation determination, from which the obliquity and libration are extracted. We take into account the errors arising from the relative positions of the spacecraft, Mercury and the Earth. We consider various error sources such as the solar thermal influence on the spacecraft bus and the Earth based tracking constraint near solar conjunctions of Mercury. The accuracy on the retrieved parameters is then interpreted in terms of accuracy on the constraints on the interior structure of the planet. Our simulations show that the achievable level of accuracy on the libration amplitude and obliquity will be sufficient to constrain Mercury interior structure models, if the orbiter follows the ESA baseline mission scenario and at least 50 landmarks are imaged at least twice over the mission duration, the libration amplitude can be determined in two Mercury years (176 days) with an accuracy of 3 arcsec or better, which is sufficient to constrain the size and physical state of the planetary core.

Improved-resolution real-time skin-dose mapping for interventional fluoroscopic procedures

NASA Astrophysics Data System (ADS)

Rana, Vijay K.; Rudin, Stephen; Bednarek, Daniel R.

2014-03-01

We have developed a dose-tracking system (DTS) that provides a real-time display of the skin-dose distribution on a 3D patient graphic during fluoroscopic procedures. Radiation dose to individual points on the skin is calculated using exposure and geometry parameters from the digital bus on a Toshiba C-arm unit. To accurately define the distribution of dose, it is necessary to use a high-resolution patient graphic consisting of a large number of elements. In the original DTS version, the patient graphics were obtained from a library of population body scans which consisted of larger-sized triangular elements resulting in poor congruence between the graphic points and the x-ray beam boundary. To improve the resolution without impacting real-time performance, the number of calculations must be reduced and so we created software-designed human models and modified the DTS to read the graphic as a list of vertices of the triangular elements such that common vertices of adjacent triangles are listed once. Dose is calculated for each vertex point once instead of the number of times that a given vertex appears in multiple triangles. By reformatting the graphic file, we were able to subdivide the triangular elements by a factor of 64 times with an increase in the file size of only 1.3 times. This allows a much greater number of smaller triangular elements and improves resolution of the patient graphic without compromising the real-time performance of the DTS and also gives a smoother graphic display for better visualization of the dose distribution.

Topographic-driven instabilities in terrestrial bodies

NASA Astrophysics Data System (ADS)

Vantieghem, S.; Cebron, D.; Herreman, W.; Lacaze, L.

2013-12-01

Models of internal planetary fluid layers (core flows, subsurface oceans) commonly assume that these fluid envelopes have a spherical shape. This approximation however entails a serious restriction from the fluid dynamics point of view. Indeed, in the presence of mechanical forcings (precession, libration, nutation or tides) due to gravitational interaction with orbiting partners, boundary topography (e.g. of the core-mantle boundary) may excite flow instabilities and space-filling turbulence. These phenomena may affect heat transport and dissipation at the main order. Here, we focus on instabilities driven by longitudinal libration. Using a suite of theoretical tools and numerical simulations, we are able to discern a parameter range for which instability may be excited. We thereby consider deformations of different azimuthal order. This study gives the first numerical evidence of the tripolar instability. Furthermore, we explore the non-linear regime and investigate the amplitude as well as the dissipation of the saturated instability. Indeed, these two quantities control the torques on the solid layers and the thermal transport. Furthermore, based on this results, we address the issue of magnetic field generation associated with these flows (by induction or by dynamo process). This instability mechanism applies to both synchronized as non-synchronized bodies. As such, our results show that a tripolar instability might be present in various terrestrial bodies (Early Moon, Gallilean moons, asteroids, etc.), where it could participate in dynamo action. Simulation of a libration-driven tripolar instability in a deformed spherical fluid layer: snapshot of the velocity magnitude, where a complex 3D flow pattern is established.

Thersites: a `jumping' Trojan?

NASA Astrophysics Data System (ADS)

Tsiganis, K.; Dvorak, R.; Pilat-Lohinger, E.

2000-02-01

In this paper, we examine the dynamical evolution of the asteroid (1868) Thersites, a member of the Trojan belt. Thersites is librating around the Lagrangian point L_4, following, however, a chaotic orbit. The equations of motion for Thersites as well as for a distribution of neighboring initial conditions are integrated numerically for 50 million years in the Outer Solar System model (OSS), which consists of the Sun and the four giant planets. Our results indicate that the probability that this asteroid will eventually escape from the Trojan swarm is rather high. In fact, 20% from our initial distribution escaped within the integration time. Many of the remaining ones also show characteristic `jumps' in the orbital elements, especially the inclination. Secular resonances involving the nodes of the outer planets are found to be responsible for this chaotic behavior. The width of libration and eccentricity values that lead to grossly unstable orbits are calculated and compared with previously known results on the stability of the Trojans. Finally, a very interesting behavior has been observed for one of the escaping asteroids as he `jumped' from L_4 to L_5 where he remained performing a highly inclined libration for ~ 2 Myrs before escaping from the Trojan swarm. According to Homer, Thersites was not only the ugliest of all Greeks that took part in the Trojan war, but also had the most intolerable personality. His nasty habit of making fun of everybody cost him his life, as the last person for whom he spoke ironically about was Achilles, the mightiest warrior of all Greeks, who killed Thersites with just one punch!

Spacecraft transfer trajectory design exploiting resonant orbits in multi-body environments

NASA Astrophysics Data System (ADS)

Vaquero Escribano, Tatiana Mar

Historically, resonant orbits have been employed in mission design for multiple planetary flyby trajectories and, more recently, as a source of long-term orbital stability. For instance, in support of a mission concept in NASA's Outer Planets Program, the Jupiter Europa Orbiter spacecraft is designed to encounter two different resonances with Europa during the 'endgame' phase, leading to Europa orbit insertion on the final pass. In 2011, the Interstellar Boundary Explorer spacecraft was inserted into a stable out-of-plane lunar-resonant orbit, the first of this type for a spacecraft in a long-term Earth orbit. However, resonant orbits have not yet been significantly explored as transfer mechanisms between non-resonant orbits in multi-body systems. This research effort focuses on incorporating resonant orbits into the design process to potentially enable the construction of more efficient or even novel transfer scenarios. Thus, the goals in this investigation are twofold: i) to expand the orbit architecture in multi-body environments by cataloging families of resonant orbits, and ii) to assess the role of such families in the design of transfer trajectories with specific patterns and itineraries. The benefits and advantages of employing resonant orbits in the design process are demonstrated through a variety of astrodynamics applications in several multi-body systems. In the Earth-Moon system, locally optimal transfer trajectories from low Earth orbit to selected libration point orbits are designed by leveraging conic arcs and invariant manifolds associated with resonant orbits. Resonant manifolds in the Earth-Moon system offer trajectories that tour the entire space within reasonable time intervals, facilitating the design of libration point orbit tours as well as Earth-Moon cyclers. In the Saturnian system, natural transitions between resonant and libration point orbits are sought and the problem of accessing Hyperion from orbits that are resonant with Titan is also examined. To add versatility to the proposed design method, a system translation technique enables the straightforward transition of solutions from the Earth-Moon system to any Sun-planet or planet-moon three-body system. The circular restricted three-body problem serves as a basis to quickly generate solutions that meet specific requirements, but candidate transfer trajectories are then transitioned to an ephemeris model for validation.

Quadratic polynomial interpolation on triangular domain

NASA Astrophysics Data System (ADS)

Li, Ying; Zhang, Congcong; Yu, Qian

2018-04-01

In the simulation of natural terrain, the continuity of sample points are not in consonance with each other always, traditional interpolation methods often can't faithfully reflect the shape information which lie in data points. So, a new method for constructing the polynomial interpolation surface on triangular domain is proposed. Firstly, projected the spatial scattered data points onto a plane and then triangulated them; Secondly, A C1 continuous piecewise quadric polynomial patch was constructed on each vertex, all patches were required to be closed to the line-interpolation one as far as possible. Lastly, the unknown quantities were gotten by minimizing the object functions, and the boundary points were treated specially. The result surfaces preserve as many properties of data points as possible under conditions of satisfying certain accuracy and continuity requirements, not too convex meantime. New method is simple to compute and has a good local property, applicable to shape fitting of mines and exploratory wells and so on. The result of new surface is given in experiments.

The motion near L{sub 4} equilibrium point under non-point mass primaries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huda, I. N., E-mail: ibnu.nurul@students.itb.ac.id; Utama, J. A.; Madley, D.

2015-09-30

The Circular Restricted Three-Body Problem (CRTBP) possesses five equilibrium points, that comprise three collinear (L{sub 1}, L{sub 2}, and L{sub 3}) and two triangular points (L{sub 4} and L{sub 5}). The classical study (with the primaries are point mass) suggests that the equilibrium points may cause the velocity of infinitesimal object relatively becomes zero and reveals the zero velocity curve. We study the motion of infinitesimal object near triangular equilibrium point (L{sub 4}) and determine its zero velocity curve. We extend the study by taking into account the effects of radiation of the bigger primary (q{sub 1} ≠ 1, q{submore » 2} = 1) and oblateness of the smaller primary (A{sub 1} = 0, A{sub 2} ≠ 0). The location of L{sub 4} is analytically derived then the stability of L{sub 4} and its zero velocity curves are studied numerically. Our study suggests that the oblateness and the radiation of primaries may affect the stability and zero velocity curve around L{sub 4}.« less

An Astronomical Glossary.

DTIC Science & Technology

1980-02-12

planet across the limb of the Sun at the end of a transit. Elements of an Orbit - See orbital elements . Elevation - The height of a point on the...That component of libration due to variations in the geometric position of the Earth relative to the Moon. 71 ś" Orbital Elements - The quantities which...completely describe the size, shape, and orientation of an object’s orbit as well as its location in it. The classical set consists of the semi-major

Skylab

NASA Image and Video Library

1973-01-01

This chart describes the Skylab student experiment Libration Clouds, proposed by Alison Hopfield of Princeton, New Jersey. This experiment utilized Skylab's astronomical telescopes to observe the two zero-force regions (Lagrangian points) within the Earth-Moon System in which small space particles were expected to accumulate. In March 1972, NASA and the National Science Teachers Association selected 25 experiment proposals for flight on Skylab. Science advisors from the Marshall Space Flight Center aided and assisted the students in developing the proposals for flight on Skylab.

Research on the transfers to Halo orbits from the view of invariant manifolds

NASA Astrophysics Data System (ADS)

Xu, Ming; Tan, Tian; Xu, ShiJie

2012-04-01

This paper discusses the evolutions of invariant manifolds of Halo orbits by low-thrust and lunar gravity. The possibility of applying all these manifolds in designing low-thrust transfer, and the presence of single-impulse trajectories under lunar gravity are also explained. The relationship between invariant manifolds and the altitude of the perigee is investigated using a Poincaré map. Six types of single-impulse transfer trajectories are then attained from the geometry of the invariant manifolds. The evolutions of controlled manifolds are surveyed by the gradient law of Jacobi energy, and the following conclusions are drawn. First, the low thrust (acceleration or deceleration) near the libration point is very inefficient that the spacecraft free-flies along the invariant manifolds. The purpose is to increase its velocity and avoid stagnation near the libration point. Second, all controlled manifolds are captured because they lie inside the boundary of Earth's gravity trap in the configuration space. The evolutions of invariant manifolds under lunar gravity are indicated from the relationship between the lunar phasic angle and the altitude of the perigee. Third and last, most of the manifolds have preserved their topologies in the circular restricted three-body problem. However, the altitudes of the perigee of few manifolds are quite non-continuous, which can be used to generate single- impulse flyby trajectories.

Secondary resonances and the boundary of effective stability of Trojan motions

NASA Astrophysics Data System (ADS)

Páez, Rocío Isabel; Efthymiopoulos, Christos

2018-02-01

One of the most interesting features in the libration domain of co-orbital motions is the existence of secondary resonances. For some combinations of physical parameters, these resonances occupy a large fraction of the domain of stability and rule the dynamics within the stable tadpole region. In this work, we present an application of a recently introduced `basic Hamiltonian model' H_b for Trojan dynamics (Páez and Efthymiopoulos in Celest Mech Dyn Astron 121(2):139, 2015; Páez et al. in Celest Mech Dyn Astron 126:519, 2016): we show that the inner border of the secondary resonance of lowermost order, as defined by H_b, provides a good estimation of the region in phase space for which the orbits remain regular regardless of the orbital parameters of the system. The computation of this boundary is straightforward by combining a resonant normal form calculation in conjunction with an `asymmetric expansion' of the Hamiltonian around the libration points, which speeds up convergence. Applications to the determination of the effective stability domain for exoplanetary Trojans (planet-sized objects or asteroids) which may accompany giant exoplanets are discussed.

Triangular lattice atomic layer of Sn(1 × 1) at graphene/SiC(0001) interface

NASA Astrophysics Data System (ADS)

Hayashi, Shingo; Visikovskiy, Anton; Kajiwara, Takashi; Iimori, Takushi; Shirasawa, Tetsuroh; Nakastuji, Kan; Miyamachi, Toshio; Nakashima, Shuhei; Yaji, Koichiro; Mase, Kazuhiko; Komori, Fumio; Tanaka, Satoru

2018-01-01

Sn atomic layers attract considerable interest owing to their spin-related physical properties caused by their strong spin-orbit interactions. We performed Sn intercalation into the graphene/SiC(0001) interface and found a new type of Sn atomic layer. Sn atoms occupy on-top sites of Si-terminated SiC(0001) with in-plane Sn-Sn bondings, resulting in a triangular lattice. Angle-resolved photoemission spectroscopy revealed characteristic dispersions at \\bar{\\text{K}} and \\bar{\\text{M}} points, which agreed well with density functional theory calculations. The Sn triangular lattice atomic layer at the interface showed no oxidation upon exposure to air, which is useful for characterization and device fabrication ex situ.

Dynamics and control of three-body tethered system in large elliptic orbits

NASA Astrophysics Data System (ADS)

Shi, Gefei; Zhu, Zhanxia; Zhu, Zheng H.

2018-03-01

This paper investigates the dynamic characteristics a three-body tethered satellite system in large elliptic orbits and the control strategy to suppress the libration of the system in orbital transfer process. The system is modeled by a two-piece dumbbell model in the domain of true anomaly. The model consists of one main satellite and two subsatellites connected with two straight, massless and inextensible tethers. Two control strategies based on the sliding mode control are developed to control the libration to the zero state and the steady state respectively. The results of numerical simulations show that the proposed control scheme has good performance in controlling the libration motion of a three-body tethered satellite system in an elliptic orbit with large eccentricity by limited control inputs. Furthermore, Hamiltonians in both states are examined and it shows that less control input is required to control the libration motion to the steady state than that of zero state.

Tridimensional morphology and kinetics of etch pit on the {l_brace}0 0 0 1{r_brace} plane of sapphire crystal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang Lunyong; Sun Jianfei, E-mail: jfsun_hit@263.net; Zuo Hongbo

2012-08-15

The tridimensional morphology and etching kinetics of the etch pit on the C-{l_brace}0 0 0 1{r_brace} plane of sapphire crystal ({alpha}-Al{sub 2}O{sub 3}) in molten KOH were studied experimentally. It was shown that the etch pit takes on tridimensional morphologies with triangular symmetry same as the symmetric property of the sapphire crystal. Pits like centric and eccentric triangular pyramid as well as hexagonal pyramid were observed, but the latter is less in density. In-depth analyses show the side walls of the etch pits belong to the {l_brace}1 1{sup Macron} 0 2{sup Macron }{r_brace} family, and the triangular pit contains edgesmore » full composed by Al{sup 3+} ions on the etching surface so it is more stable than the hexagonal pit since its edges on the etching surface contains Al{sup 2+} ions. The etch pits developed in a manner of kinematic wave by the step moving with constant speed, which is controlled by the chemical reaction with activation energy of 96.6 kJ/mol between Al{sub 2}O{sub 3} and KOH. - Graphical abstract: Schematic showing the atomic configuration of the predicted side walls of regular triangular pyramid shaped etch pit on the C-{l_brace}0 0 0 1{r_brace} plane of sapphire crystal. Highlights: Black-Right-Pointing-Pointer Observed the tridimensional morphology of etch pits. Black-Right-Pointing-Pointer Figured out the atomic configuration origin of the etch pits. Black-Right-Pointing-Pointer Quantitatively determined the etch rates of the etch pits.« less

Enceladus's ice shell thickness and ocean depth from gravity, topography, and libration measurements

NASA Astrophysics Data System (ADS)

Trinh, A.; Rivoldini, A.; Beuthe, M.; Rekier, J.; Baland, R. M.; Van Hoolst, T.

2017-12-01

One of Cassini's major achievements is the discovery of a global ocean a few kilometres beneath Enceladus's south polar terrain. Here we infer the thickness of Enceladus's ice shell and ocean from Cassini's observations using our latest models of isostatic compensation, shell libration, and ocean dynamics.

Libration Point Orbit Utilization for Tactical Advantage in Communications, Surveillance, and Risk Mitigation

DTIC Science & Technology

2014-10-27

Ephemeris model in the orbit analysis software Satellite Took Kit ( STK ). As the first step, a study was conducted to find the visibility coverage using...northern L1 and L3 halo orbits. Figure 55. Average visibility by latitude at different ephemeris epochs for an L1 orbiter from STK analysis . Figure...56. Average visibility by latitude at different ephemeris epochs for an L3 orbiter from STK analysis . Figure 57. Average percent visibility of the

Development of Euler's ideas at the Moscow State Regional University

NASA Astrophysics Data System (ADS)

Vysikaylo, P. I.; Belyaev, V. V.

2018-03-01

In honor of the 250th anniversary of Euler's discovery of three libration points in Russia in 1767 in the area of two rotating gravitational attractors in 2017 an International Interdisciplinary Conference “Euler Readings MRSU 2017” was held in Moscow Region State University (MRSU). The Conference demonstrated that the Euler's ideas continue to remain relevant at the present time. This paper summarizes the main achievements on the basis of Leonard Euler's ideas presented at the Conference.

Normal modes of synchronous rotation

NASA Astrophysics Data System (ADS)

Varadi, Ferenc; Musotto, Susanna; Moore, William; Schubert, Gerald

2005-07-01

The dynamics of synchronous rotation and physical librations are revisited in order to establish a conceptually simple and general theoretical framework applicable to a variety of problems. Our motivation comes from disagreements between the results of numerical simulations and those of previous theoretical studies, and also because different theoretical studies disagree on basic features of the dynamics. We approach the problem by decomposing the orientation matrix of the body into perfectly synchronous rotation and deviation from the equilibrium state. The normal modes of the linearized equations are computed in the case of a circular satellite orbit, yielding both the periods and the eigenspaces of three librations. Libration in longitude decouples from the other two, vertical modes. There is a fast vertical mode with a period very close to the average rotational period. It corresponds to tilting the body around a horizontal axis while retaining nearly principal-axis rotation. In the inertial frame, this mode appears as nutation and free precession. The other vertical mode, a slow one, is the free wobble. The effects of the nodal precession of the orbit are investigated from the point of view of Cassini states. We test our theory using numerical simulations of the full equations of the dynamics and discuss the disagreements among our study and previous ones. The numerical simulations also reveal that in the case of eccentric orbits large departures from principal-axis rotation are possible due to a resonance between free precession and wobble. We also revisit the history of the Moon's rotational state and show that it switched from one Cassini state to another when it was at 46.2 Earth radii. This number disagrees with the value 34.2 derived in a previous study.

A triangular thin shell finite element: Nonlinear analysis. [structural analysis

NASA Technical Reports Server (NTRS)

Thomas, G. R.; Gallagher, R. H.

1975-01-01

Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.

On the stability of triangular points in the relativistic R3BP when the bigger primary is oblate and the smaller one radiating with application on Cen X-4 binary system

NASA Astrophysics Data System (ADS)

Bello, Nakone; Umar, Aishetu

2018-06-01

In the framework of the relativistic R3BP, we examine the effects of oblateness of the primary body and radiation pressure of the secondary on the positions and stability of the triangular points L4,5. It is found that the parameters involved all affect the positions and increase in any of the parameters leads to a reduction in the size of the region of stability. Thus establishing their destabilizing tendencies. The presence of positive real roots or positive real part in complex roots affirms the instability of L4,5 of the problem when applied to Cen X-4.

Terahertz emission from the intrinsic Josephson junctions of high-symmetry thermally-managed Bi2Sr2CaCu2O8+δ microstrip antennas

NASA Astrophysics Data System (ADS)

Klemm, Richard A.; Davis, Andrew E.; Wang, Qing X.; Yamamoto, Takashi; Cerkoney, Daniel P.; Reid, Candy; Koopman, Maximiliaan L.; Minami, Hidetoshi; Kashiwagi, Takanari; Rain, Joseph R.; Doty, Constance M.; Sedlack, Michael A.; Morales, Manuel A.; Watanabe, Chiharu; Tsujimoto, Manabu; Delfanazari, Kaveh; Kadowaki, Kazuo

2017-12-01

We show for high-symmetry disk, square, or equilateral triangular thin microstrip antennas of any composition respectively obeying C ∞v , C 4v , and C 3v point group symmetries, that the transverse magnetic electromagnetic cavity mode wave functions are restricted in form to those that are one-dimensional representations of those point groups. Plots of the common nodal points of the ten lowest-energy non-radiating two-dimensional representations of each of these three symmetries are presented. For comparison with symmetry-broken disk intrinsic Josephson junction microstrip antennas constructed from the highly anisotropic layered superconductor Bi2Sr2CaCu2O8+δ (BSCCO), we present plots of the ten lowest frequency orthonormal wave functions and of their emission power angular distributions. These results are compared with previous results for square and equilateral triangular thin microstrip antennas.

Effect of Stellar Wind and Poynting-Robertson Drag on Photogravitational Elliptic Restricted Three Body Problem

NASA Astrophysics Data System (ADS)

Chakraborty, A.; Narayan, A.

2018-03-01

The existence and linear stability of the planar equilibrium points for photogravitational elliptical restricted three body problem is investigated in this paper. Assuming that the primaries, one of which is radiating are rotating in an elliptical orbit around their common center of mass. The effect of the radiation pressure, forces due to stellar wind and Poynting-Robertson drag on the dust particles are considered. The location of the five equilibrium points are found using analytical methods. It is observed that the collinear equilibrium points L 1, L 2 and L 3 do not lie on the line joining the primaries but are shifted along the y-coordinate. The instability of the libration points due to the presence of the drag forces is demonstrated by Lyapunov's first method of stability.

Entropically Stabilized Colloidal Crystals Hold Entropy in Collective Modes

NASA Astrophysics Data System (ADS)

Antonaglia, James; van Anders, Greg; Glotzer, Sharon

Ordered structures can be stabilized by entropy if the system has more ordered microstates available than disordered ones. However, ``locating'' the entropy in an ordered system is challenging because entropic ordering is necessarily a collective effort emerging from the interactions of large numbers of particles. Yet, we can characterize these crystals using simple traditional tools, because entropically stabilized crystals exhibit collective motion and effective stiffness. For a two-dimensional system of hard hexagons, we calculate the dispersion relations of both vibrational and librational collective modes. We find the librational mode is gapped, and the gap provides an emergent, macroscopic, and density-dependent length scale. We quantify the entropic contribution of each collective mode and find that below this length scale, the dominant entropic contributions are librational, and above this length scale, vibrations dominate. This length scale diverges in the high-density limit, so entropy is found predominantly in libration near dense packing. National Science Foundation Graduate Research Fellowship Program Grant No. DGE 1256260, Advanced Research Computing at the University of Michigan, Ann Arbor, and the Simons Foundation.

Combined effect of oblateness, radiation and a circular cluster of material points on the stability of triangular liberation points in the R3BP

NASA Astrophysics Data System (ADS)

Singh, Jagadish; Taura, Joel John

2014-06-01

This paper studies the motion of an infinitesimal mass in the framework of the restricted three-body problem (R3BP) under the assumption that the primaries of the system are radiating-oblate spheroids, enclosed by a circular cluster of material points. It examines the effects of radiation and oblateness up to J 4 of the primaries and the potential created by the circular cluster, on the linear stability of the liberation locations of the infinitesimal mass. The liberation points are found to be stable for 0< μ< μ c and unstable for , where μ c is the critical mass value depending on terms which involve parameters that characterize the oblateness, radiation forces and the circular cluster of material points. The oblateness up to J 4 of the primaries and the gravitational potential from the circular cluster of material points have stabilizing propensities, while the radiation of the primaries and the oblateness up to J 2 of the primaries have destabilizing tendencies. The combined effect of these perturbations on the stability of the triangular liberation points is that, it has stabilizing propensity.

Motion in a modified Chermnykh's restricted three-body problem with oblateness

NASA Astrophysics Data System (ADS)

Singh, Jagadish; Leke, Oni

2014-03-01

In this paper, the restricted problem of three bodies is generalized to include a case when the passively gravitating test particle is an oblate spheroid under effect of small perturbations in the Coriolis and centrifugal forces when the first primary is a source of radiation and the second one an oblate spheroid, coupled with the influence of the gravitational potential from the belt. The equilibrium points are found and it is seen that, in addition to the usual three collinear equilibrium points, there appear two new ones due to the potential from the belt and the mass ratio. Two triangular equilibrium points exist. These equilibria are affected by radiation of the first primary, small perturbation in the centrifugal force, oblateness of both the test particle and second primary and the effect arising from the mass of the belt. The linear stability of the equilibrium points is explored and the stability outcome of the collinear equilibrium points remains unstable. In the case of the triangular points, motion is stable with respect to some conditions which depend on the critical mass parameter; influenced by the small perturbations, radiating effect of the first primary, oblateness of the test body and second primary and the gravitational potential from the belt. The effects of each of the imposed free parameters are analyzed. The potential from the belt and small perturbation in the Coriolis force are stabilizing parameters while radiation, small perturbation in the centrifugal force and oblateness reduce the stable regions. The overall effect is that the region of stable motion increases under the combine action of these parameters. We have also found the frequencies of the long and short periodic motion around stable triangular points. Illustrative numerical exploration is rendered in the Sun-Jupiter and Sun-Earth systems where we show that in reality, for some values of the system parameters, the additional equilibrium points do not in general exist even when there is a belt to interact with.

GPU surface extraction using the closest point embedding

NASA Astrophysics Data System (ADS)

Kim, Mark; Hansen, Charles

2015-01-01

Isosurface extraction is a fundamental technique used for both surface reconstruction and mesh generation. One method to extract well-formed isosurfaces is a particle system; unfortunately, particle systems can be slow. In this paper, we introduce an enhanced parallel particle system that uses the closest point embedding as the surface representation to speedup the particle system for isosurface extraction. The closest point embedding is used in the Closest Point Method (CPM), a technique that uses a standard three dimensional numerical PDE solver on two dimensional embedded surfaces. To fully take advantage of the closest point embedding, it is coupled with a Barnes-Hut tree code on the GPU. This new technique produces well-formed, conformal unstructured triangular and tetrahedral meshes from labeled multi-material volume datasets. Further, this new parallel implementation of the particle system is faster than any known methods for conformal multi-material mesh extraction. The resulting speed-ups gained in this implementation can reduce the time from labeled data to mesh from hours to minutes and benefits users, such as bioengineers, who employ triangular and tetrahedral meshes

Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field

NASA Astrophysics Data System (ADS)

Feng, Jinglang; Hou, Xiyun

2017-07-01

Using tools such as periodic orbits and invariant manifolds, the global dynamics around equilibrium points (EPs) in a rotating second-order and degree gravitational field are studied. For EPs on the long axis, planar and vertical periodic families are computed, and their stability properties are investigated. Invariant manifolds are also computed, and their relation to the first-order resonances is briefly discussed. For EPs on the short axis, planar and vertical periodic families are studied, with special emphasis on the genealogy of the planar periodic families. Our studies show that the global dynamics around EPs are highly similar to those around libration points in the circular restricted three-body problem, such as spatial halo orbits, invariant manifolds, and the genealogy of planar periodic families.

LLR data analysis and impact on lunar dynamics from recent developments at OCA LLR Station

NASA Astrophysics Data System (ADS)

Viswanathan, Vishnu; Fienga, Agnes; Courde, Clement; Torre, Jean-Marie; Exertier, Pierre; Samain, Etienne; Feraudy, Dominique; Albanese, Dominique; Aimar, Mourad; Mariey, Hervé; Viot, Hervé; Martinot-Lagarde, Gregoire

2016-04-01

Since late 2014, OCA LLR station has been able to range with infrared wavelength (1064nm). IR ranging provides both temporal and spatial improvement in the LLR observations. IR detection also permits in densification of normal points, including the L1 and L2 retroreflectors due to better signal to noise ratio. This contributes to a better modelisation of the lunar libration. The hypothesis of lunar dust and environmental effects due to the chromatic behavior noticed on returns from L2 retroreflector is discussed. In addition, data analysis shows that the effect of retroreflector tilt and the use of calibration profile for the normal point deduction algorithm, contributes to improving the precision of normal points, thereby impacting lunar dynamical models and inner physics.

Stability and periodicity in the Sitnikov three-body problem when primaries are oblate spheroids

NASA Astrophysics Data System (ADS)

Rahman, M. A.; Garain, D. N.; Hassan, M. R.

2015-05-01

This paper deals with the effect of oblateness of the primaries of equal masses on the series solutions of the Sitnikov problem of three bodies. Effects of oblateness have also been shown on the stability of libration points and Poincare surface of section. Here series solutions have been developed with the help of iteration process of Green's function and by the Lindstedt-Poincare method. Following Murray and Dermott (Solar System Dynamics, Cambridge University Press, Cambridge, 1999) we have checked the stability of the equilibrium points in the Sitnikov problem. Periodicity and quasi-periodicity have been examined by drawing the Poincare surfaces of section using the mathematical software.

Lissajous Orbit Control for the Deep Space Climate Observatory Sun-Earth L1 Libration Point Mission

NASA Technical Reports Server (NTRS)

Roberts, Craig; Case, Sarah; Reagoso, John

2015-01-01

DSCOVR Lissajous Orbit sized such that orbit track never extends beyond 15 degrees from Earth-Sun line (as seen from Earth). Requiring delta-V maneuvers, control orbit to obey a Solar Exclusion Zone (SEZ) cone of half-angle 4 degrees about the Earth-Sun line. Spacecraft should never be less than 4 degrees from solar center as seen from Earth. Following Lissajous Orbit Insertion (LOI), DSCOVR should be in an opening phase that just skirts the 4-degree SEZ. Maximizes time to the point where a closing Lissajous will require avoidance maneuvers to keep it out of the SEZ. Station keeping maneuvers should take no more than 15 minutes.

To development of analytical theory of rotational motion of the Moon

NASA Astrophysics Data System (ADS)

Barkin, Yu. V.; Ferrandiz, J. M.; Navarro, J. F.

2009-04-01

Resume. In the work the analytical theory of forced librations of the Moon considered as a celestial body with a liquid core and rigid non-spherical mantle is developed. For the basic variables: Andoyer, Poincare and Eulerian angles, and also for various dynamic characteristics of the Moon the tables for amplitudes, periods and phases of perturbations of the first order have been constructed. Resonant periods of free librations have been estimated. The influence of a liquid core results in decreasing of the period of free librations in longitude approximately on 0.316 day, and in change of the period of free pole wobble of the Moon on 25.8 days. In the first approximation the liquid core does not render influence on the value of Cassini's inclination and on the period of precession of the angular momentum vector. However it causes an additional "quasi-diurnal" librations with period about 27.165 days. In comparison with model of rigid non-spherical of the Moon the presence of a liquid core should result in increase of amplitudes of the Moon librations in longitude on 0.06 %. 1 Development of analytical theory of rotational motion of the Moon with liquid core and rigid mantle. The work has been realized in following stages. 1. Canonical equations of rotation of the Moon with liquid core and elastic mantle in Andoyer and Poincare variables have been constructed. Developments of second harmonic of force function of the Moon in pointed variables have been obtained for accurate trigonometric presentation of perturbations of the Moon orbital motion. 2. Two approaches (two methods) of construction of analytical theory have been developed. These approaches use different principles for eliminating of singularities for axial rotation of the Moon. One is based on direct application of Andoyer variables by changing of notations of moments of inertia [1]. Second is based on application of Poincare elements. For comparison both approaches are developed. 3. The main equation for determination of Cassini's inclination and its solution has been obtained in the case of accurate orbit of the Moon. An dynamical explanation of Cassini's laws has been done for model of the Moon with liquid core [2]. 4. Compact formulae for perturbations of the first (and second) order have been constructed for general used variables and for different kinematical and dynamical characteristics of the Moon (23 variables and characteristics: Andoyer-Poincare variables, classical variables, components of angular velocity and angular momentums of the Moon and its core). 5. Analytical formulae for 4 periods of free librations of the Moon have been constructed: for librations in longitude, in pole wobble, for free precession, and "quasi-diurnal" librations, caused by the liquid core. 6. The dynamical effects in the Moon rotation, caused by secular orbital perturbations of the Earth and Sun, have been studied. 2 Structure perturbations of the first order and their tabulation. For example, perturbations (periodic and of mixed type) in inclination ?and in node h of angular momentum of the Moon are determined by formulae: ? = ?0 + ‘ ???(1) cosθv, h = ? + ‘ ¥?¥h?(1) sinθ?. Here ?0 = 1033′50" is the Cassini's inclination of the Moon; ??(1), h?(1)are constant coefficients; θv = v1lM + v2lS + v3F + v4D, ? = (v1,v2,v3,v4)Tare combinations of known classical arguments of the Moon orbital theory; v1,v2,v3 and v4 are integer. 3 Influence of the liquid core and its ellipticity ɛ on amplitudes of the Moon forced and free librations. An influence of the liquid core and its ellipticity is determined by positive correction to amplitudes of librations for model of the rigid Moon. If the amplitudes of librations of rigid Moon we note as 1, so the corresponding amplitudes of librations of the Moon with the liquid core will be characterized by parameter 1 + L, where correction for liquid core is determined by formula L = Cc(1- ɛ2)•C ? Cc•C = 0.5996 × 10-3, where Cand Ccis the polar moments of inertia of the Moon and its core;ɛ = (a2 - b2)• (a2 + b2)? (a - b)•a is an ellipticity of equatorial ellipse of core cavity with semi-axes a and b. So all amplitudes of librations in longitude due to the liquid core are increased on 0.06%. A small effect of ellipticity has more smaller order. Here as example we present formula for perturbations of the first order of the Moon in longitude: (1) 21-+-L λ = 6n0 I C22Ã- ‘ ‘ D (1) (? )- D(-1) (? ) Ã- (- 1)?5-?1.?2.?3+2.?4.?5--0----?1.?2.?3-2.?4.?25-0-sin(v1lM + v2lS + v3F + v4D ) ¥?¥>0 ?5 (v1nM + v2nS + v3nF + v4nD) I = C•(mr2) is the dimensionless moment of inertia of the Moon (m and rare it's the mass and mean radius). Kinoshita's inclination functions D?1.?2.?3.?4.?5(±1)(? 0) are determined by known formulae through the value of Cassini's angle? = 1033′50". v1nM + v2nS + v3nF + v4nD = ˙θv1,v2,v3,v4 are derivatives with respect to the time of corresponding linear combinations of classical arguments of lunar orbit theory; nM,nS,nF and nD are velocities of changes of these arguments; C22 is the selenopotential coefficient; n02 = fm⊕•a3, a is an unperturbed value of semi-axis major of lunar orbit, fis a gravitational constant. The perturbations of the first order for others variables and considered dynamical characteristics have the structure similar to the formula for ˜λ(1). In given table 1 we present amplitudes of forced librations in longitude of intermediate Andoyer plane λ?1,?2,?3,?4 (in arc seconds) and perturbations of angular velocity of the Moon axial rotation ??1,?2,?3,?4 (in units10-4nF). T?1,?2,?3,?4are periods of corresponding perturbations. Table 1. Main perturbations in the Moon librations in longitude. ?1 ?2 ?3 ?4 T?1,?2,?3,?4 λ?1,?2,?3,?4 0 1 0 0 365.26 81"02 1 0 0 0 27.555 -15"65 1 -1 0 -1 -3232.9 9"85 2 0 0 -2 205.89 9"69 1 0 0 -2 31.81 4"15 1 0 0 -1 411.78 -2"98 2 0 -2 0 -1095.2 -1"86 2 -1 0 -2 471.89 0"74 0 0 0 2 14.77 -0"61 The results of tabulations of amplitudes of perturbations in the Moon rotation give good agreement with earlier constructed theories for its rigid model. Barkin's work partially was financially accepted by Spanish grants, Japanese-Russian grant N-07-02-91212 and by RFBR grant N 08-02-00367. References [1] Barkin, Yu. (1987) An Analytical Theory of the Lunar Rotational Motion. In: Figure and Dynamics of the Earth, Moon and Planets/ Proceedings of the Int. Symp. (Prague, Czechoslovakia, Sept. 15-20, 1986)/ Monogr. Ser. of UGTK, Prague. pp. 657-677. [2] Ferrandiz, J., Barkin, Yu. (2003) New approach to development of Moon rotation theory. Procced. of Inter. Conf. "Astrometry, Geodynamics and Solar System Dynamics". Journees 2003 (Sept. 22-25, 2003, St. Peters., Russia). IPA RAS, 199-200.

Terahertz VRT spectroscopy of the water hexamer-d12 prism: Dramatic enhancement of bifurcation tunneling upon librational excitation

NASA Astrophysics Data System (ADS)

Cole, William T. S.; Farrell, James D.; Sheikh, Akber A.; Yönder, Öezlem; Fellers, Raymond S.; Viant, Mark R.; Wales, David J.; Saykally, Richard J.

2018-03-01

Using diode laser vibration-rotation-tunneling spectroscopy near 15 Thz (500 cm-1), we have measured and assigned 142 transitions to three a-type librational subbands of the water hexamer-d12 prism. These subbands reveal dramatically enhanced (ca. 1000×) tunneling splittings relative to the ground state. This enhancement is in agreement with that observed for the water dimer, trimer, and pentamer in this same frequency region. The water prism tunneling motion has been predicted to potentially describe the motions of water in interfacial and confined environments; hence, the results presented here indicate that excitation of librational vibrations has a significant impact on the hydrogen bond dynamics in these macroscopic environments.

The librational band of water ice in AFGL 961: revisited

NASA Astrophysics Data System (ADS)

Smith, R. G.; Wright, C. M.

2011-07-01

Of all the water ice absorption bands seen in the laboratory, the librational band near 12-13 μ m has proven the most difficult to conclusively identify in observational spectra. Cox reported the detection of this band in the IRAS spectrum of the massive protostar AFGL 961 near 13.6 μ m; however, the details of the structure of the band were limited by the quality of the IRAS spectrum and the accuracy of the subtracted silicate absorption. AFGL 961 is also a double system comprising two point-like components separated by ˜6 arcsec (AFGL 961E and AFGL 961W) so the IRAS aperture included both components - it is unclear how the combination of the intrinsic spectra of these two sources may have affected the resultant IRAS spectrum. In this paper we report Spitzer and European Southern Observatory (ESO) 3.6-m mid-infrared spectroscopic observations of each component of AFGL 961. We find a broad absorption feature near 13.1 μ m common to both AFGL 961E and W. The profile and peak wavelength of this feature are well matched by the laboratory spectrum of the librational band of amorphous H2O ice in the temperature range 10-30 K, in agreement with the Cox result. Both AFGL 961E and W also have strong CO2 ice absorption near 15.2 μ m, indistinguishable in profile between the two. However, AFGL 961E shows silicates in absorption near 9.7 μ m, while AFGL 961W shows polycyclic aromatic hydrocarbons in emission and, in a small aperture, also silicates in emission. Uncertainty in where the true continuum lies in the 8-13 μ m spectral region for both AFGL 961E and W means we cannot rule out the possibility that a combination of silicate emission and absorption could be responsible for at least some of the features we see in this region. In this case, a much weaker librational band could still be present, but not as a distinct feature. In either case, the ice must be located in a cool, outer envelope surrounding both stars or a cool foreground cloud, far enough away that the ice is not appreciably modified by the local environment of either one.

Long Term Missions at the Sun-Earth Libration Point L1: ACE, SOHO, and WIND

NASA Technical Reports Server (NTRS)

Roberts, Craig E.

2011-01-01

Three heliophysics missions -- the Advanced Composition Explorer (ACE), Solar Heliospheric Observatory (SOHO), and the Global Geoscience WIND -- have been orbiting the Sun-Earth interior libration point L1 continuously since 1997, 1996, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center (GSFC). While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND has had also a remarkable 10-year career flying a deep-space, multiple lunar-flyby trajectory prior to 2004. That era featured 36 targeted lunar flybys with excursions to both L1 and L2 before its final insertion in L1 orbit. A figure depicts the orbits of the three spacecraft, showing projections of the orbits onto the orthographic planes of a solar rotating ecliptic frame of reference. The SOHO orbit is a quasi-periodic halo orbit, where the frequencies of the in-plane and out-of-plane motions are practically equal. Such an orbit is seen to repeat itself with a period of approximately 178 days. For ACE and WIND, the frequencies of the in-plane and out-of-plane motions are unequal, giving rise to the characteristic Lissajous motion. ACE's orbit is of moderately small amplitude, whereas WIND's orbit is a large-amplitude Lissajous of dimensions close to those of the SOHO halo orbit. As motion about the collinear points is inherently unstable, stationkeeping maneuvers are necessary to prevent orbital decay and eventual escape from the L1 region. Though the three spacecraft are dissimilar (SOHO is a 3-axis stabilized Sun pointer, WIND is a spin-stabilized ecliptic pole pointer, and ACE is also spin-stabilized with its spin axis maintained between 4 and 20 degrees of the Sun), the stationkeeping technique for the three is fundamentally the same. The technique consists of correcting the energy of the orbit via a delta-V directed parallel or anti-parallel to the Spacecraft-to-Sun line. SOHO achieves this using thrusters oriented in line with the solar direction. WIND achieves the delta-V via pulsing radial thrusters when aligned with the Sun. ACE uses axial thrusters to apply delta-V with a component that is 94% or more aligned with the ACE-Sun line. Sunward thrust adds energy to the orbit preventing decay back toward Earth. Thrust directed anti-Sunward takes energy out of the L1 orbit, thereby preventing escape from the Earth-Moon system into independent heliocentric orbit. Libration point orbit stationkeeping delta-V costs grow exponentially with time elapsed from the last maneuver performed. The doubling time constant is approximately 16 days. For the sake of fuel conservation, and for limiting the absolute magnitude of propulsion performance errors, stationkeeping maneuvers should be performed before the delta-V grows too large; for our purposes 'too large' is considered to be greater than 0.5 m/sec. In practice, the typical interval between burns for this trio is about three months, and the typical delta-V is much smaller than 0.5 m/sec. Typical annual stationkeeping costs have been around 1.0 m/sec for ACE and WIND, and much less than that for SOHO. All three spacecraft have ample fuel remaining; barring contingencies all three could, in principle, be maintained at L1 for decades to come. This paper will review the L1 orbits and the mission history of ACE, WIND, and SOHO, and describe the stationkeeping techniques and orbit maneuver experience. The Lissajous phase control that was practiced for ACE during the period from 1999 to 2001 will also be briefly discussed. The final section will consider the future of these ongoing missions.

Cislunar Near Rectilinear Halo Orbit for Human Space Exploration

NASA Technical Reports Server (NTRS)

Whitley, Ryan; Martinez, Roland; Condon, Gerald; Williams, Jacob; Lee, David; Davis, Diane; Barton, Gregg; Bhatt, Sagar; Jang, Jiann-Woei; Clark, Fred;

Using Geological Implications of a Physical Libration to Constrain Enceladus' Libration State

NASA Technical Reports Server (NTRS)

Hurford, T. A.; Bills, B. G.; Helfenstein, P.; Greenberg, R.; Hoppa, G. V.; Hamilton, D. P.

2009-01-01

Observations of Enceladus' south pole revealed large rifts in the crust, called "tiger stripes", which exhibit higher temperatures than the surrounding terrain and are likely sources of observed eruptions. Tidal stress may periodically open the tiger stripe rifts, controlling the timing and location of eruptions. Moreover, shear motion along rifts may produce the heat to drive eruptions.

Benchmark Problems for Space Mission Formation Flying

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell; Leitner, Jesse A.; Folta, David C.; Burns, Richard

2003-01-01

To provide a high-level focus to distributed space system flight dynamics and control research, several benchmark problems are suggested for space mission formation flying. The problems cover formation flying in low altitude, near-circular Earth orbit, high altitude, highly elliptical Earth orbits, and large amplitude lissajous trajectories about co-linear libration points of the Sun-Earth/Moon system. These problems are not specific to any current or proposed mission, but instead are intended to capture high-level features that would be generic to many similar missions that are of interest to various agencies.

Multi-Body Orbit Architectures for Lunar South Pole Coverage

NASA Technical Reports Server (NTRS)

Grebow, D. J.; Ozimek, M. T.; Howell, K. C.; Folta, D. C.

2006-01-01

A potential ground station at the lunar south pole has prompted studies of orbit architectures that ensure adequate coverage. Constant communications can be achieved with two spacecraft in different combinations of Earth-Moon libration point orbits. Halo and vertical families, as well as other orbits near L1 and L2 are considered. The investigation includes detailed results using nine different orbits with periods ranging from 7 to 16 days. Natural solutions are generated in a full ephemeris model, including solar perturbations. A preliminary station-keeping analysis is also completed.

Minimum impulse three-body trajectories.

NASA Technical Reports Server (NTRS)

D'Amario, L.; Edelbaum, T. N.

1973-01-01

A rapid and accurate method of calculating optimal impulsive transfers in the restricted problem of three bodies has been developed. The technique combines a multi-conic method of trajectory integration with primer vector theory and an accelerated gradient method of trajectory optimization. A unique feature is that the state transition matrix and the primer vector are found analytical without additional integrations or differentiations. The method has been applied to the determination of optimal two and three impulse transfers between the L2 libration point and circular orbits about both the earth and the moon.

Earth to Moon Transfers - Direct vs Via Libration Points (L1, L2)

NASA Technical Reports Server (NTRS)

Condon, Gerald L.; Wilson, Sam

2002-01-01

Recommend Direct Remote Ocean Area impact disposal for caseswithout hazardous (e.g., radioactive) material on LTV kickstage Controlled Earth contact. Relatively small disposal AV. Avoids close encounter with Moon. Trajectories can be very sensitive to initial conditions (at disposalmaneuver).V to correct for errors is small. Recommend Heliocentric Orbit disposal for cases with hazardousmaterial on LTV kickstage. No Earth or Lunar disposal issues (e.g.. impact location, debris footprint,litter). Relatively low disposal AV cost. Further study required to determine possibility of re-contact with Earth.

Proposed gravity-gradient dynamics experiments in lunar orbit using the RAE-B spacecraft

NASA Technical Reports Server (NTRS)

Blanchard, D. L.; Walden, H.

1973-01-01

A series of seven gravity-gradient dynamics experiments is proposed utilizing the Radio Astronomy Explorer (RAE-B) spacecraft in lunar orbit. It is believed that none of the experiments will impair the spacecraft structure or adversely affect the continuation of the scientific mission of the satellite. The first experiment is designed to investigate the spacecraft dynamical behavior in the absence of libration damper action and inertia. It requires stable gravity-gradient capture of the spacecraft in lunar orbit with small amplitude attitude librations as a prerequisite. Four subsequent experiments involve partial retraction, ultimately followed by full redeployment, of one or two of the 230-meter booms forming the lunar-directed Vee-antenna. These boom length change operations will induce moderate amplitude angular librations of the spacecraft.

Reconfirmation of the anatomy of the left triangular ligament and the appendix fibrosa hepatis in human livers, and its implication in abdominal surgery.

PubMed

Kogure, Kimitaka; Kojima, Itaru; Kuwano, Hiroyuki; Matsuzaki, Toshiyuki; Yorifuji, Hiroshi; Takata, Kuniaki; Makuuchi, Masatoshi

2014-12-01

The aim of the present study was to clarify the anatomy between the left triangular ligament (LTL) and the appendix fibrosa hepatis (AFH) in order not to sever the AFH when dissecting the LTL. Totals of 43 and 27 cadaveric livers were examined macroscopically and histologically, respectively. The LTL attached itself to the diaphragmatic surface of the AFH through almost all lengths of the AFH. This might be the reason why AFH is so often dissected together with the LTL. There were two types of relation between the LTL and the AFH; in one type, the starting point of the LTL existed on the left liver and in the other type, it was on the AFH. Twenty-five of 27 AFH included remnants of the bile duct and 12 of 25 AFH had comparatively large bile ducts, which was unexceptionally accompanied by the well-developed peribiliary vascular plexus. AFH showed a variety of shapes, such as rectangular (6/43), long triangular (4/43), short triangular (7/43), triangular plus cordlike (11/43), cordlike (12/43) and bifurcated (3/43) types. As AFH sometimes includes relatively large bile ducts, it is recommended for surgeons to sever the AFH not just simply by electrocautery but by ligating its stump securely. © 2014 Japanese Society of Hepato-Biliary-Pancreatic Surgery.

Sample Archaeological Survey of Public Use Areas, Milford Lake, Kansas

DTIC Science & Technology

1982-09-01

6,000 B.C. Llano -(Clovis projectile points) Lindenmeier - (Folsom projectile points) Plano -(Plainview, Angostora, Hell Gap, Scotts- bluff, etc...plain, flaring or S-form rims, shell tempered, plain surfaced pottery with low rolled rims 0 and incised alternating hatched triangles on the...tempered pottery with a marked collar rim incised with zig-zags, herringbone and hatched alternating triangles; unnotched triangular arrow points; French

Cavity mode enhancement of terahertz emission from equilateral triangular microstrip antennas of the high-Tc superconductor Bi2Sr2CaCu2O8+δ

NASA Astrophysics Data System (ADS)

Doty, Constance; Cerkoney, Daniel; Gramajo, Ashley; Campbell, Tyler; Reid, Candy; Morales, Manuel; Delfanazari, Kaveh; Yamamoto, Takashi; Tsujimoto, Manabu; Kashiwagi, Takanari; Watanabe, Chiharu; Minami, Hidetoshi; Kadowaki, Kazuo; Klemm, Richard

We study the transverse magnetic (TM) electromagnetic cavity mode wave functions for an ideal equilateral triangular microstrip antenna exhibiting C3v point group symmetry, which restricts the number of TM(n,m) modes to | m - n | = 3 p , where the integer p > 0 for the modes odd and even about the three mirror planes, but p = 0 can also exist for the even modes. We calculate the wave functions and the power distribution forms from the uniform Josephson current source and from the excitation of one of these cavity modes, and fit data on an early equilateral triangular Bi2Sr2CaCu2O8+δ mesa, for which the C3v symmetry was apparently broken. Work supported in part by the UCF RAMP, JSPS Fellowship, CREST-JST, and WPI-MANA.

Spin-Chirality-Driven Ferroelectricity on a Perfect Triangular Lattice Antiferromagnet

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mitamura, H.; Watanuki, R.; Kaneko, Koji

Magnetic field (B) variation of the electrical polarization P c ( ∥c) of the perfect triangular lattice antiferromagnet RbFe(MoO 4) 2 is examined up to the saturation point of the magnetization for B⊥c. P c is observed only in phases for which chirality is predicted in the in-plane magnetic structures. No strong anomaly is observed in P c at the field at which the spin modulation along the c axis, and hence the spin helicity, exhibits a discontinuity to the commensurate state. These results indicate that the ferroelectricity in this compound originates predominantly from the spin chirality, the explanation ofmore » which would require a new mechanism for magnetoferroelectricity. Lastly, the obtained field-temperature phase diagrams of ferroelectricity well agree with those theoretically predicted for the spin chirality of a Heisenberg spin triangular lattice antiferromagnet.« less

Spin-Chirality-Driven Ferroelectricity on a Perfect Triangular Lattice Antiferromagnet

DOE PAGES

Mitamura, H.; Watanuki, R.; Kaneko, Koji; ...

2014-10-01

Magnetic field (B) variation of the electrical polarization P c ( ∥c) of the perfect triangular lattice antiferromagnet RbFe(MoO 4) 2 is examined up to the saturation point of the magnetization for B⊥c. P c is observed only in phases for which chirality is predicted in the in-plane magnetic structures. No strong anomaly is observed in P c at the field at which the spin modulation along the c axis, and hence the spin helicity, exhibits a discontinuity to the commensurate state. These results indicate that the ferroelectricity in this compound originates predominantly from the spin chirality, the explanation ofmore » which would require a new mechanism for magnetoferroelectricity. Lastly, the obtained field-temperature phase diagrams of ferroelectricity well agree with those theoretically predicted for the spin chirality of a Heisenberg spin triangular lattice antiferromagnet.« less

Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Feng, Jinglang; Hou, Xiyun, E-mail: jinglang@nju.edu.cn, E-mail: silence@nju.edu.cn

2017-07-01

Using tools such as periodic orbits and invariant manifolds, the global dynamics around equilibrium points (EPs) in a rotating second-order and degree gravitational field are studied. For EPs on the long axis, planar and vertical periodic families are computed, and their stability properties are investigated. Invariant manifolds are also computed, and their relation to the first-order resonances is briefly discussed. For EPs on the short axis, planar and vertical periodic families are studied, with special emphasis on the genealogy of the planar periodic families. Our studies show that the global dynamics around EPs are highly similar to those around libration points in the circularmore » restricted three-body problem, such as spatial halo orbits, invariant manifolds, and the genealogy of planar periodic families.« less

Investigations at Supersonic Speeds of 22 Triangular Wings Representing Two Airfoil Sections for Each of 11 Apex Angles

NASA Technical Reports Server (NTRS)

Love, Eugene S

1955-01-01

The results of tests of 22 triangular wings, representing two leading-edge shapes for each of 11 apex angles, at Mach numbers 1.62, 1.92, and 1.40 are presented and compared with theory. All wings have a common thickness ratio of 8 percent and a common maximum-thickness point at 18 percent chord. Lift, drag, and pitching moment are given for all wings at each Mach number. The relation of transition in the boundary layer, shocks on the wing surfaces, and characteristics of the pressure distributions is discussed for several wings.

Lattice dynamics of solid N2 with an ab initio intermolecular potential

NASA Astrophysics Data System (ADS)

Luty, T.; van der Avoird, A.; Berns, R. M.

1980-11-01

We have performed harmonic and self-consistent phonon lattice dynamics calculations for α and γ N2 crystals using an intermolecular potential from ab initio calculations. This potential contains electrostatic (multipole) interactions, up to all R-9 terms inclusive, anisotropic dispersion interactions up to all R-10 terms inclusive, and anisotropic overlap interactions caused by charge penetration and exchange between the molecules. The lattice constants, cohesion energy, the frequencies of the translational phonon modes and the Grüneisen parameters for the librational modes are in good agreement with experimental values, confirming the quality of the potential. The frequencies of the librational modes and those of the mixed modes are less well reproduced, especially at temperatures near the α-β phase transition. Probably, the self-consistent phonon method used does not fully account for the anharmonicity in the librations.

Electron spin control and spin-libration coupling of a levitated nanodiamond

NASA Astrophysics Data System (ADS)

Hoang, Thai; Ma, Yue; Ahn, Jonghoon; Bang, Jaehoon; Robicheaux, Francis; Gong, Ming; Yin, Zhang-Qi; Li, Tongcang

2017-04-01

Hybrid spin-mechanical systems have great potentials in sensing, macroscopic quantum mechanics, and quantum information science. Recently, we optically levitated a nanodiamond and demonstrated electron spin control of its built-in nitrogen-vacancy (NV) centers in vacuum. We also observed the libration (torsional vibration) of a nanodiamond trapped by a linearly polarized laser beam in vacuum. We propose to achieve strong coupling between the electron spin of a NV center and the libration of a levitated nanodiamond with a uniform magnetic field. With a uniform magnetic field, multiple spins can couple to the torsional vibration at the same time. We propose to use this strong coupling to realize the Lipkin-Meshkov-Glick (LMG) model and generate rotational superposition states. This work is supported by the National Science Foundation under Grant No. 1555035-PHY.

Orbit determination error analysis and comparison of station-keeping costs for Lissajous and halo-type libration point orbits and sensitivity analysis using experimental design techniques

NASA Technical Reports Server (NTRS)

Gordon, Steven C.

1993-01-01

Spacecraft in orbit near libration point L1 in the Sun-Earth system are excellent platforms for research concerning solar effects on the terrestrial environment. One spacecraft mission launched in 1978 used an L1 orbit for nearly 4 years, and future L1 orbital missions are also being planned. Orbit determination and station-keeping are, however, required for these orbits. In particular, orbit determination error analysis may be used to compute the state uncertainty after a predetermined tracking period; the predicted state uncertainty levels then will impact the control costs computed in station-keeping simulations. Error sources, such as solar radiation pressure and planetary mass uncertainties, are also incorporated. For future missions, there may be some flexibility in the type and size of the spacecraft's nominal trajectory, but different orbits may produce varying error analysis and station-keeping results. The nominal path, for instance, can be (nearly) periodic or distinctly quasi-periodic. A periodic 'halo' orbit may be constructed to be significantly larger than a quasi-periodic 'Lissajous' path; both may meet mission requirements, but perhaps the required control costs for these orbits are probably different. Also for this spacecraft tracking and control simulation problem, experimental design methods can be used to determine the most significant uncertainties. That is, these methods can determine the error sources in the tracking and control problem that most impact the control cost (output); it also produces an equation that gives the approximate functional relationship between the error inputs and the output.

Absolute, SI-traceable lunar irradiance tie-points for the USGS Lunar Model

NASA Astrophysics Data System (ADS)

Brown, Steven W.; Eplee, Robert E.; Xiong, Xiaoxiong J.

2017-10-01

The United States Geological Survey (USGS) has developed an empirical model, known as the Robotic Lunar Observatory (ROLO) Model, that predicts the reflectance of the Moon for any Sun-sensor-Moon configuration over the spectral range from 350 nm to 2500 nm. The lunar irradiance can be predicted from the modeled lunar reflectance using a spectrum of the incident solar irradiance. While extremely successful as a relative exo-atmospheric calibration target, the ROLO Model is not SI-traceable and has estimated uncertainties too large for the Moon to be used as an absolute celestial calibration target. In this work, two recent absolute, low uncertainty, SI-traceable top-of-the-atmosphere (TOA) lunar irradiances, measured over the spectral range from 380 nm to 1040 nm, at lunar phase angles of 6.6° and 16.9° , are used as tie-points to the output of the ROLO Model. Combined with empirically derived phase and libration corrections to the output of the ROLO Model and uncertainty estimates in those corrections, the measurements enable development of a corrected TOA lunar irradiance model and its uncertainty budget for phase angles between +/-80° and libration angles from 7° to 51° . The uncertainties in the empirically corrected output from the ROLO model are approximately 1 % from 440 nm to 865 nm and increase to almost 3 % at 412 nm. The dominant components in the uncertainty budget are the uncertainty in the absolute TOA lunar irradiance and the uncertainty in the fit to the phase correction from the output of the ROLO model.

33 CFR 334.1125 - Pacific Ocean Naval Air Weapons Station, Point Mugu, Small Arms Range, Ventura County, California...

Code of Federal Regulations, 2014 CFR

2014-07-01

... Station, Point Mugu, Small Arms Range, Ventura County, California; danger zone. 334.1125 Section 334.1125 Navigation and Navigable Waters CORPS OF ENGINEERS, DEPARTMENT OF THE ARMY, DEPARTMENT OF DEFENSE DANGER ZONE... Arms Range, Ventura County, California; danger zone. (a) The area. A triangular area extending...

33 CFR 334.1125 - Pacific Ocean Naval Air Weapons Station, Point Mugu, Small Arms Range, Ventura County, California...

Code of Federal Regulations, 2012 CFR

2012-07-01

... Station, Point Mugu, Small Arms Range, Ventura County, California; danger zone. 334.1125 Section 334.1125 Navigation and Navigable Waters CORPS OF ENGINEERS, DEPARTMENT OF THE ARMY, DEPARTMENT OF DEFENSE DANGER ZONE... Arms Range, Ventura County, California; danger zone. (a) The area. A triangular area extending...

33 CFR 334.1125 - Pacific Ocean Naval Air Weapons Station, Point Mugu, Small Arms Range, Ventura County, California...

Code of Federal Regulations, 2013 CFR

2013-07-01

... Station, Point Mugu, Small Arms Range, Ventura County, California; danger zone. 334.1125 Section 334.1125 Navigation and Navigable Waters CORPS OF ENGINEERS, DEPARTMENT OF THE ARMY, DEPARTMENT OF DEFENSE DANGER ZONE... Arms Range, Ventura County, California; danger zone. (a) The area. A triangular area extending...

Analytical investigation of the dynamics of tethered constellations in Earth orbit, phase 2

NASA Astrophysics Data System (ADS)

Lorenzini, E. C.; Arnold, D. A.; Cosmo, M.; Grossi, M. D.

1986-10-01

The following topics related to the dynamics of the 4-mass tethered system are addressed: (1) the development of damping algorithms for damping the out-of-plane libration of the system and the interaction of the out-of-plane control with the other degrees of freedom; and (2) the development of environmental models to be added to the dynamics simulation computer code. The environmental models are specifically a new drag routine based on the Jacchia's 1977 model, a J(2) model and an accurate thermal model of the wire. Regarding topic (1) a survey of various out-of-plane libration control laws was carried out. Consequently a yo-yo control law with amplitude of the tether length variation proportional to the amplitude of the out-of-game libration has been selected. This control law provides good damping when applied to a (theoretical) two-dimensional system. In the actual 3-dimensional 4-mass tethered system, however, energy is transferred to the least damped degrees of freedom (the out-of-plane lateral deflections are still undamped in the present simulations) in such a way as to decrease the effectiveness of the algorithm for out-of-plane libration control. The addition of damping algorithms for the out-of-plane lateral deflections is therefore necessary.

Analytical investigation of the dynamics of tethered constellations in Earth orbit, phase 2

NASA Technical Reports Server (NTRS)

Lorenzini, E. C.; Arnold, D. A.; Cosmo, M.; Grossi, M. D.

1986-01-01

The following topics related to the dynamics of the 4-mass tethered system are addressed: (1) the development of damping algorithms for damping the out-of-plane libration of the system and the interaction of the out-of-plane control with the other degrees of freedom; and (2) the development of environmental models to be added to the dynamics simulation computer code. The environmental models are specifically a new drag routine based on the Jacchia's 1977 model, a J(2) model and an accurate thermal model of the wire. Regarding topic (1) a survey of various out-of-plane libration control laws was carried out. Consequently a yo-yo control law with amplitude of the tether length variation proportional to the amplitude of the out-of-game libration has been selected. This control law provides good damping when applied to a (theoretical) two-dimensional system. In the actual 3-dimensional 4-mass tethered system, however, energy is transferred to the least damped degrees of freedom (the out-of-plane lateral deflections are still undamped in the present simulations) in such a way as to decrease the effectiveness of the algorithm for out-of-plane libration control. The addition of damping algorithms for the out-of-plane lateral deflections is therefore necessary.

Resonance Occupation in the Kuiper Belt: Case Examples of the 5:2 and Trojan Resonances

NASA Astrophysics Data System (ADS)

Chiang, E. I.; Jordan, A. B.; Millis, R. L.; Buie, M. W.; Wasserman, L. H.; Elliot, J. L.; Kern, S. D.; Trilling, D. E.; Meech, K. J.; Wagner, R. M.

2003-07-01

As part of our ongoing Deep Ecliptic Survey (DES) of the Kuiper belt, we report on the occupation of the 1:1 (Trojan), 4:3, 3:2, 7:4, 2:1, and 5:2 Neptunian mean motion resonances (MMRs). The previously unrecognized occupation of the 1:1 and 5:2 MMRs is not easily understood within the standard model of resonance sweeping by a migratory Neptune over an initially dynamically cold belt. Among all resonant Kuiper belt objects (KBOs), the three observed members of the 5:2 MMR discovered by DES possess the largest semimajor axes (a~55.4 AU), the highest eccentricities (e~0.4), and substantial orbital inclinations (i~10deg). Objects (38084) 1999HB12 and possibly 2001KC77 can librate with modest amplitudes of ~90° within the 5:2 MMR for at least 1 Gyr. Their trajectories cannot be explained by close encounters with Neptune alone, given the latter's current orbit. The dynamically hot orbits of such 5:2 resonant KBOs, unlike hot orbits of previously known resonant KBOs, may imply that these objects were preheated to large inclination and large eccentricity prior to resonance capture by a migratory Neptune. Our first discovered Neptunian Trojan, 2001QR322, may not owe its existence to Neptune's migration at all. The trajectory of 2001QR322 is remarkably stable; the object can undergo tadpole-type libration about Neptune's leading Lagrange (L4) point for at least 1 Gyr with a libration amplitude of 24°. Trojan capture probably occurred while Neptune accreted the bulk of its mass. For an assumed albedo of 12%-4%, our Trojan is ~130-230 km in diameter. Model-dependent estimates place the total number of Neptune Trojans resembling 2001QR322 at ~20-60. Their existence helps to rule out violent orbital histories for Neptune.

Spin-Label CW Microwave Power Saturation and Rapid Passage with Triangular Non-Adiabatic Rapid Sweep (NARS) and Adiabatic Rapid Passage (ARP) EPR Spectroscopy

PubMed Central

Kittell, Aaron W.; Hyde, James S.

2015-01-01

Non-adiabatic rapid passage (NARS) electron paramagnetic resonance (EPR) spectroscopy was introduced by Kittell, A.W., Camenisch, T.G., Ratke, J.J. Sidabras, J.W., Hyde, J.S., 2011 as a general purpose technique to collect the pure absorption response. The technique has been used to improve sensitivity relative to sinusoidal magnetic field modulation, increase the range of inter-spin distances that can be measured under near physiological conditions, and enhance spectral resolution in copper (II) spectra. In the present work, the method is extended to CW microwave power saturation of spin-labeled T4 Lysozyme (T4L). As in the cited papers, rapid triangular sweep of the polarizing magnetic field was superimposed on slow sweep across the spectrum. Adiabatic rapid passage (ARP) effects were encountered in samples undergoing very slow rotational diffusion as the triangular magnetic field sweep rate was increased. The paper reports results of variation of experimental parameters at the interface of adiabatic and non-adiabatic rapid sweep conditions. Comparison of the forward (up) and reverse (down) triangular sweeps is shown to be a good indicator of the presence of rapid passage effects. Spectral turning points can be distinguished from spectral regions between turning points in two ways: differential microwave power saturation and differential passage effects. Oxygen accessibility data are shown under NARS conditions that appear similar to conventional field modulation data. However, the sensitivity is much higher, permitting, in principle, experiments at substantially lower protein concentrations. Spectral displays were obtained that appear sensitive to rotational diffusion in the range of rotational correlation times of 10−3 to 10−7 s in a manner that is analogous to saturation transfer spectroscopy. PMID:25917132

Significance of specific force models in two applications: Solar sails to sun-earth L4/L5 and grail data analysis suggesting lava tubes and buried craters on the moon

NASA Astrophysics Data System (ADS)

Sood, Rohan

In the trajectory design process, gravitational interaction between the bodies of interest plays a key role in developing the over-arching force model. However, non-gravitational forces, such as solar radiation pressure (SRP), can significantly influence the motion of a spacecraft. Incorporating SRP within the dynamical model can assist in estimating the trajectory of a spacecraft with greater precision, in particular, for a spacecraft with a large area-to-mass ratio, i.e., solar sails. Subsequently, in the trajectory design process, solar radiation pressure can be leveraged to maneuver the sail-based spacecraft. First, to construct low energy transfers, the invariant manifolds are explored that form an important tool in the computation and design of complex trajectories. The focus is the investigation of trajectory design options, incorporating solar sail dynamics, from the Earth parking orbit to the vicinity of triangular Lagrange points. Thereafter, an optimization scheme assisted in investigating the ?V requirement to depart from the Earth parking orbit. Harnessing the solar radiation pressure, the spacecraft is delivered to the vicinity of the displaced Lagrange point and maintains a trajectory close to the artificial libration point with the help of the solar sail. However, these trajectories are converged in a model formulated as a three-body problem with additional acceleration from solar radiation pressure. Thus, the trajectories are transitioned to higher fidelity ephemeris model to account for additional perturbing accelerations that may dominate the sail-craft dynamics and improve upon the trajectory design process. Alternatively, precise knowledge of the motion of a spacecraft about a central body and the contribution of the SRP can assist in deriving a highly accurate gravity field model. The high resolution gravity data can potentially assist in exploring the surface and subsurface properties of a particular body. With the goal of expanding human presence beyond Earth, sub-surface empty lava tubes on other worlds form ideal candidates for creating a permanent habitation environment safe from cosmic radiation, micrometeorite impacts and temperature extremes. In addition, gravitational analysis has also revealed large buried craters under thick piles of mare basalt, shedding light on Moon's dynamic and hostile past. In this work, gravity mapping observations from NASA's Gravity Recovery and Interior Laboratory (GRAIL) are employed to detect the presence of potential empty lava tubes and large impact craters buried beneath the lunar maria.

A study of thin liquid sheet flows

NASA Technical Reports Server (NTRS)

Chubb, Donald L.; Calfo, Frederick D.; Mcconley, Marc W.; Mcmaster, Matthew S.; Afjeh, Abdollah A.

1993-01-01

This study was a theoretical and experimental investigation of thin liquid sheet flows in vacuum. A sheet flow created by a narrow slit of width, W, coalesces to a point at a distance, L, as a result of surface tension forces acting at the sheet edges. As the flow coalesces, the fluid accumulates in the sheet edges. The observed triangular shape of the sheet agrees with the calculated triangular result. Experimental results for L/W as a function of Weber number, We, agree with the calculated result, L/W = the sq. root of 8We. The edge cross sectional shape is found to oscillate from elliptic to 'cigar' like to 'peanut' like and then back to elliptic in the flow direction. A theoretical one-dimensional model was developed that yielded only elliptic solutions for the edge cross section. At the points where the elliptic shapes occur, there is agreement between theory and experiment.

A note on an attempt at more efficient Poisson series evaluation. [for lunar libration

NASA Technical Reports Server (NTRS)

Shelus, P. J.; Jefferys, W. H., III

1975-01-01

A substantial reduction has been achieved in the time necessary to compute lunar libration series. The method involves eliminating many of the trigonometric function calls by a suitable transformation and applying a short SNOBOL processor to the FORTRAN coding of the transformed series, which obviates many of the multiplication operations during the course of series evaluation. It is possible to accomplish similar results quite easily with other Poisson series.

Inertial wave beams and inertial wave modes in a rotating cylinder with time-modulated rotation rate

NASA Astrophysics Data System (ADS)

Borcia, Ion D.; Ghasemi V., Abouzar; Harlander, Uwe

2014-05-01

Inertial gravity waves play an crucial role in atmospheres, oceans, and the fluid inside of planets and moons. In the atmosphere, the effect of rotation is neglected for small wavelength and the waves bear the character of internal gravity waves. For long waves, the hydrostatic assumption is made which in turn makes the atmosphere inelastic with respect to inertial motion. In contrast, in the Earth's interior, pure inertial waves are considered as an important fundamental part of the motion. Moreover, as the deep ocean is nearly homogeneous, there the inertial gravity waves bear the character of inertial waves. Excited at the oceans surface mainly due to weather systems the waves can propagate downward and influence the deep oceans motion. In the light of the aforesaid it is important to understand better fundamental inertial wave dynamics. We investigate inertial wave modes by experimental and numerical methods. Inertial modes are excited in a fluid filled rotating annulus by modulating the rotation rate of the outer cylinder and the upper and lower lids. This forcing leads to inertial wave beams emitted from the corner regions of the annulus due to periodic motions in the boundary layers (Klein et al., 2013). When the forcing frequency matches with the eigenfrequency of the rotating annulus the beam pattern amplitude is increasing, the beams broaden and mode structures can be observed (Borcia et al., 2013a). The eigenmodes are compared with analytical solutions of the corresponding inviscid problem (Borcia et al, 2013b). In particular for the pressure field a good agreement can be found. However, shear layers related to the excited wave beams are present for all frequencies. This becomes obvious in particular in the experimental visualizations that are done by using Kalliroscope particles, highlighting relative motion in the fluid. Comparing the eigenfrequencies we find that relative to the analytical frequencies, the experimental and numerical ones show a small shift towards higher frequencies. This frequency shift is due to the reduction of the effective resonance volume that results from the existence of a Stokes boundary layer at the outer librating wall. Due to the symmetry of the forcing not all possible modes can be excited. It is shown that only symmetric modes with respect to the rotation axis exist. From a fundamental perspective, the study might help to understand better inertial mode excitation in librating planets and moons where inertial waves are emitted from critical points on the inner or outer spherical boundary. Recently, Zhang et al. (2013) pointed out the resonance should not occur in symmetric librating bodies without precession. We will discuss how this assumption depends on the boundary conditions. It might turn out that even when the projection of the Euler (or Poincare) force on the modes is zero, the projection of the excited wave beams on the modes is non-zero. K. Zhang, K. H. Chan, X. Liao, and J. M. Aurnou. The non-resonant response of fluid in a rapidly rotating sphere undergoing longitudinal libration, J. Fluid Mech.,720, 212-235, 2013. I. D. Borcia and U. Harlander. Inertial waves in a rotating annulus with inclined inner cylinder, Theoret. Comp. Fluid Dynamics, 27, 397-413, 2013. I. D. Borcia, A. Ghasemi V., and U. Harlander. Inertial wave mode excitation inside a rotating cylindrical container with librating walls, submitted to Fluid Dyn. Res.,2013. M. Klein, T. Seelig, M. V. Kurgansky, A. Ghasemi V., I. D. Borcia, A. Will, E. Schaller, C. Egbers, and Uwe Harlander. Inertial wave excitation and focusing in a liquid bounded by a frustum and a cylinder, submitted to J. Fluid Mech., 2013.

Computation of the Quantities Describing the Lunar Librations in the Astronomical Almanac

DTIC Science & Technology

2010-08-01

this system ~e ( COS( -(3) cost >. + 180’ - tt)) cost -(3) sine>. + 180’ - tt) sin(-(3) , (1) Consid~r neXt, point M referred to axes OX’’z’ iIi...now write (7) as the three equl\\tions " cos b cos(1 + LM - tt) = cosj3 cost >. - tt - N) cos b sin(1 + LM - tt) ,= cos Lcosj3si,n(>’,- tt -’N) ,- sin...8217?’~ on . .the sel~~~centric sphere. The geocentric right ascension and declination of the Moon are 0:, 0 and so the right ascension and declination of

A new method for automated discontinuity trace mapping on rock mass 3D surface model

NASA Astrophysics Data System (ADS)

Li, Xiaojun; Chen, Jianqin; Zhu, Hehua

2016-04-01

This paper presents an automated discontinuity trace mapping method on a 3D surface model of rock mass. Feature points of discontinuity traces are first detected using the Normal Tensor Voting Theory, which is robust to noisy point cloud data. Discontinuity traces are then extracted from feature points in four steps: (1) trace feature point grouping, (2) trace segment growth, (3) trace segment connection, and (4) redundant trace segment removal. A sensitivity analysis is conducted to identify optimal values for the parameters used in the proposed method. The optimal triangular mesh element size is between 5 cm and 6 cm; the angle threshold in the trace segment growth step is between 70° and 90°; the angle threshold in the trace segment connection step is between 50° and 70°, and the distance threshold should be at least 15 times the mean triangular mesh element size. The method is applied to the excavation face trace mapping of a drill-and-blast tunnel. The results show that the proposed discontinuity trace mapping method is fast and effective and could be used as a supplement to traditional direct measurement of discontinuity traces.

Spin and charge controlled by antisymmetric spin-orbit coupling in a triangular-triple-quantum-dot Kondo system

NASA Astrophysics Data System (ADS)

Koga, M.; Matsumoto, M.; Kusunose, H.

2018-05-01

We study a local antisymmetric spin-orbit (ASO) coupling effect on a triangular-triple-quantum-dot (TTQD) system as a theoretical proposal for a new application of the Kondo physics to nanoscale devices. The electric polarization induced by the Kondo effect is strongly correlated with the spin configurations and molecular orbital degrees of freedom in the TTQD. In particular, an abrupt sign reversal of the emergent electric polarization is associated with a quantum critical point in a magnetic field, which can also be controlled by the ASO coupling that changes the mixing weight of different orbital components in the TTQD ground state.

The Suess-Urey mission (return of solar matter to Earth).

PubMed

Rapp, D; Naderi, F; Neugebauer, M; Sevilla, D; Sweetnam, D; Burnett, D; Wiens, R; Smith, N; Clark, B; McComas, D; Stansbery, E

1996-01-01

The Suess-Urey (S-U) mission has been proposed as a NASA Discovery mission to return samples of matter from the Sun to the Earth for isotopic and chemical analyses in terrestrial laboratories to provide a major improvement in our knowledge of the average chemical and isotopic composition of the solar system. The S-U spacecraft and sample return capsule will be placed in a halo orbit around the L1 Sun-Earth libration point for two years to collect solar wind ions which implant into large passive collectors made of ultra-pure materials. Constant Spacecraft-Sun-Earth geometries enable simple spin stabilized attitude control, simple passive thermal control, and a fixed medium gain antenna. Low data requirements and the safety of a Sun-pointed spinner, result in extremely low mission operations costs.

Spaceflight mechanics 1992; Proceedings of the 2nd AAS/AIAA Meeting, Colorado Springs, CO, Feb. 24-26, 1992. Pts. 1 & 2

NASA Astrophysics Data System (ADS)

Diehl, Roger E.; Schinnerer, Ralph G.; Williamson, Walton E.; Boden, Daryl G.

The present conference discusses topics in orbit determination, tethered satellite systems, celestial mechanics, guidance optimization, flexible body dynamics and control, attitude dynamics and control, Mars mission analyses, earth-orbiting mission analysis/debris, space probe mission analyses, and orbital computation numerical analyses. Attention is given to electrodynamic forces for control of tethered satellite systems, orbiting debris threats to asteroid flyby missions, launch velocity requirements for interceptors of short range ballistic missiles, transfers between libration-point orbits in the elliptic restricted problem, minimum fuel spacecraft reorientation, orbital guidance for hitting a fixed point at maximum speed, efficient computation of satellite visibility periods, orbit decay and reentry prediction for space debris, and the determination of satellite close approaches.

Active and Passive Sensing from Geosynchronous and Libration Orbits

NASA Technical Reports Server (NTRS)

Schoeberl, Mark; Raymond, Carol; Hildebrand, Peter

2003-01-01

The development of the LEO (EOS) missions has led the way to new technologies and new science discoveries. However, LEO measurements alone cannot cost effectively produce high time resolution measurements needed to move the science to the next level. Both GEO and the Lagrange points, L1 and L2, provide vantage points that will allow higher time resolution measurements. GEO is currently being exploited by weather satellites, but the sensors currently operating at GEO do not provide the spatial or spectral resolution needed for atmospheric trace gas, ocean or land surface measurements. It is also may be possible to place active sensors in geostationary orbit. It seems clear, that the next era in earth observation and discovery will be opened by sensor systems operating beyond near earth orbit.

Determination of Phobos' rotational parameters by an inertial frame bundle block adjustment

NASA Astrophysics Data System (ADS)

Burmeister, Steffi; Willner, Konrad; Schmidt, Valentina; Oberst, Jürgen

2018-01-01

A functional model for a bundle block adjustment in the inertial reference frame was developed, implemented and tested. This approach enables the determination of rotation parameters of planetary bodies on the basis of photogrammetric observations. Tests with a self-consistent synthetic data set showed that the implementation converges reliably toward the expected values of the introduced unknown parameters of the adjustment, e.g., spin pole orientation, and that it can cope with typical observational errors in the data. We applied the model to a data set of Phobos using images from the Mars Express and the Viking mission. With Phobos being in a locked rotation, we computed a forced libration amplitude of 1.14^circ ± 0.03^circ together with a control point network of 685 points.

Spaceflight mechanics 1992; Proceedings of the 2nd AAS/AIAA Meeting, Colorado Springs, CO, Feb. 24-26, 1992. Pts. 1 & 2

NASA Technical Reports Server (NTRS)

Diehl, Roger E. (Editor); Schinnerer, Ralph G. (Editor); Williamson, Walton E. (Editor); Boden, Daryl G. (Editor)

1992-01-01

The present conference discusses topics in orbit determination, tethered satellite systems, celestial mechanics, guidance optimization, flexible body dynamics and control, attitude dynamics and control, Mars mission analyses, earth-orbiting mission analysis/debris, space probe mission analyses, and orbital computation numerical analyses. Attention is given to electrodynamic forces for control of tethered satellite systems, orbiting debris threats to asteroid flyby missions, launch velocity requirements for interceptors of short range ballistic missiles, transfers between libration-point orbits in the elliptic restricted problem, minimum fuel spacecraft reorientation, orbital guidance for hitting a fixed point at maximum speed, efficient computation of satellite visibility periods, orbit decay and reentry prediction for space debris, and the determination of satellite close approaches.

Computer simulating observations of the Lunar physical libration for the Japanese Lunar project ILOM

NASA Astrophysics Data System (ADS)

Petrova, Natalia; Hanada, Hideo

2010-05-01

In the frame of the second stage of the Japanese space mission SELENE-2 (Hanada et al. 2009) the project ILOM (In-situ Lunar Orientation Measurement) planned after 2017years is a kind of instrument for positioning on the Moon. It will be set near the lunar pole and will determine parameters of lunar physical libration by positioning of several tens of stars in the field of view regularly for longer than one year. Presented work is dedicated to analyses of computer simulating future observations. It's proposed that for every star crossing lunar prime meridian its polar distance will be to measure. The methods of optimal star observation are being developed for the future experiment. The equations are constructed to determine libration angles ? (t),ρ(t),σ(t)- on the basis of observed polar distances pobs: (| f1(?,ρ,Iσ,pobs) = 0 |{ f2(?,ρ,Iσ,pobs) = 0 | f3(?,ρ,Iσ,pobs) = 0 |( or f(X) = 0, where ; f = ? f1 ? | f2 | |? f3 |? X = ? ? ? | ρ | |? Iσ |? (1) At the present stage we have developed the software for selection of stars for these future polar observations. Stars were taken from various stellar catalogues, such as the UCAC2-BSS, Hipparcos, Tycho and FK6. The software reduces ICRS coordinates of star to selenographical system at the epoch of observation (Petrova et al., 2009). For example, to the epochs 2017 - 2018 more than 50 stars brighter than m = 12 were selected for the northern pole. In total, these stars give about 600 crossings of the prime meridian during one year. Nevertheless, only a few stars (2-5) may be observed in a vicinity of the one moment. This is not enough to have sufficient sample to exclude various kind of errors. The software includes programmes which can determine the moment of transition of star across the meridian and theoretical values of libration angles at this moments. A serious problem arises when we try to solve equations (1) with the purpose to determine libration angles on the basis of simulated pobs.. Polar distances are calculated using the analytical theory of physical libration Petrova et al. (2008; 2009). We cannot use Newton's method for solution of the equation, because the Jacobian | | || δδfx11 δδfx12 δδf1x3-|| || δδfx2 δδfx2 δδf2x-|| J(X ) = || δf13 δf23 δ3f3-|| = 0. || δx1 δx2 δx3 || We transformed equations to the iteration form xi = φi(X). Used iteration methods have unsatisfactory convergence: inaccuracy in polar distance of 1 milliseconds of arc causes inaccuracy of 0.01arcsec in ρ and in Iσ, and 0.1 arcsec in ?. Results of our computer simulating showed It's necessary to carry out measuring of polar distances of stars in several meridians simultaneously to increase sample of stars. It's necessary to find additional links (relations) between observed parameters and libration angles to have stable mathematical methods to receive solutions for lunar rotation with high accuracy. The research was supported by the Russian-Japanese grant RFFI-JSPS 09-02-92113, (2009-2010) References: Hanada H., Noda H., Kikuchi F. et al., 2009. Different kind of observations of lunar rotation and gravity for SELENE-2. Proc of conf. Astrokazan-2009, August 19 - 26, Kazan, Russia. p. 172-175 Petrova N., Gusev A., Kawano N., Hanada H., 2008. Free librations of the two-layer Moon and the possibilities of their detection. Advances in Space Res., v 42, p. 1398-1404 Petrova N., Gusev A., Hanada H., Ivanova T., Akutina V., 2009. Application of the analytical theory of Lunar physical libration for simulating observations of stars for the future Japanese project ILOM. Proc of conf. Astrokazan-2009, August 19 - 26, Kazan, Russia. p.197 - 201.

Weighted optimization of irradiance for photodynamic therapy of port wine stains

NASA Astrophysics Data System (ADS)

He, Linhuan; Zhou, Ya; Hu, Xiaoming

2016-10-01

Planning of irradiance distribution (PID) is one of the foremost factors for on-demand treatment of port wine stains (PWS) with photodynamic therapy (PDT). A weighted optimization method for PID was proposed according to the grading of PWS with a three dimensional digital illumination instrument. Firstly, the point clouds of lesions were filtered to remove the error or redundant points, the triangulation was carried out and the lesion was divided into small triangular patches. Secondly, the parameters such as area, normal vector and orthocenter for optimization of each triangular patch were calculated, and the weighted coefficients were determined by the erythema indexes and areas of patches. Then, the optimization initial point was calculated based on the normal vectors and orthocenters to optimize the light direction. In the end, the irradiation can be optimized according to cosine values of irradiance angles and weighted coefficients. Comparing the irradiance distribution before and after optimization, the proposed weighted optimization method can make the irradiance distribution match better with the characteristics of lesions, and has the potential to improve the therapeutic efficacy.

Aesthetic judgment of triangular shape: compactness and not the golden ratio determines perceived attractiveness

PubMed Central

Friedenberg, Jay

2012-01-01

Many studies over a period of more than a century have investigated the influence of the golden ratio on perceived geometric beauty. Surprisingly, very few of these studies used triangular shapes. In Experiment 1, we presented right triangles that differed in regard to their elongation determined by increasing the length of one side relative to another. Attractiveness ratings did not peak at the golden ratio, but there was a very strong influence of axis ratio overall. Participant ratings were a negative decreasing function of ratio. Triangles that pointed upward were judged as significantly more attractive than those that pointed down. We interpret these results according to a compactness hypothesis: triangles that are more compact are less likely to move or break and are thus considered more pleasing. Orientation also affects aesthetics. Upward-pointing triangles with a base parallel to the ground, regardless of their compactness, are also considered more perceptually stable and attractive. These findings were replicated across stimulus type in a second experiment with isosceles triangles and across testing procedure in a third experiment using a paired comparison technique. PMID:23145277

3D animation of facial plastic surgery based on computer graphics

NASA Astrophysics Data System (ADS)

Zhang, Zonghua; Zhao, Yan

2013-12-01

More and more people, especial women, are getting desired to be more beautiful than ever. To some extent, it becomes true because the plastic surgery of face was capable in the early 20th and even earlier as doctors just dealing with war injures of face. However, the effect of post-operation is not always satisfying since no animation could be seen by the patients beforehand. In this paper, by combining plastic surgery of face and computer graphics, a novel method of simulated appearance of post-operation will be given to demonstrate the modified face from different viewpoints. The 3D human face data are obtained by using 3D fringe pattern imaging systems and CT imaging systems and then converted into STL (STereo Lithography) file format. STL file is made up of small 3D triangular primitives. The triangular mesh can be reconstructed by using hash function. Top triangular meshes in depth out of numbers of triangles must be picked up by ray-casting technique. Mesh deformation is based on the front triangular mesh in the process of simulation, which deforms interest area instead of control points. Experiments on face model show that the proposed 3D animation facial plastic surgery can effectively demonstrate the simulated appearance of post-operation.

Competition between dynamic and structural disorder in a doped triangular antiferromagnet RbFe(MoO4)2

NASA Astrophysics Data System (ADS)

Smirnov, A. I.; Soldatov, T. A.; Petrenko, O. A.; Takata, A.; Kida, T.; Hagiwara, M.; Zhitomirsky, M. E.; Shapiro, A. Ya

2018-03-01

Magnetisation measurements and electron spin resonance (ESR) spectra of a doped quasi two dimensional (2D) antiferromagnet on a triangular lattice Rb1 ‑ x K x Fe(MoO4)2 reveal a crucial change of the ground state spin configuration and a disappearance of a characteristic 1/3-magnetisation plateau at x = 0.15. According to theory for triangular antiferromagnets with a weak random modulation of the exchange bonds, this is a result of the competition between the structural and dynamic disorders. The dynamic zero-point or thermal fluctuations are known to lift the degeneracy of the mean field ground state of a triangular antiferromagnet and cause the spin configuration to be the most collinear, while the static disorder provides another selection of the ground state, with the least collinear structure. Low-level doping (x ≤ 0.15) was found to decrease the Néel temperature and saturation field by only few percent, while the magnetisation plateau disappears completely and the spin configuration is drastically changed. ESR spectra confirm an impurity-induced change of the so-called Y-type structure to an inverted Y-structure for x = 0.15. For x = 0.075 the intermediate regime with the decrease of width and weakening of flattening of 1/3-plateau was found.

A technique for processing of planetary images with heterogeneous characteristics for estimating geodetic parameters of celestial bodies with the example of Ganymede

NASA Astrophysics Data System (ADS)

Zubarev, A. E.; Nadezhdina, I. E.; Brusnikin, E. S.; Karachevtseva, I. P.; Oberst, J.

2016-09-01

The new technique for generation of coordinate control point networks based on photogrammetric processing of heterogeneous planetary images (obtained at different time, scale, with different illumination or oblique view) is developed. The technique is verified with the example for processing the heterogeneous information obtained by remote sensing of Ganymede by the spacecraft Voyager-1, -2 and Galileo. Using this technique the first 3D control point network for Ganymede is formed: the error of the altitude coordinates obtained as a result of adjustment is less than 5 km. The new control point network makes it possible to obtain basic geodesic parameters of the body (axes size) and to estimate forced librations. On the basis of the control point network, digital terrain models (DTMs) with different resolutions are generated and used for mapping the surface of Ganymede with different levels of detail (Zubarev et al., 2015b).

Secular dynamics of an exterior test particle: the inverse Kozai and other eccentricity-inclination resonances

NASA Astrophysics Data System (ADS)

Vinson, Benjamin R.; Chiang, Eugene

2018-03-01

The behaviour of an interior test particle in the secular three-body problem has been studied extensively. A well-known feature is the Lidov-Kozai resonance in which the test particle's argument of periastron librates about ±90° and large oscillations in eccentricity and inclination are possible. Less explored is the inverse problem: the dynamics of an exterior test particle and an interior perturber. We survey numerically the inverse secular problem, expanding the potential to hexadecapolar order and correcting an error in the published expansion. Four secular resonances are uncovered that persist in full N-body treatments (in what follows, ϖ and Ω are the longitudes of periapse and of ascending node, ω is the argument of periapse, and subscripts 1 and 2 refer to the inner perturber and the outer test particle): (i) an orbit-flipping quadrupole resonance requiring a non-zero perturber eccentricity e1, in which Ω2 - ϖ1 librates about ±90°; (ii) a hexadecapolar resonance (the `inverse Kozai' resonance) for perturbers that are circular or nearly so and inclined by I ≃ 63°/117°, in which ω2 librates about ±90° and which can vary the particle eccentricity by Δe2 ≃ 0.2 and lead to orbit crossing; (iii) an octopole `apse-aligned' resonance at I ≃ 46°/107° wherein ϖ2 - ϖ1 librates about 0° and Δe2 grows with e1; and (iv) an octopole resonance at I ≃ 73°/134° wherein ϖ2 + ϖ1 - 2Ω2 librates about 0° and Δe2 can be as large as 0.3 for small but non-zero e1. Qualitatively, the more eccentric the perturber, the more the particle's eccentricity and inclination vary; also, more polar orbits are more chaotic. Our solutions to the inverse problem have potential application to the Kuiper belt and debris discs, circumbinary planets, and hierarchical stellar systems.

Measurements of Mercury's spin state and inferences about its interior

NASA Astrophysics Data System (ADS)

Margot, J.; Padovan, S.; Peale, S. J.; Solomon, S. C.

2011-12-01

Over the past nine years we have used the Green Bank Telescope (GBT) in conjunction with the Goldstone Solar System Radar (GSSR) to characterize the spin state and interior of Mercury. We implemented a technique [1,2] that provides instantaneous spin rate measurements with 10-5 fractional precision and spin orientation measurements at the arcsecond level. On the basis of measurements at 21 distinct epochs between 2002 and 2006, we found observational evidence that Mercury closely follows a Cassini state and that it exhibits forced librations in longitude [3], as predicted by theory [4,5]. A long-period (˜12 year) libration signature may be present in the data. Since 2006 we have secured measurements at 11 additional epochs (out of 23 attempts). We are in the process of re-analyzing the entire set of observations with the goals of (1) refining the determination of the obliquity and of the libration amplitude, two parameters that are critical in the determination of the core size; (2) confirming the presence or absence of a long-period libration component, with the prospect of elucidating the excitation mechanism; (3) quantifying deviations of the pole from the strict Cassini state, which could inform us about dissipation due to solid-body tides and core-mantle interactions. Our first goal is particularly important now that MESSENGER is securing measurements of the low-degree gravitational harmonics with an expected precision of better than 1%. The core-size error budget indicates that the precision of the ground-based estimates of obliquity and librations will ultimately dictate the quality of the core size determination, as well as the attendant inferences regarding the interior structure, thermal evolution, and magnetic field generation of the planet. [1] Green, in Radar Astronomy, McGraw-Hill, 1968. [2] Holin, Radiophys. Quant. Elec. 31, 1988. [3] Margot et al, Science 316, 2007. [4] Peale, Nature 262, 1976. [5] Peale, in Mercury, U. of Arizona Press, 1988.

Natural motion around the Martian moon Phobos: the dynamical substitutes of the Libration Point Orbits in an elliptic three-body problem with gravity harmonics

NASA Astrophysics Data System (ADS)

Zamaro, M.; Biggs, J. D.

2015-07-01

The Martian moon Phobos is becoming an appealing destination for future scientific missions. The orbital dynamics around this planetary satellite is particularly complex due to the unique combination of both small mass-ratio and length-scale of the Mars-Phobos couple: the resulting sphere of influence of the moon is very close to its surface, therefore both the classical two-body problem and circular restricted three-body problem (CR3BP) do not provide an accurate approximation to describe the spacecraft's dynamics in the vicinity of Phobos. The aim of this paper is to extend the model of the CR3BP to consider the orbital eccentricity and the highly-inhomogeneous gravity field of Phobos, by incorporating the gravity harmonics series expansion into an elliptic R3BP, named ER3BP-GH. Following this, the dynamical substitutes of the Libration Point Orbits (LPOs) are computed in this more realistic model of the relative dynamics around Phobos, combining methodologies from dynamical systems theory and numerical continuation techniques. Results obtained show that the structure of the periodic and quasi-periodic LPOs differs substantially from the classical case without harmonics. Several potential applications of these natural orbits are presented to enable unique low-cost operations in the proximity of Phobos, such as close-range observation, communication, and passive radiation shielding for human spaceflight. Furthermore, their invariant manifolds are demonstrated to provide high-performance natural landing and take-off pathways to and from Phobos' surface, and transfers from and to Martian orbits. These orbits could be exploited in upcoming and future space missions targeting the exploration of this Martian moon.

Rotation-libration in a hierarchic supramolecular rotor-stator system: arrhenius activation and retardation by local interaction.

PubMed

Wahl, Markus; Stöhr, Meike; Spillmann, Hannes; Jung, Thomas A; Gade, Lutz H

2007-04-07

Fourfold symmetric zinc-octaethylporphyrin (OEP) has been incorporated in the holes of the hexagonal molecular network generated by thermal dehydrogenation of 4,9-diaminoperylene-quinone-3,10-diimine (DPDI) on a Cu(111) surface and displayed hindered rotation; the reorganization between the potential minima, a rotation-libration, which is characterized by an activation energy of ED=0.17+/-0.03 eV, has been monitored in the STM tunnelling currents as a bi-state "switching".

The strange case of the missing apocentric librators in the 3:2 resonance. [in asteroidal belt

NASA Technical Reports Server (NTRS)

Ip, W.-H.

1976-01-01

From a comparison of the 2:1 and 3:2 resonances (in the asteroidal belt) two possible explanations to the absence of 3:2 apocentric librators are suggested. The first one is that such 3:2 resonant motion is dynamically unstable. The second interpretation requires the absence of near-circular orbits originally at 4 AU. The latter view, if correct, is inconsistent with cosmogonic models which predict the original orbits of the asteroids to be nearly circular.

LASER APPLICATIONS AND OTHER TOPICS IN QUANTUM ELECTRONICS: Study of the subpicosecond rotational molecular dynamics in liquids

NASA Astrophysics Data System (ADS)

Nikiforov, V. G.; Lobkov, Vladimir S.

2006-10-01

The parameters of the femtosecond vibration—rotation molecular dynamics of liquid acetonitrile CH3CN, trimethylacetonitrile (CH3)3CCN, propionitrile CH3CH2CN, fluoroform CHF3, and chloroform CHCl3 are found by analysing the ultrafast optical Kerr effect. The influence of the molecular structure on the features of rotational (diffusion and libration) motions is studied. It is shown that the distribution of libration frequencies is described by the Maxwell distribution.

Structure and Reversibility of 2D von Neumann Cellular Automata Over Triangular Lattice

NASA Astrophysics Data System (ADS)

Uguz, Selman; Redjepov, Shovkat; Acar, Ecem; Akin, Hasan

2017-06-01

Even though the fundamental main structure of cellular automata (CA) is a discrete special model, the global behaviors at many iterative times and on big scales could be a close, nearly a continuous, model system. CA theory is a very rich and useful phenomena of dynamical model that focuses on the local information being relayed to the neighboring cells to produce CA global behaviors. The mathematical points of the basic model imply the computable values of the mathematical structure of CA. After modeling the CA structure, an important problem is to be able to move forwards and backwards on CA to understand their behaviors in more elegant ways. A possible case is when CA is to be a reversible one. In this paper, we investigate the structure and the reversibility of two-dimensional (2D) finite, linear, triangular von Neumann CA with null boundary case. It is considered on ternary field ℤ3 (i.e. 3-state). We obtain their transition rule matrices for each special case. For given special triangular information (transition) rule matrices, we prove which triangular linear 2D von Neumann CAs are reversible or not. It is known that the reversibility cases of 2D CA are generally a much challenged problem. In the present study, the reversibility problem of 2D triangular, linear von Neumann CA with null boundary is resolved completely over ternary field. As far as we know, there is no structure and reversibility study of von Neumann 2D linear CA on triangular lattice in the literature. Due to the main CA structures being sufficiently simple to investigate in mathematical ways, and also very complex to obtain in chaotic systems, it is believed that the present construction can be applied to many areas related to these CA using any other transition rules.

Transition-metal oxides with triangular lattices: generation of new magnetic and electronic properties.

PubMed

Maignan, A; Kobayashi, W; Hébert, S; Martinet, G; Pelloquin, D; Bellido, N; Simon, Ch

2008-10-06

The search for multifunctional materials as multiferroics to be applied in microelectronic or for new, chemically stable and nontoxic, thermoelectric materials to recover waste heat is showing a common interest in the oxides whose structures contain a triangular network of transition-metal cations. To illustrate this point, two ternary systems, Ba-Co-O and Ca-Co-O, have been chosen. It is shown that new phases with a complex triangular structure can be discovered, for instance, by introduction of Ga (3+) into the Ba-Co-O system to stabilize Ba 6Ga 2Co 11O 26 and Ba 2GaCo 8O 14, which both belong to a large family of compounds with formula [Ba(Co,Ga)O 3-delta] n [BaCo 8O 11]. In the latter, both sublattices contain triangular networks derived from the hexagonal perovskite and the spinel structure. Among the hexagonal perovskite, the Ca 3Co 2O 6 crystals give clear evidence where the coupling of charges and spins is at the origin of a magnetocapacitance effect. In particular, the ferrimagnetic to ferromagnetic transition, with a one-third plateau on the M( H) curve characteristic of triangular magnetism, is accompanied by a peak in the dielectric constant. A second class of cobaltites is the focus of much interest. Their 2D structure, containing CoO 2 planes isostructural to a CdI 2 slice that are stacked in an incommensurate way with rock salt type layers, is referred to misfit cobaltite. The 2D triangular network of edge-shared CoO 6 octahedra is believed to be responsible for large values of the Seebeck coefficient and low electrical resistivity. A clear relationship between the structuresincommensurability ratiosand the electronic properties is evidenced, showing that the charge carrier concentration can be tuned via the control of the ionic radius of the cations in the separating layers.

Existence and instability of steady states for a triangular cross-diffusion system: A computer-assisted proof

NASA Astrophysics Data System (ADS)

Breden, Maxime; Castelli, Roberto

2018-05-01

In this paper, we present and apply a computer-assisted method to study steady states of a triangular cross-diffusion system. Our approach consist in an a posteriori validation procedure, that is based on using a fixed point argument around a numerically computed solution, in the spirit of the Newton-Kantorovich theorem. It allows to prove the existence of various non homogeneous steady states for different parameter values. In some situations, we obtain as many as 13 coexisting steady states. We also apply the a posteriori validation procedure to study the linear stability of the obtained steady states, proving that many of them are in fact unstable.

Emittance Measurements for a Thin Liquid Sheet Flow

NASA Technical Reports Server (NTRS)

Englehart, Amy N.; McConley, Marc W.; Chubb, Donald L.

1996-01-01

The Liquid Sheet Radiator (LSR) is an external flow radiator that uses a triangular-shaped flowing liquid sheet as the radiating surface. It has potentially much lower mass than solid wall radiators such as pumped loop and heat pipe radiators, along with being nearly immune to micrometeoroid penetration. The LSR has an added advantage of simplicity. Surface tension causes a thin (100-300 microns) liquid sheet to coalesce to a point, causing the sheet flow to have a triangular shape. Such a triangular sheet is desirable since it allows for simple collection of the flow at a single point. A major problem for all external flow radiators is the requirement that the working fluid be of very low (approx. 10(sup -8) torr) vapor pressure to keep evaporative losses low. As a result, working fluids are limited to certain oils (such as used in diffusion pumps) for low temperatures (300-400 K) and liquid metals for higher temperatures. Previous research on the LSR has been directed at understanding the fluid mechanics of thin sheet flows and assessing the stability of such flows, especially with regard to the formation of holes in the sheet. Taylor studied extensively the stability of thin liquid sheets both theoretically and experimentally. He showed that thin sheets in a vacuum are stable. The latest research has been directed at determining the emittance of thin sheet flows. The emittance was calculated from spectral transmittance data for the Dow Corning 705 silicone oil. By experimentally setting up a sheet flow, the emittance was also determined as a function of measurable quantities, most importantly, the temperature drop between the top of the sheet and the temperature at the coalescence point of the sheet. Temperature fluctuations upstream of the liquid sheet were a potential problem in the analysis and were investigated.

Normalization of Hamiltonian and nonlinear stability of the triangular equilibrium points in non-resonance case with perturbations

NASA Astrophysics Data System (ADS)

Kishor, Ram; Kushvah, Badam Singh

2017-09-01

For the study of nonlinear stability of a dynamical system, normalized Hamiltonian of the system is very important to discuss the dynamics in the vicinity of invariant objects. In general, it represents a nonlinear approximation to the dynamics, which is very helpful to obtain the information as regards a realistic solution of the problem. In the present study, normalization of the Hamiltonian and analysis of nonlinear stability in non-resonance case, in the Chermnykh-like problem under the influence of perturbations in the form of radiation pressure, oblateness, and a disc is performed. To describe nonlinear stability, initially, quadratic part of the Hamiltonian is normalized in the neighborhood of triangular equilibrium point and then higher order normalization is performed by computing the fourth order normalized Hamiltonian with the help of Lie transforms. In non-resonance case, nonlinear stability of the system is discussed using the Arnold-Moser theorem. Again, the effects of radiation pressure, oblateness and the presence of the disc are analyzed separately and it is observed that in the absence as well as presence of perturbation parameters, triangular equilibrium point is unstable in the nonlinear sense within the stability range 0<μ<μ1=\\bar{μc} due to failure of the Arnold-Moser theorem. However, perturbation parameters affect the values of μ at which D4=0, significantly. This study may help to analyze more generalized cases of the problem in the presence of some other types of perturbations such as P-R drag and solar wind drag. The results are limited to the regular symmetric disc but it can be extended in the future.

Use of Invariant Manifolds for Transfers Between Three-Body Systems

NASA Technical Reports Server (NTRS)

Beckman, Mark; Howell, Kathleen

2003-01-01

The Lunar L1 and L2 libration points have been proposed as gateways granting inexpensive access to interplanetary space. To date, only individual solutions to the transfer between three-body systems have been found. The methodology to solve the problem for arbitrary three-body systems and entire families of orbits does not exist. This paper presents the initial approaches to solve the general problem for single and multiple impulse transfers. Two different methods of representing and storing 7-dimensional invariant manifold data are presented. Some particular solutions are presented for the transfer problem, though the emphasis is on developing methodology for solving the general problem.

End of Life Disposal for Three Libration Point Missions through Manipulation of the Jacobi Constant and Zero Velocity Curves

NASA Technical Reports Server (NTRS)

Peterson, Jeremy D.; Brown, Jonathan M.

2015-01-01

The aim of this investigation is to determine the feasibility of mission disposal by inserting the spacecraft into a heliocentric orbit along the unstable manifold and then manipulating the Jacobi constant to prevent the spacecraft from returning to the Earth-Moon system. This investigation focuses around L1 orbits representative of ACE, WIND, and SOHO. It will model the impulsive delta-V necessary to close the zero velocity curves after escape through the L1 gateway in the circular restricted three body model and also include full ephemeris force models and higher fidelity finite maneuver models for the three spacecraft.

Representations of Invariant Manifolds for Applications in Three-Body Systems

NASA Technical Reports Server (NTRS)

Howell, K.; Beckman, M.; Patterson, C.; Folta, D.

2004-01-01

The Lunar L1 and L2 libration points have been proposed as gateways granting inexpensive access to interplanetary space. To date, only individual solutions to the transfer between three-body systems have been found. The methodology to solve the problem for arbitrary three-body systems and entire families of orbits is currently being studied. This paper presents an initial approach to solve the general problem for single and multiple impulse transfers. Two different methods of representing and storing the invariant manifold data are presented. Some particular solutions are presented for two types of transfer problems, though the emphasis is on developing the methodology for solving the general problem.

Orbit Maintenance and Navigation of Human Spacecraft at Cislunar Near Rectilinear Halo Orbits

NASA Technical Reports Server (NTRS)

Davis, Diane; Bhatt, Sagar; Howell, Kathleen; Jang, Jiann-Woei; Whitley, Ryan; Clark, Fred; Guzzetti, Davide; Zimovan, Emily; Barton, Gregg

2017-01-01

Multiple studies have concluded that Earth-Moon libration point orbits are attractive candidates for staging operations. The Near Rectilinear Halo Orbit (NRHO), a member of the Earth-Moon halo orbit family, has been singularly demonstrated to meet multi-mission architectural constraints. In this paper, the challenges associated with operating human spacecraft in the NRHO are evaluated. Navigation accuracies and human vehicle process noise effects are applied to various station keeping strategies in order to obtain a reliable orbit maintenance algorithm. Additionally, the ability to absorb missed burns, construct phasing maneuvers to avoid eclipses and conduct rendezvous and proximity operations are examined.

Sun-Earth L1 Region Halo-To-Halo Orbit and Halo-To-LisaJous Orbit Transfers

NASA Technical Reports Server (NTRS)

Roberts, Craig E.; DeFazio, Robert

2004-01-01

Practical techniques for designing transfer trajectories between Libration Point Orbits (LPOs) are presented. Motivation for development of these techniques was provided by a hardware contingency experienced by the Solar Heliospheric Observatory (SOHO), a joint mission of the European Space Agency (ESA) and the National Aeronautics and Space Administration (NASA) orbiting the L1 point of the Sun-Earth system. A potential solution to the problem involved a transfer from SOHO s periodic halo orbit to a new LPO of substantially different dimensions. Assuming the SOHO halo orbit as the departure orbit, several practical LPO transfer techniques were developed to obtain new Lissajous or periodic halo orbits that satisfy mission requirements and constraints. While not implemented for the SOHO mission, practical LPO transfer techniques were devised that are generally applicable to current and future LPO missions.

COMMENTS ON THE PAPER 'ON THE STABILITY OF TRIANGULAR LAGRANGIAN POINTS IN THE RESTRICTED THREE-BODY PROBLEM' (2008, AJ, 135, 187)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ivanov, A. P.

2009-06-15

In the referenced paper an analytical approach was introduced, which allows one to demonstrate the instability in linearly stable systems, specifically, in a classical three-body problem. These considerations are disproved here.

Ultrafast dynamics of liquid water: Energy relaxation and transfer processes of the OH stretch and the HOH bend

DOE Office of Scientific and Technical Information (OSTI.GOV)

Imoto, Sho; Xantheas, Sotiris S.; Saito, Shinji

2015-08-27

The vibrational energy relaxation and transfer processes of the OH stretching and the HOH bending vibrations in liquid water are investigated via the theoretical calculation of the pump-probe spectra obtained from non-equilibrium molecular dynamics simulations with the TTM3-F interaction potential. The excitation of the OH stretch induces an instantaneous response of the high frequency librational motions in the 600-1000 cm-1 range. In addition, the excess energy of the OH stretch of a water molecule quickly transfers to the OH stretches of molecules in its first hydration shell with a time constant of ~50 fs, followed by relaxation to the HOHmore » bends of the surrounding molecules with a time constant of 230 fs. The excitation of the HOH bend also results in the ultrafast excitation of the high frequency librational motions. The energy of the excited HOH bend of a water molecule decays, with a time constant of 200 fs, mainly to the relaxation of the HOH bends of its surrounding molecules. The energies of the HOH bends were found to transfer quickly to the intermolecular motions via the coupling with the high frequency librational motions. The excess energy of the OH stretch or the HOH bend relaxes to the high frequency intermolecular librational motions and eventually to the hot ground state with a time scale of ~1 ps via the coupling with the librational and translational motions. The energy relaxation and transfer processes were found to depend on the local hydrogen bonding network; the relaxations of the excess energy of the OH stretch and the HOH bend of four- and five-coordinated molecules are faster than those of a three-coordinated molecule due to the delocalization of the vibrational motions of the former (four- and five-coordinated molecules) compared to those of the later (three-coordinated molecules). The present results highlight the importance of the high frequency intermolecular librational modes in facilitating the ultrafast energy relaxation process in liquid water via their strong nonlinear couplings with the intramolecular OH stretching and HOH bending vibrations. S.S.X. acknowledges the support of the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences. Pacific Northwest National Laboratory (PNNL) is a multiprogram national laboratory operated for DOE by Battelle. The calculation was carried out using the computing resources at the Research Center for Computational Science in Okazaki, Japan.« less

ELAS: A general-purpose computer program for the equilibrium problems of linear structures. Volume 2: Documentation of the program. [subroutines and flow charts

NASA Technical Reports Server (NTRS)

Utku, S.

1969-01-01

A general purpose digital computer program for the in-core solution of linear equilibrium problems of structural mechanics is documented. The program requires minimum input for the description of the problem. The solution is obtained by means of the displacement method and the finite element technique. Almost any geometry and structure may be handled because of the availability of linear, triangular, quadrilateral, tetrahedral, hexahedral, conical, triangular torus, and quadrilateral torus elements. The assumption of piecewise linear deflection distribution insures monotonic convergence of the deflections from the stiffer side with decreasing mesh size. The stresses are provided by the best-fit strain tensors in the least squares at the mesh points where the deflections are given. The selection of local coordinate systems whenever necessary is automatic. The core memory is used by means of dynamic memory allocation, an optional mesh-point relabelling scheme and imposition of the boundary conditions during the assembly time.

Grey-Markov prediction model based on background value optimization and central-point triangular whitenization weight function

NASA Astrophysics Data System (ADS)

Ye, Jing; Dang, Yaoguo; Li, Bingjun

2018-01-01

Grey-Markov forecasting model is a combination of grey prediction model and Markov chain which show obvious optimization effects for data sequences with characteristics of non-stationary and volatility. However, the state division process in traditional Grey-Markov forecasting model is mostly based on subjective real numbers that immediately affects the accuracy of forecasting values. To seek the solution, this paper introduces the central-point triangular whitenization weight function in state division to calculate possibilities of research values in each state which reflect preference degrees in different states in an objective way. On the other hand, background value optimization is applied in the traditional grey model to generate better fitting data. By this means, the improved Grey-Markov forecasting model is built. Finally, taking the grain production in Henan Province as an example, it verifies this model's validity by comparing with GM(1,1) based on background value optimization and the traditional Grey-Markov forecasting model.

Design and characterization of planar capacitive imaging probe based on the measurement sensitivity distribution

NASA Astrophysics Data System (ADS)

Yin, X.; Chen, G.; Li, W.; Huthchins, D. A.

2013-01-01

Previous work indicated that the capacitive imaging (CI) technique is a useful NDE tool which can be used on a wide range of materials, including metals, glass/carbon fibre composite materials and concrete. The imaging performance of the CI technique for a given application is determined by design parameters and characteristics of the CI probe. In this paper, a rapid method for calculating the whole probe sensitivity distribution based on the finite element model (FEM) is presented to provide a direct view of the imaging capabilities of the planar CI probe. Sensitivity distributions of CI probes with different geometries were obtained. Influencing factors on sensitivity distribution were studied. Comparisons between CI probes with point-to-point triangular electrode pair and back-to-back triangular electrode pair were made based on the analysis of the corresponding sensitivity distributions. The results indicated that the sensitivity distribution could be useful for optimising the probe design parameters and predicting the imaging performance.

Cause and Cure - Deterioration in Accuracy of CFD Simulations with Use of High-Aspect-Ratio Triangular/Tetrahedral Grids

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Chang, Chau-Lyan; Venkatachari, Balaji Shankar

2017-01-01

Traditionally high-aspect ratio triangular/tetrahedral meshes are avoided by CFD researchers in the vicinity of a solid wall, as it is known to reduce the accuracy of gradient computations in those regions. Although for certain complex geometries, the use of high-aspect ratio triangular/tetrahedral elements in the vicinity of a solid wall can be replaced by quadrilateral/prismatic elements, ability to use triangular/tetrahedral elements in such regions without any degradation in accuracy can be beneficial from a mesh generation point of view. The benefits also carry over to numerical frameworks such as the space-time conservation element and solution element (CESE), where simplex elements are the mandatory building blocks. With the requirement of the CESE method in mind, a rigorous mathematical framework that clearly identifies the reason behind the difficulties in use of such high-aspect ratio simplex elements is formulated using two different approaches and presented here. Drawing insights from the analysis, a potential solution to avoid that pitfall is also provided as part of this work. Furthermore, through the use of numerical simulations of practical viscous problems involving high-Reynolds number flows, how the gradient evaluation procedures of the CESE framework can be effectively used to produce accurate and stable results on such high-aspect ratio simplex meshes is also showcased.

Large longitude libration of Mercury reveals a molten core.

PubMed

Margot, J L; Peale, S J; Jurgens, R F; Slade, M A; Holin, I V

2007-05-04

Observations of radar speckle patterns tied to the rotation of Mercury establish that the planet occupies a Cassini state with obliquity of 2.11 +/- 0.1 arc minutes. The measurements show that the planet exhibits librations in longitude that are forced at the 88-day orbital period, as predicted by theory. The large amplitude of the oscillations, 35.8 +/- 2 arc seconds, together with the Mariner 10 determination of the gravitational harmonic coefficient C22, indicates that the mantle of Mercury is decoupled from a core that is at least partially molten.

Nucleic acid binding drugs. Part XIII. Molecular motion in a drug-nucleic acid model system: thermal motion analysis of a proflavine-dinucleoside crystal structure.

PubMed Central

Aggarwal, A K; Neidle, S

1985-01-01

The high-resolution crystal structure of the intercalation complex between proflavine and cytidylyl-3',5'-guanosine (CpG) has been studied by thermalmotion analysis. This has provided information on the translational and librational motions of individual groups in the complex. Many of these motions are similar to, though of larger magnitude than in uncomplexed dinucleosides. Pronounced librational effects were observed along the base pairs and in the plane of the drug chromophore. PMID:4034394

The Rényi entanglement entropy of a general quantum dimer model at the RK point: a highly efficient algorithm.

PubMed

Pei, Jiquan; Han, Steve; Liao, Haijun; Li, Tao

2014-01-22

A highly efficient and simple-to-implement Monte Carlo algorithm is proposed for the evaluation of the Rényi entanglement entropy (REE) of the quantum dimer model (QDM) at the Rokhsar-Kivelson (RK) point. It makes possible the evaluation of REE at the RK point to the thermodynamic limit for a general QDM. We apply the algorithm to a QDM defined on the triangular and the square lattice in two dimensions and the simple and the face centered cubic (fcc) lattice in three dimensions. We find the REE on all these lattices follows perfect linear scaling in the thermodynamic limit, apart from an even-odd oscillation in the case of the square lattice. We also evaluate the topological entanglement entropy (TEE) with both a subtraction and an extrapolation procedure. We find the QDMs on both the triangular and the fcc lattice exhibit robust Z2 topological order. The expected TEE of ln2 is clearly demonstrated in both cases. Our large scale simulation also proves the recently proposed extrapolation procedure in cylindrical geometry to be a highly reliable way to extract the TEE of a topologically ordered system.

A new standing-wave-type linear ultrasonic motor based on in-plane modes.

PubMed

Shi, Yunlai; Zhao, Chunsheng

2011-05-01

This paper presents a new standing-wave-type linear ultrasonic motor using combination of the first longitudinal and the second bending modes. Two piezoelectric plates in combination with a metal thin plate are used to construct the stator. The superior point of the stator is its isosceles triangular structure part of the stator, which can amplify the displacement in horizontal direction of the stator in perpendicular direction when the stator is operated in the first longitudinal mode. The influence of the base angle θ of the triangular structure part on the amplitude of the driving foot has been analyzed by numerical analysis. Four prototype stators with different angles θ have been fabricated and the experimental investigation of these stators has validated the numerical simulation. The overall dimensions of the prototype stators are no more than 40 mm (length) × 20 mm (width) × 5 mm (thickness). Driven by an AC signal with the driving frequency of 53.3 kHz, the no-load speed and the maximal thrust of the prototype motor using the stator with base angle 20° were 98 mm/s and 3.2N, respectively. The effective elliptical motion trajectory of the contact point of the stator can be achieved by the isosceles triangular structure part using only two PZTs, and thus it makes the motor low cost in fabrication, simple in structure and easy to realize miniaturization. Copyright © 2010 Elsevier B.V. All rights reserved.

Large area multi-channel plasmonic absorber based on the touching triangular dimers fabricated by angle controlled colloidal nanolithography

NASA Astrophysics Data System (ADS)

Hamidi, S. M.; Behjati, S.

2018-02-01

Here we introduce large area plasmonic touching triangular dimers by angle controlled colloidal nanolithography to use them as an efficient multi channel absorber and also high figure of merit sensors. For this purpose, we coated gold thin films onto nanometric and also micrometric polystyrene hexagonal closed packed masks in different deposition angles and also diverse substrate polar angles. Our prepared samples, after remove masks, show large area touching triangular pattern with different inter particle distances in greater polar angles. To get more sense about optical response of the samples such as transmittance and also electric field distribution, we use finite difference time domain method in simulation part. The transmittance plot shows one narrow or multi-channel adjustable deep depend on inter-particle distances which can be controlled by azimuthally angle in nano lithography process. Also, due to the isoelliptical points in the transmittance spectra; we can see the bright and dark plasmon modes coupling and thus the Fano like resonance takes place in the optical spectral region which is very useful for refractive index measurement.

Cavity mode enhancement of terahertz emission from equilateral triangular microstrip antennas of the high-T c superconductor Bi2Sr2CaCu2O8 + δ.

PubMed

Cerkoney, Daniel P; Reid, Candy; Doty, Constance M; Gramajo, Ashley; Campbell, Tyler D; Morales, Manuel A; Delfanazari, Kaveh; Tsujimoto, Manabu; Kashiwagi, Takanari; Yamamoto, Takashi; Watanabe, Chiharu; Minami, Hidetoshi; Kadowaki, Kazuo; Klemm, Richard A

2017-01-11

We study the transverse magnetic (TM) electromagnetic cavity mode wave functions for an ideal equilateral triangular microstrip antenna (MSA) exhibiting C 3v point group symmetry. When the C 3v operations are imposed upon the antenna, the TM(m,n) modes with wave vectors [Formula: see text] are much less dense than commonly thought. The R 3 operations restrict the integral n and m to satisfy [Formula: see text], where [Formula: see text] and [Formula: see text] for the modes even and odd under reflections about the three mirror planes, respectively. We calculate the forms of representative wave functions and the angular dependence of the output power when these modes are excited by the uniform and non-uniform ac Josephson current sources in thin, ideally equilateral triangular MSAs employing the intrinsic Josephson junctions in the high transition temperature T c superconductor Bi 2 Sr 2 CaCu 2 [Formula: see text], and fit the emissions data from an earlier sample for which the C 3v symmetry was apparently broken.

Space station architectural elements model study

NASA Technical Reports Server (NTRS)

Taylor, T. C.; Spencer, J. S.; Rocha, C. J.; Kahn, E.; Cliffton, E.; Carr, C.

1987-01-01

The worksphere, a user controlled computer workstation enclosure, was expanded in scope to an engineering workstation suitable for use on the Space Station as a crewmember desk in orbit. The concept was also explored as a module control station capable of enclosing enough equipment to control the station from each module. The concept has commercial potential for the Space Station and surface workstation applications. The central triangular beam interior configuration was expanded and refined to seven different beam configurations. These included triangular on center, triangular off center, square, hexagonal small, hexagonal medium, hexagonal large and the H beam. Each was explored with some considerations as to the utilities and a suggested evaluation factor methodology was presented. Scale models of each concept were made. The models were helpful in researching the seven beam configurations and determining the negative residual (unused) volume of each configuration. A flexible hardware evaluation factor concept is proposed which could be helpful in evaluating interior space volumes from a human factors point of view. A magnetic version with all the graphics is available from the author or the technical monitor.

Balanced Central Schemes for the Shallow Water Equations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron

2004-01-01

We present a two-dimensional, well-balanced, central-upwind scheme for approximating solutions of the shallow water equations in the presence of a stationary bottom topography on triangular meshes. Our starting point is the recent central scheme of Kurganov and Petrova (KP) for approximating solutions of conservation laws on triangular meshes. In order to extend this scheme from systems of conservation laws to systems of balance laws one has to find an appropriate discretization of the source terms. We first show that for general triangulations there is no discretization of the source terms that corresponds to a well-balanced form of the KP scheme. We then derive a new variant of a central scheme that can be balanced on triangular meshes. We note in passing that it is straightforward to extend the KP scheme to general unstructured conformal meshes. This extension allows us to recover our previous well-balanced scheme on Cartesian grids. We conclude with several simulations, verifying the second-order accuracy of our scheme as well as its well-balanced properties.

Cause and Cure - Deterioration in Accuracy of CFD Simulations With Use of High-Aspect-Ratio Triangular Tetrahedral Grids

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Chang, Chau-Lyan; Venkatachari, Balaji Shankar

2017-01-01

Traditionally high-aspect ratio triangular/tetrahedral meshes are avoided by CFD re-searchers in the vicinity of a solid wall, as it is known to reduce the accuracy of gradient computations in those regions and also cause numerical instability. Although for certain complex geometries, the use of high-aspect ratio triangular/tetrahedral elements in the vicinity of a solid wall can be replaced by quadrilateral/prismatic elements, ability to use triangular/tetrahedral elements in such regions without any degradation in accuracy can be beneficial from a mesh generation point of view. The benefits also carry over to numerical frameworks such as the space-time conservation element and solution element (CESE), where triangular/tetrahedral elements are the mandatory building blocks. With the requirement of the CESE method in mind, a rigorous mathematical framework that clearly identities the reason behind the difficulties in use of such high-aspect ratio triangular/tetrahedral elements is presented here. As will be shown, it turns out that the degree of accuracy deterioration of gradient computation involving a triangular element is hinged on the value of its shape factor Gamma def = sq sin Alpha1 + sq sin Alpha2 + sq sin Alpha3, where Alpha1; Alpha2 and Alpha3 are the internal angles of the element. In fact, it is shown that the degree of accuracy deterioration increases monotonically as the value of Gamma decreases monotonically from its maximal value 9/4 (attained by an equilateral triangle only) to a value much less than 1 (associated with a highly obtuse triangle). By taking advantage of the fact that a high-aspect ratio triangle is not necessarily highly obtuse, and in fact it can have a shape factor whose value is close to the maximal value 9/4, a potential solution to avoid accuracy deterioration of gradient computation associated with a high-aspect ratio triangular grid is given. Also a brief discussion on the extension of the current mathematical framework to the tetrahedral-grid case along with some of the practical results of this extension is also provided. Furthermore, through the use of numerical simulations of practical viscous problems involving high-Reynolds number flows, the effectiveness of the gradient evaluation procedures within the CESE framework (that have their basis on the analysis presented here) to produce accurate and stable results on such high-aspect ratio meshes is also showcased.

Mimas: Constraints on Origin and Evolution from Libration Data

NASA Astrophysics Data System (ADS)

Neveu, Marc; Rhoden, Alyssa R.

2016-10-01

In stark contrast with its neighbor moon Enceladus, Mimas is surprisingly geologically quiet, despite an orbital configuration prone to levels of tidal dissipation 30 times higher. While Mimas' lack of activity could be due to a stiff, frigid interior, libration data from the Cassini spacecraft suggest its interior is not homogeneous [1]. Here, we present 1-D models of Mimas' thermal and structural evolution under two accretion scenarios: primordial, undifferentiated formation in the Saturnian subnebula [2]; and late, layered formation from a debris ring created by the disruption of one or more previous moons [3]. In the primordial scenario, our simulations yield two possible outcomes. If tidal dissipation proceeds at levels higher than those obtained using an Andrade rheology [4], Mimas differentiates and an ocean persists until the present day. This should quickly circularize its orbit, but the current orbit is eccentric. In addition, Mimas lacks surface fractures that should result from strong tidal stresses in an ice shell atop an ocean [5]. If dissipation proceeds at lower levels obtained using a Maxwell rheology, it is too weak to drive differentiation; this does not match the observed libration [1]. In the late accretion scenario, Mimas forms already differentiated. As a result, even its deepest ice is within only 100 km of the frigid surface, and poorly insulated by overlying thermally conductive crystalline ice. Thus, all ice remains cold and poorly dissipative, even if dissipation is an order of magnitude above that provided by the Andrade rheology [4]. If Mimas' rocky core is slightly non-hydrostatic [1], this matches the observed libration. We conclude that Mimas' libration is compatible with a late origin from a debris ring, but not with primordial accretion. Consistent with findings from many authors (e.g. [6]), these models cannot produce an ocean on Enceladus unless its orbital eccentricity is higher than observed.References:[1] Tajeddine et al. (2014) Science 346, 322[2] Peale (1999) Annu Rev Astron Astrophys 37, 533[3] Charnoz et al. (2011) Icarus 216, 535[4] McCarthy & Cooper (2016) EPSL 443, 185[5] Rhoden et al., JGR: Planets, submitted[6] Roberts & Nimmo (2008) Icarus 194, 675

Simulating the Librational Behaviour of Propeller Moons In The Saturnian Ring System

NASA Astrophysics Data System (ADS)

Seiler, Michael; Seiss, Martin; Hoffmann, Holger; Spahn, Frank

2016-10-01

The propeller structure Blériot orbiting in the outer A ring of the Saturnian ring system has been one of the tremendous discoveries of the spacecraft Cassini [Tiscareno et al., 2010, ApJL]. The reconstruction of the orbital evolution of Blériot from recurrent observations in the ISS images yielded a systematic offset motion from the expected Keplerian orbit. This offset motion can be well described by three sinusoidal harmonics with amplitudes and periods of 1845, 152, 58 km and 11.1, 3.7 and 2.2 years, respectively [Sremčević et al., 2014, EPSC]. Oscillatory deviations from the Keplerian orbit are a known phenomenon for the Saturnian moons, which can be explained by resonant interactions with other moons [Spitale et al., 2006, AJ] and which look similar to the observation of Blériot.In this work we present our results from N-Body simulations, where we integrated the orbital evolution of a test particle, orbiting at the radial position of the propeller Blériot and 15 other moons of Saturn. Our simulation yield, that gravitational interactions with the larger moons result in reasonable and observable frequencies, but the resulting amplitudes of the librations are by far too small to explain the observations. Further mechanisms are needed, to amplify the amplitudes of the forced librations -- as e.g. by moonlet-ring interactions. Inspired by the recent work of Pan and Chiang [2010, ApJL; 2012, AJ] we introduce an alternative, physically more reasonable model. In our model, the moonlet is allowed to be slightly displaced with respect to its created gaps, resulting in a repulsive force. As a result, the moonlet's longitude starts to oscillate. In the presence of the additional external forcing by the outer moons the libration amplitude gets amplified, if the forcing frequency is close to the eigenfrequency of the system. Applying our model to Blériot, we can indeed reproduce a libration period of 13 years with an amplitude of about 2000 km.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu, Yuan; Zuo, Xu, E-mail: xzuo@nankai.edu.cn; Feng, Min

Motivated by recent theoretical predications for Dirac cone in two-dimensional (2D) triangular lattice [H. Ishizuka, Phys. Rev. Lett. 109, 237207 (2012)], first-principles studies are performed to predict Dirac cones in artificial structures of 3d transitional-metals (TM = Ti, V, Cr, Mn, Fe, Co, Ni, and Cu) doped Mg-Al spinels. In investigated artificial structures, TM dopants substitute specific positions of the B sub-lattice in Mg-Al spinel, and form a quasi-2D triangular lattice in the a-b plane. Calculated results illustrate the existence of the spin-polarized Dirac cones formed in d-wave bands at (around) the K-point in the momentum space. The study provides a promisingmore » route for engineering Dirac physics in condensed matters.« less

The analytical and numerical approaches to the theory of the Moon's librations: Modern analysis and results

NASA Astrophysics Data System (ADS)

Petrova, N.; Zagidullin, A.; Nefedyev, Y.; Kosulin, V.; Andreev, A.

2017-11-01

Observing physical librations of celestial bodies and the Moon represents one of the astronomical methods of remotely assessing the internal structure of a celestial body without conducting expensive space experiments. The paper contains a review of recent advances in studying the Moon's structure using various methods of obtaining and applying the lunar physical librations (LPhL) data. In this article LPhL simulation methods of assessing viscoelastic and dissipative properties of the lunar body and lunar core parameters, whose existence has been recently confirmed during the seismic data reprocessing of ;Apollo; space mission, are described. Much attention is paid to physical interpretation of the free librations phenomenon and the methods for its determination. In the paper the practical application of the most accurate analytical LPhL tables (Rambaux and Williams, 2011) is discussed. The tables were built on the basis of complex analytical processing of the residual differences obtained when comparing long-term series of laser observations with the numerical ephemeris DE421. In the paper an efficiency analysis of two approaches to LPhL theory is conducted: the numerical and the analytical ones. It has been shown that in lunar investigation both approaches complement each other in various aspects: the numerical approach provides high accuracy of the theory, which is required for the proper processing of modern observations, the analytical approach allows to comprehend the essence of the phenomena in the lunar rotation, predict and interpret new effects in the observations of lunar body and lunar core parameters.

Inelastic neutron scattering and molecular simulation of the dynamics of interlayer water in smectite clay minerals

DOE PAGES

Cygan, Randall T.; Daemen, Luke L.; Ilgen, Anastasia G.; ...

2015-11-16

The study of mineral–water interfaces is of great importance to a variety of applications including oil and gas extraction, gas subsurface storage, environmental contaminant treatment, and nuclear waste repositories. Understanding the fundamentals of that interface is key to the success of those applications. Confinement of water in the interlayer of smectite clay minerals provides a unique environment to examine the interactions among water molecules, interlayer cations, and clay mineral surfaces. Smectite minerals are characterized by a relatively low layer charge that allows the clay to swell with increasing water content. Montmorillonite and beidellite varieties of smectite were investigated to comparemore » the impact of the location of layer charge on the interlayer structure and dynamics. Inelastic neutron scattering of hydrated and dehydrated cation-exchanged smectites was used to probe the dynamics of the interlayer water (200–900 cm –1 spectral region) and identify the shift in the librational edge as a function of the interlayer cation. Molecular dynamics simulations of equivalent phases and power spectra, derived from the resulting molecular trajectories, indicate a general shift in the librational behavior with interlayer cation that is generally consistent with the neutron scattering results for the monolayer hydrates. Both neutron scattering and power spectra exhibit librational structures affected by the location of layer charge and by the charge of the interlayer cation. Furthermore, divalent cations (Ba 2+ and Mg 2+) characterized by large hydration enthalpies typically exhibit multiple broad librational peaks compared to monovalent cations (Cs + and Na +), which have relatively small hydration enthalpies.« less

The cislunar low-thrust trajectories via the libration point

NASA Astrophysics Data System (ADS)

Qu, Qingyu; Xu, Ming; Peng, Kun

2017-05-01

The low-thrust propulsion will be one of the most important propulsion in the future due to its large specific impulse. Different from traditional low-thrust trajectories (LTTs) yielded by some optimization algorithms, the gradient-based design methodology is investigated for LTTs in this paper with the help of invariant manifolds of LL1 point and Halo orbit near the LL1 point. Their deformations under solar gravitational perturbation are also presented to design LTTs in the restricted four-body model. The perturbed manifolds of LL1 point and its Halo orbit serve as the free-flight phase to reduce the fuel consumptions as much as possible. An open-loop control law is proposed, which is used to guide the spacecraft escaping from Earth or captured by Moon. By using a two-dimensional search strategy, the ON/OFF time of the low-thrust engine in the Earth-escaping and Moon-captured phases can be obtained. The numerical implementations show that the LTTs achieved in this paper are consistent with the one adopted by the SMART-1 mission.

A Direct Method for Fuel Optimal Maneuvers of Distributed Spacecraft in Multiple Flight Regimes

NASA Technical Reports Server (NTRS)

Hughes, Steven P.; Cooley, D. S.; Guzman, Jose J.

2005-01-01

We present a method to solve the impulsive minimum fuel maneuver problem for a distributed set of spacecraft. We develop the method assuming a non-linear dynamics model and parameterize the problem to allow the method to be applicable to multiple flight regimes including low-Earth orbits, highly-elliptic orbits (HEO), Lagrange point orbits, and interplanetary trajectories. Furthermore, the approach is not limited by the inter-spacecraft separation distances and is applicable to both small formations as well as large constellations. Semianalytical derivatives are derived for the changes in the total AV with respect to changes in the independent variables. We also apply a set of constraints to ensure that the fuel expenditure is equalized over the spacecraft in formation. We conclude with several examples and present optimal maneuver sequences for both a HE0 and libration point formation.

Launch Window Trade Analysis for the James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Yu, Wayne H.; Richon, Karen

2014-01-01

The James Webb Space Telescope (JWST) is a large-scale space telescope mission designed to study fundamental astrophysical questions ranging from the formation of the universe to the origin of planetary systems and the origins of life. JWSTs orbit design is a Libration Point Orbit (LPO) around the Sun-Earth/Moon (SEM) L2 point for a planned mission lifetime of 10.5 years. The launch readiness period for JWST is from Oct 1st, 2018 November 30th, 2018. This paper presents the first launch window analysis for the JWST observatory using finite-burn modeling; previous analysis assumed a single impulsive midcourse correction to achieve the mission orbit. The physical limitations of the JWST hardware stemming primarily from propulsion, communication and thermal requirements alongside updated mission design requirements result in significant launch window within the launch readiness period. Future plans are also discussed.

James Webb Space Telescope Launch Window Trade Analysis

NASA Technical Reports Server (NTRS)

Yu, Wayne; Richon, Karen

2014-01-01

The James Webb Space Telescope (JWST) is a large-scale space telescope mission designed to study fundamental astrophysical questions ranging from the formation of the universe to the origin of planetary systems and the origins of life. JWSTs orbit design is a Libration Point Orbit (LPO) around the Sun-EarthMoon (SEM) L2 point for a planned mission lifetime of 10.5 years. The launch readiness period for JWST is from Oct 1st, 2018 November 30th, 2018. This paper presents the first launch window analysis for the JWST observatory using finite-burn modeling; previous analysis assumed a single impulsive midcourse correction to achieve the mission orbit. The physical limitations of the JWST hardware stemming primarily from propulsion, communication and thermal requirements alongside updated mission design requirements result in significant launch window within the launch readiness period. Future plans are also discussed.

Laser spectroscopy and dynamics of crystal lattices of chirally pure and racemic phases of amino acids

NASA Astrophysics Data System (ADS)

Belyanchikov, M. A.; Gorelik, V. S.; Gorshunov, B. P.; Pyatyshev, A. Yu.

2017-03-01

Strong sharp lines due to the librational modes characterized by a pseudoscalar symmetry type have been found in the low-frequency Raman spectra of the lattices of glycine and tyrosine amino acids. The intensities of these lines exceed those for Raman scattering in the region of intramolecular vibrations. The spectra of chirally pure and racemic phases of amino acids differ significantly. The results obtained can be used to observe stimulated Raman scattering from the librational modes of crystalline amino acids and monitor the chiral purity of bioactive preparations containing amino acids.

Applications of Multi-Body Dynamical Environments: The ARTEMIS Transfer Trajectory Design

NASA Technical Reports Server (NTRS)

Folta, David C.; Woodard, Mark; Howell, Kathleen; Patterson, Chris; Schlei, Wayne

2010-01-01

The application of forces in multi-body dynamical environments to pennit the transfer of spacecraft from Earth orbit to Sun-Earth weak stability regions and then return to the Earth-Moon libration (L1 and L2) orbits has been successfully accomplished for the first time. This demonstrated transfer is a positive step in the realization of a design process that can be used to transfer spacecraft with minimal Delta-V expenditures. Initialized using gravity assists to overcome fuel constraints; the ARTEMIS trajectory design has successfully placed two spacecraft into EarthMoon libration orbits by means of these applications.

Efficient computer algebra algorithms for polynomial matrices in control design

NASA Technical Reports Server (NTRS)

Baras, J. S.; Macenany, D. C.; Munach, R.

1989-01-01

The theory of polynomial matrices plays a key role in the design and analysis of multi-input multi-output control and communications systems using frequency domain methods. Examples include coprime factorizations of transfer functions, cannonical realizations from matrix fraction descriptions, and the transfer function design of feedback compensators. Typically, such problems abstract in a natural way to the need to solve systems of Diophantine equations or systems of linear equations over polynomials. These and other problems involving polynomial matrices can in turn be reduced to polynomial matrix triangularization procedures, a result which is not surprising given the importance of matrix triangularization techniques in numerical linear algebra. Matrices with entries from a field and Gaussian elimination play a fundamental role in understanding the triangularization process. In the case of polynomial matrices, matrices with entries from a ring for which Gaussian elimination is not defined and triangularization is accomplished by what is quite properly called Euclidean elimination. Unfortunately, the numerical stability and sensitivity issues which accompany floating point approaches to Euclidean elimination are not very well understood. New algorithms are presented which circumvent entirely such numerical issues through the use of exact, symbolic methods in computer algebra. The use of such error-free algorithms guarantees that the results are accurate to within the precision of the model data--the best that can be hoped for. Care must be taken in the design of such algorithms due to the phenomenon of intermediate expressions swell.

Cultural Resources Inventory of Lands Adjacent to Big Sandy Lake. Volume 1,

DTIC Science & Technology

1979-01-18

population density. Late Prehistoric: 300 - 1640 A.D. Intensive wild rice -bison economic systems; St. Croix, Kathio, Clam River, Balckduck and Sandy...type are located on W- streams and near lake outlets that tend to be good wild rice harvesting .1. areas. Projectile points are either ososceles...triangular br side-notched points. The subsistence pattern of these people is that of hunting deer and smaller mammals and wild rice gathering. The time

Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Wenjian; Singh, Rajiv R. P.; Scalettar, Richard T.

Here, we apply unsupervised machine learning techniques, mainly principal component analysis (PCA), to compare and contrast the phase behavior and phase transitions in several classical spin models - the square and triangular-lattice Ising models, the Blume-Capel model, a highly degenerate biquadratic-exchange spin-one Ising (BSI) model, and the 2D XY model, and examine critically what machine learning is teaching us. We find that quantified principal components from PCA not only allow exploration of different phases and symmetry-breaking, but can distinguish phase transition types and locate critical points. We show that the corresponding weight vectors have a clear physical interpretation, which ismore » particularly interesting in the frustrated models such as the triangular antiferromagnet, where they can point to incipient orders. Unlike the other well-studied models, the properties of the BSI model are less well known. Using both PCA and conventional Monte Carlo analysis, we demonstrate that the BSI model shows an absence of phase transition and macroscopic ground-state degeneracy. The failure to capture the 'charge' correlations (vorticity) in the BSI model (XY model) from raw spin configurations points to some of the limitations of PCA. Finally, we employ a nonlinear unsupervised machine learning procedure, the 'antoencoder method', and demonstrate that it too can be trained to capture phase transitions and critical points.« less

Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination

DOE PAGES

Hu, Wenjian; Singh, Rajiv R. P.; Scalettar, Richard T.

2017-06-19

Here, we apply unsupervised machine learning techniques, mainly principal component analysis (PCA), to compare and contrast the phase behavior and phase transitions in several classical spin models - the square and triangular-lattice Ising models, the Blume-Capel model, a highly degenerate biquadratic-exchange spin-one Ising (BSI) model, and the 2D XY model, and examine critically what machine learning is teaching us. We find that quantified principal components from PCA not only allow exploration of different phases and symmetry-breaking, but can distinguish phase transition types and locate critical points. We show that the corresponding weight vectors have a clear physical interpretation, which ismore » particularly interesting in the frustrated models such as the triangular antiferromagnet, where they can point to incipient orders. Unlike the other well-studied models, the properties of the BSI model are less well known. Using both PCA and conventional Monte Carlo analysis, we demonstrate that the BSI model shows an absence of phase transition and macroscopic ground-state degeneracy. The failure to capture the 'charge' correlations (vorticity) in the BSI model (XY model) from raw spin configurations points to some of the limitations of PCA. Finally, we employ a nonlinear unsupervised machine learning procedure, the 'antoencoder method', and demonstrate that it too can be trained to capture phase transitions and critical points.« less

Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination

NASA Astrophysics Data System (ADS)

Hu, Wenjian; Singh, Rajiv R. P.; Scalettar, Richard T.

2017-06-01

We apply unsupervised machine learning techniques, mainly principal component analysis (PCA), to compare and contrast the phase behavior and phase transitions in several classical spin models—the square- and triangular-lattice Ising models, the Blume-Capel model, a highly degenerate biquadratic-exchange spin-1 Ising (BSI) model, and the two-dimensional X Y model—and we examine critically what machine learning is teaching us. We find that quantified principal components from PCA not only allow the exploration of different phases and symmetry-breaking, but they can distinguish phase-transition types and locate critical points. We show that the corresponding weight vectors have a clear physical interpretation, which is particularly interesting in the frustrated models such as the triangular antiferromagnet, where they can point to incipient orders. Unlike the other well-studied models, the properties of the BSI model are less well known. Using both PCA and conventional Monte Carlo analysis, we demonstrate that the BSI model shows an absence of phase transition and macroscopic ground-state degeneracy. The failure to capture the "charge" correlations (vorticity) in the BSI model (X Y model) from raw spin configurations points to some of the limitations of PCA. Finally, we employ a nonlinear unsupervised machine learning procedure, the "autoencoder method," and we demonstrate that it too can be trained to capture phase transitions and critical points.

Deconfined quantum critical point on the triangular lattice

NASA Astrophysics Data System (ADS)

Jian, Chao-Ming; Thomson, Alex; Rasmussen, Alex; Bi, Zhen; Xu, Cenke

2018-05-01

In this work we propose a theory for the deconfined quantum critical point (DQCP) for spin-1/2 systems on a triangular lattice, which is a direct unfine-tuned quantum phase transition between the standard "√{3 }×√{3 } " noncollinear antiferromagnetic order (or the so-called 120∘ state) and the "√{12 }×√{12 } " valence solid bond (VBS) order, both of which are very standard ordered phases often observed in numerical simulations. This transition is beyond the standard Landau-Ginzburg paradigm and is also fundamentally different from the original DQCP theory on the square lattice due to the very different structures of both the magnetic and VBS order on frustrated lattices. We first propose a topological term in the effective-field theory that captures the "intertwinement" between the √{3 }×√{3 } antiferromagnetic order and the √{12 }×√{12 } VBS order. Then using a controlled renormalization-group calculation, we demonstrate that an unfine-tuned direct continuous DQCP exists between the two ordered phases mentioned above. This DQCP is described by the Nf=4 quantum electrodynamics (QED) with an emergent PSU(4)=SU(4)/Z4 symmetry only at the critical point. The aforementioned topological term is also naturally derived from the Nf=4 QED. We also point out that physics around this DQCP is analogous to the boundary of a 3 d bosonic symmetry- protected topological state with only on-site symmetries.

Automating Initial Guess Generation for High Fidelity Trajectory Optimization Tools

NASA Technical Reports Server (NTRS)

Villa, Benjamin; Lantoine, Gregory; Sims, Jon; Whiffen, Gregory

2013-01-01

Many academic studies in spaceflight dynamics rely on simplified dynamical models, such as restricted three-body models or averaged forms of the equations of motion of an orbiter. In practice, the end result of these preliminary orbit studies needs to be transformed into more realistic models, in particular to generate good initial guesses for high-fidelity trajectory optimization tools like Mystic. This paper reviews and extends some of the approaches used in the literature to perform such a task, and explores the inherent trade-offs of such a transformation with a view toward automating it for the case of ballistic arcs. Sample test cases in the libration point regimes and small body orbiter transfers are presented.

Environmental control and life support technologies for advanced manned space missions

NASA Technical Reports Server (NTRS)

Powell, F. T.; Wynveen, R. A.; Lin, C.

1986-01-01

Regenerative environmental control and life support system (ECLSS) technologies are found by the present evaluation to have reached a degree of maturity that recommends their application to long duration manned missions. The missions for which regenerative ECLSSs are attractive in virtue of the need to avoid expendables and resupply requirements have been identified as that of the long duration LEO Space Station, long duration stays at GEO, a permanently manned lunar base (or colony), manned platforms located at the earth-moon libration points L4 or L5, a Mars mission, deep space exploration, and asteroid exploration. A comparison is made between nonregenerative and regenerative ECLSSs in the cases of 10 essential functions.

NASA's Decadal Planning Team Mars Mission Analysis Summary

NASA Astrophysics Data System (ADS)

Drake, Bret G.

2007-02-01

In June 1999 the NASA Administrator chartered an internal NASA task force, termed the Decadal Planning Team, to create new integrated vision and strategy for space exploration. The efforts of the Decadal Planning Team evolved into the Agency-wide team known as the NASA Exploration Team (NEXT). This team was also instructed to identify technology roadmaps to enable the science-driven exploration vision, established a cross-Enterprise, cross-Center systems engineering team with emphasis focused on revolutionary not evolutionary approaches. The strategy of the DPT and NEXT teams was to "Go Anywhere, Anytime" by conquering key exploration hurdles of space transportation, crew health and safety, human/robotic partnerships, affordable abundant power, and advanced space systems performance. Early emphasis was placed on revolutionary exploration concepts such as rail gun and electromagnetic launchers, propellant depots, retrograde trajectories, nano structures, and gas core nuclear rockets to name a few. Many of these revolutionary concepts turned out to be either not feasible for human exploration missions or well beyond expected technology readiness for near-term implementation. During the DPT and NEXT study cycles, several architectures were analyzed including missions to the Earth-Sun Libration Point (L2), the Earth-Moon Gateway and L1, the lunar surface, Mars (both short and long stays), one-year round trip Mars, and near-Earth asteroids. Common emphasis of these studies included utilization of the Earth-Moon Libration Point (L1) as a staging point for exploration activities, current (Shuttle) and near-term launch capabilities (EELV), advanced propulsion, and robust space power. Although there was much emphasis placed on utilization of existing launch capabilities, the team concluded that missions in near-Earth space are only marginally feasible and human missions to Mars were not feasible without a heavy lift launch capability. In addition, the team concluded that missions in Earth s neighborhood, such as to the Moon, can serve as stepping-stones toward further deep-space missions in terms of proving systems, technologies, and operational concepts. The material contained in this presentation was compiled to capture the work performed by the Mars Sub-Team of the DPT NEXT efforts in the late 1999-2001 timeframe.

NASA's Decadal Planning Team Mars Mission Analysis Summary

NASA Technical Reports Server (NTRS)

Drake, Bret G. (Editor)

2007-01-01

In June 1999 the NASA Administrator chartered an internal NASA task force, termed the Decadal Planning Team, to create new integrated vision and strategy for space exploration. The efforts of the Decadal Planning Team evolved into the Agency-wide team known as the NASA Exploration Team (NEXT). This team was also instructed to identify technology roadmaps to enable the science-driven exploration vision, established a cross-Enterprise, cross-Center systems engineering team with emphasis focused on revolutionary not evolutionary approaches. The strategy of the DPT and NEXT teams was to "Go Anywhere, Anytime" by conquering key exploration hurdles of space transportation, crew health and safety, human/robotic partnerships, affordable abundant power, and advanced space systems performance. Early emphasis was placed on revolutionary exploration concepts such as rail gun and electromagnetic launchers, propellant depots, retrograde trajectories, nano structures, and gas core nuclear rockets to name a few. Many of these revolutionary concepts turned out to be either not feasible for human exploration missions or well beyond expected technology readiness for near-term implementation. During the DPT and NEXT study cycles, several architectures were analyzed including missions to the Earth-Sun Libration Point (L2), the Earth-Moon Gateway and L1, the lunar surface, Mars (both short and long stays), one-year round trip Mars, and near-Earth asteroids. Common emphasis of these studies included utilization of the Earth-Moon Libration Point (L1) as a staging point for exploration activities, current (Shuttle) and near-term launch capabilities (EELV), advanced propulsion, and robust space power. Although there was much emphasis placed on utilization of existing launch capabilities, the team concluded that missions in near-Earth space are only marginally feasible and human missions to Mars were not feasible without a heavy lift launch capability. In addition, the team concluded that missions in Earth s neighborhood, such as to the Moon, can serve as stepping-stones toward further deep-space missions in terms of proving systems, technologies, and operational concepts. The material contained in this presentation was compiled to capture the work performed by the Mars Sub-Team of the DPT NEXT efforts in the late 1999-2001 timeframe.

The Space Review

NASA Technical Reports Server (NTRS)

Thronson, Harley; Lester, Dan; Hatfield, Skip

2011-01-01

Human space flight in the US and other space-faring countries is faced with a twin challenge that is likely to persist for many years: flat or declining budgets along with an expectation of continuing, significant achievements. A partial solution may involve increased participation by multiple commercial competitors with the promise - albeit yet to be fully demonstrated - of much-reduced costs. That said, most commercial goals are concentrated on low-Earth orbit (LEO) for the time being, leaving human trips beyond Earth orbit (BED) as governmental initiatives. The past decade, beginning with the 1999/2000 Decadal Planning Team (DPT)/NASA Exploration Team (NExT) human space flight studies for the White House Office of Management and Budget (http://history.nasa.gov/DPT/DPT.htm), can arguably be described as a Golden Age of engineering design, strategic planning, technology capability prioritization, and development programs on the International Space Station (ISS). However, cynics have criticized the same period as little more than PowerPoint presentations, and unfocused technology investments with only limited progress toward a goal of human space flight beyond the immediate vicinity of the Earth. We disagree with the cynics. Experience with the ISS on increasingly sophisticated capabilities have prepared international partners to deploy a major "stepping stone" for human space flight: a habitation system in free space beyond low-Earth orbit. Such an achievement would be a major milestone in human space flight and, very likely, an essential demonstration site for subsequent, very ambitious exploration missions such as to Mars. Developing critical capabilities for human voyages beyond LEO, such as Earth-Moon libration points, offers, as just one example, easy return to Earth within days (see, e.g., Farquhar 1971 (Aeronautics & Astronautics, July, p. 59ff), Thronson, Lester, and Talay 2011 (http://www.thespacereview.com/article/1756/1), and Lester 2012 (http://www.thespacereview.com/article/1650/1). Use of Earth-Moon libration points as sites for early demonstrations of capabilities necessary for human missions to Mars, for example, contrasts sharply with using missions to near-Earth asteroids (NEAs) for that purpose.

Integrable Seven-Point Discrete Equations and Second-Order Evolution Chains

NASA Astrophysics Data System (ADS)

Adler, V. E.

2018-04-01

We consider differential-difference equations defining continuous symmetries for discrete equations on a triangular lattice. We show that a certain combination of continuous flows can be represented as a secondorder scalar evolution chain. We illustrate the general construction with a set of examples including an analogue of the elliptic Yamilov chain.

Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling

NASA Astrophysics Data System (ADS)

Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José

2017-05-01

The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant-Friedrichs-Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational efficiency, the OTSEM is more efficient than the Fekete-based TSEM, although it is slightly costlier than the QSEM when a comparable numerical accuracy is required.

Assessment of uncertainty in ROLO lunar irradiance for on-orbit calibration

USGS Publications Warehouse

Stone, T.C.; Kieffer, H.H.; Barnes, W.L.; Butler, J.J.

2004-01-01

A system to provide radiometric calibration of remote sensing imaging instruments on-orbit using the Moon has been developed by the US Geological Survey RObotic Lunar Observatory (ROLO) project. ROLO has developed a model for lunar irradiance which treats the primary geometric variables of phase and libration explicitly. The model fits hundreds of data points in each of 23 VNIR and 9 SWIR bands; input data are derived from lunar radiance images acquired by the project's on-site telescopes, calibrated to exoatmospheric radiance and converted to disk-equivalent reflectance. Experimental uncertainties are tracked through all stages of the data processing and modeling. Model fit residuals are ???1% in each band over the full range of observed phase and libration angles. Application of ROLO lunar calibration to SeaWiFS has demonstrated the capability for long-term instrument response trending with precision approaching 0.1% per year. Current work involves assessing the error in absolute responsivity and relative spectral response of the ROLO imaging systems, and propagation of error through the data reduction and modeling software systems with the goal of reducing the uncertainty in the absolute scale, now estimated at 5-10%. This level is similar to the scatter seen in ROLO lunar irradiance comparisons of multiple spacecraft instruments that have viewed the Moon. A field calibration campaign involving NASA and NIST has been initiated that ties the ROLO lunar measurements to the NIST (SI) radiometric scale.

Phase diagram of the triangular-lattice Potts antiferromagnet

DOE PAGES

Jacobsen, Jesper Lykke; Salas, Jesus; Scullard, Christian R.

2017-07-28

Here, we study the phase diagram of the triangular-lattice Q-state Potts model in the realmore » $(Q, v)$ -plane, where $$v={\\rm e}^J-1$$ is the temperature variable. Our first goal is to provide an obviously missing feature of this diagram: the position of the antiferromagnetic critical curve. This curve turns out to possess a bifurcation point with two branches emerging from it, entailing important consequences for the global phase diagram. We have obtained accurate numerical estimates for the position of this curve by combining the transfer-matrix approach for strip graphs with toroidal boundary conditions and the recent method of critical polynomials. The second goal of this work is to study the corresponding $$A_{p-1}$$ RSOS model on the torus, for integer $$p=4, 5, \\ldots, 8$$ . We clarify its relation to the corresponding Potts model, in particular concerning the role of boundary conditions. For certain values of p, we identify several new critical points and regimes for the RSOS model and we initiate the study of the flows between the corresponding field theories.« less

Conventional wallboard with latent heat storage for passive solar applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kedl, R.J.

1990-01-01

Conventional wallboard impregnated with octadecane paraffin (Melting Point -- 73.5{degree}F) is being developed as a building material with latent heat storage for passive solar applications. Impregnation was accomplished simply by soaking the wallboard in molten paraffin. Concentrations of paraffin in the combined product as high as 35{percent} by weight were achieved. In support of this concept, a computer model was developed to describe thermal transport and storage by a phase change material (PCM) dispersed in a porous media. The computer model was confirmed by comparison with known analytical solutions where the PCM melts at a specific melting point. However, agreementmore » between the model and an experimentally produced thermal transient involving impregnated wallboard was only good after the model was modified to allow the paraffin to melt over a temperature range. This was accomplished by replacing the heat of fusion with a triangular heat capacity relationship that mimics the triangular melt curve found through differential scanning calorimetry. When this change was made, agreement between the model and the experimental transient was very good. 4 refs., 8 figs.« less

Conventional wallboard with latent heat storage for passive solar applications

NASA Astrophysics Data System (ADS)

Kedl, R. J.

Conventional wallboard impregnated with octadecane paraffin (melting point -- 73.5 F) is being developed as a building material with latent heat storage for passive solar applications. Impregnation was accomplished simply by soaking the wallboard in molten paraffin. Concentrations of paraffin in the combined product as high as 35 percent by weight were achieved. In support of this concept, a computer model was developed to describe thermal transport and storage by a phase change material (PCM) dispersed in a porous media. The computer model was confirmed by comparison with known analytical solutions where the PCM melts at a specific melting point. However, agreement between the model and an experimentally produced thermal transient involving impregnated wallboard was only good after the model was modified to allow the paraffin to melt over a temperature range. This was accomplished by replacing the heat of fusion with a triangular heat capacity relationship that mimics the triangular melt curve found through differential scanning calorimetry. When this change was made, agreement between the model and the experimental transient was very good.

Dirac cones in artificial structures of 3d transitional-metals doped Mg-Al spinels

NASA Astrophysics Data System (ADS)

Lu, Yuan; Feng, Min; Shao, Bin; Zuo, Xu

2014-05-01

Motivated by recent theoretical predications for Dirac cone in two-dimensional (2D) triangular lattice [H. Ishizuka, Phys. Rev. Lett. 109, 237207 (2012)], first-principles studies are performed to predict Dirac cones in artificial structures of 3d transitional-metals (TM = Ti, V, Cr, Mn, Fe, Co, Ni, and Cu) doped Mg-Al spinels. In investigated artificial structures, TM dopants substitute specific positions of the B sub-lattice in Mg-Al spinel, and form a quasi-2D triangular lattice in the a-b plane. Calculated results illustrate the existence of the spin-polarized Dirac cones formed in d-wave bands at (around) the K-point in the momentum space. The study provides a promising route for engineering Dirac physics in condensed matters.

Comparative Analysis of Membership Function on Mamdani Fuzzy Inference System for Decision Making

NASA Astrophysics Data System (ADS)

harliana, Putri; Rahim, Robbi

2017-12-01

Membership function is a curve that shows mapping the input data points into the value or degree of membership which has an interval between 0 and 1. One way to get membership value is through a function approach. There are some membership functions can be used on mamdani fuzzy inference system. They are triangular, trapezoid, singleton, sigmoid, Gaussian, etc. In this paper only discuss three membership functions, are triangular, trapezoid and Gaussian. These three membership functions will be compared to see the difference in parameter values and results obtained. For case study in this paper is admission of students at popular school. There are three variable can be used, they are students’ report, IQ score and parents’ income. Which will then be created if-then rules.

Investigations at supersonic speeds of 22 triangular wings representing two airfoil sections for each of 11 apex angles

NASA Technical Reports Server (NTRS)

Love, Eugene S

1949-01-01

Data obtained from wind tunnel investigations of two series of 11 triangular wings conducted at Mach numbers of 1.62, 1.92, and 1.40 to determine the effect of leading-edge shape and to compare actual test values with the nonviscous linear theory are presented. The two series of wings had identical plan forms, a constant thickness ratio of 8 percent, a constant location of maximum-thickness point of 18 percent, and a range of apex half-angles from 10 degrees to forty-five degrees. The first series has an elliptical leading edge and the second series a wedge leading edge. Measurements were made of lift, drag, pitching moment, and pressure distribution, the latter being confined to three wings at one Mach number.

The effect of the Earth's oblateness on the Moon's physical libration in latitude

NASA Astrophysics Data System (ADS)

Kondratyev, B. P.

2013-05-01

The Moon's physical libration in latitude generated by gravitational forces caused by the Earth's oblateness has been examined by a vector analytical method. Libration oscillations are described by a close set of five linear inhomogeneous differential equations, the dispersion equation has five roots, one of which is zero. A complete solution is obtained. It is revealed that the Earth's oblateness: a) has little effect on the instantaneous axis of Moon's rotation, but causes an oscillatory rotation of the body of the Moon with an amplitude of 0.072″ and pulsation period of 16.88 Julian years; b) causes small nutations of poles of the orbit and of the ecliptic along tight spirals, which occupy a disk with a cut in a center and with radius of 0.072″. Perturbations caused by the spherical Earth generate: a) physical librations in latitude with an amplitude of 34.275″; b) nutational motion for centers of small spiral nutations of orbit (ecliptic) pole over ellipses with semi-major axes of 113.850″ (85.158″) and the first pole rotates round the second one along a circle with radius of 28.691″; c) nutation of the Moon's celestial pole over an ellipse with a semi-major axis of 45.04″ and with an axes ratio of about 0.004 with a period of T = 27.212 days. The principal ellipse's axis is directed tangentially with respect to the precession circumference, along which the celestial pole moves nonuniformly nearly in one dimension. In contrast to the accepted concept, the latitude does not change while the Moon's poles of rotation move. The dynamical reason for the inclination of the Moon's mean equator with respect to the ecliptic is oblateness of the body of the Moon.

Dynamics of axial torsional libration under the mantle-inner core gravitational interaction

NASA Astrophysics Data System (ADS)

Chao, B. F.

2017-01-01

The aims of this paper are (i) formulating the dynamics of the mantle-inner core gravitational (MICG) interaction in terms of the spherical-harmonic multipoles of mass density. The modeled MICG system is composed of two concentric rigid bodies (mantle and inner core) of near-spherical but otherwise heterogeneous configuration, with a fluid outer core in between playing a passive role. We derive the general equation of motion for the vector rotation but only focus on the polar component that describes the MICG axial torsional libration. The torsion constant and hence the square of the natural frequency of the libration is proportional to the product of the equatorial ellipticities of the mantle and inner-core geoid embodied in their multipoles (of two different types) of degree 2 and order 2 (such as the Large Low-Shear-Velocity Provinces above the core-mantle boundary) and (ii) studying the geophysical implications upon equating the said MICG libration to the steady 6 year oscillation that are observed in the Earth's spin rate or the length-of-day variation (ΔLOD). In particular, the MICG torsion constant is found to be Γ>˜z = CIC σz2 ≈ 6.5 × 1019 N m, while the inner core's (BIC - AIC) ≈ 1.08 × 1031 kg m2 gives the inner core triaxiality (BIC - AIC)/CIC ≈ 1.8 × 10-4, about 8 times the whole-Earth value. It is also asserted that the required inner-core ellipticity amounts to no more than 140 m in geoid height, much smaller than the sensitivity required for the seismic wave travel time to resolve the variation of the inner core.

The tidally-modulated plume of Enceladus: an update

NASA Astrophysics Data System (ADS)

Nimmo, F.; Porco, C.; Mitchell, C. J.; Van Hoolst, T.; Hedman, M. M.

2016-12-01

The brightness of the ice grain plume of Enceladus is observed to vary on a diurnal timescale [1,2], consistent with predictions that the plume's mass is modulated by normal tidal stresses, which open and close cracks that reach the ocean [3]. Here we extend our previous analysis [2] to a larger set of ISS plume observations, including images taken since 2010, extending the temporal baseline by more than a factor of two. The observations were reduced using the same approach as in [2]. Fits were performed as in [2] but now include two different assumptions of how plume brightness responds to stresses [4] plus an updated calculation of the effects of long-period librations [5]. An apparent phase lag of 30-60 degrees between the modelled and observed response is robustly present, irrespective of the data set and assumptions used. This phase lag may be the result of the viscosity structure of the ice shell [2,4], an eruptive delay caused by the hydrodynamics within tidally-pumped cracks [6], or other as yet unknown processes. An earlier suggestion [2], that the phase lag is caused by the additional stresses arising from an 0.8 degree 1:1 physical libration in the moon's ice shell, can be rejected now that this libration has been measured with an amplitude of 0.12 degrees [7]. We also find in ISS images a secular decrease in plume brightness over the ten years of Cassini observations; this decrease may be due to long-period (forced) librations of Enceladus. [1] Hedman et al., Nature 2013 [2] Nimmo et al., Astron. J. 2014 [3] Hurford et al., Nature 2007 [4] Behounkova et al., Nature Geosci. 2015 [5] Yseboodt & Van Hoolst, Fall AGU, 2015 [6] Kite & Rubin, PNAS 2016 [7] Thomas et al., Icarus 2016

Simulations of Dissipative Circular Restricted Three-body Problems Using the Velocity-scaling Correction Method

NASA Astrophysics Data System (ADS)

Wang, Shoucheng; Huang, Guoqing; Wu, Xin

2018-02-01

In this paper, we survey the effect of dissipative forces including radiation pressure, Poynting–Robertson drag, and solar wind drag on the motion of dust grains with negligible mass, which are subjected to the gravities of the Sun and Jupiter moving in circular orbits. The effect of the dissipative parameter on the locations of five Lagrangian equilibrium points is estimated analytically. The instability of the triangular equilibrium point L4 caused by the drag forces is also shown analytically. In this case, the Jacobi constant varies with time, whereas its integral invariant relation still provides a probability for the applicability of the conventional fourth-order Runge–Kutta algorithm combined with the velocity scaling manifold correction scheme. Consequently, the velocity-only correction method significantly suppresses the effects of artificial dissipation and a rapid increase in trajectory errors caused by the uncorrected one. The stability time of an orbit, regardless of whether it is chaotic or not in the conservative problem, is apparently longer in the corrected case than in the uncorrected case when the dissipative forces are included. Although the artificial dissipation is ruled out, the drag dissipation leads to an escape of grains. Numerical evidence also demonstrates that more orbits near the triangular equilibrium point L4 escape as the integration time increases.

Evidence for a spinon Fermi surface in a triangular-lattice quantum-spin-liquid candidate

DOE PAGES

Shen, Yao; Li, Yao-Dong; Wo, Hongliang; ...

2016-12-05

A quantum spin liquid is an exotic quantum state of matter in which spins are highly entangled and remain disordered down to zero temperature. Such a state of matter is potentially relevant to high-temperature superconductivity and quantum-information applications, and experimental identification of a quantum spin liquid state is of fundamental importance for our understanding of quantum matter. Theoretical studies have proposed various quantum-spin-liquid ground states, most of which are characterized by exotic spin excitations with fractional quantum numbers (termed ‘spinons’). In this paper, we report neutron scattering measurements of the triangular-lattice antiferromagnet YbMgGaO 4 that reveal broad spin excitations coveringmore » a wide region of the Brillouin zone. The observed diffusive spin excitation persists at the lowest measured energy and shows a clear upper excitation edge, consistent with the particle–hole excitation of a spinon Fermi surface. Finally, our results therefore point to the existence of a quantum spin liquid state with a spinon Fermi surface in YbMgGaO 4, which has a perfect spin-1/2 triangular lattice as in the original proposal of quantum spin liquids.« less

Cavity mode enhancement of terahertz emission from equilateral triangular microstrip antennas of the high-T c superconductor Bi2Sr2CaCu2O8 + δ

NASA Astrophysics Data System (ADS)

Cerkoney, Daniel P.; Reid, Candy; Doty, Constance M.; Gramajo, Ashley; Campbell, Tyler D.; Morales, Manuel A.; Delfanazari, Kaveh; Tsujimoto, Manabu; Kashiwagi, Takanari; Yamamoto, Takashi; Watanabe, Chiharu; Minami, Hidetoshi; Kadowaki, Kazuo; Klemm, Richard A.

2017-01-01

We study the transverse magnetic (TM) electromagnetic cavity mode wave functions for an ideal equilateral triangular microstrip antenna (MSA) exhibiting C 3v point group symmetry. When the C 3v operations are imposed upon the antenna, the TM(m,n) modes with wave vectors \\propto \\sqrt{{{m}2}+nm+{{n}2}} are much less dense than commonly thought. The R 3 operations restrict the integral n and m to satisfy |m-n| =3p , where p≥slant 0 and p≥slant 1 for the modes even and odd under reflections about the three mirror planes, respectively. We calculate the forms of representative wave functions and the angular dependence of the output power when these modes are excited by the uniform and non-uniform ac Josephson current sources in thin, ideally equilateral triangular MSAs employing the intrinsic Josephson junctions in the high transition temperature T c superconductor Bi2Sr2CaCu2 {{\\text{O}}8+δ} , and fit the emissions data from an earlier sample for which the C 3v symmetry was apparently broken.

One dimensionalization in the spin-1 Heisenberg model on the anisotropic triangular lattice

NASA Astrophysics Data System (ADS)

Gonzalez, M. G.; Ghioldi, E. A.; Gazza, C. J.; Manuel, L. O.; Trumper, A. E.

2017-11-01

We investigate the effect of dimensional crossover in the ground state of the antiferromagnetic spin-1 Heisenberg model on the anisotropic triangular lattice that interpolates between the regime of weakly coupled Haldane chains (J'≪J ) and the isotropic triangular lattice (J'=J ). We use the density-matrix renormalization group (DMRG) and Schwinger boson theory performed at the Gaussian correction level above the saddle-point solution. Our DMRG results show an abrupt transition between decoupled spin chains and the spirally ordered regime at (J'/J) c˜0.42 , signaled by the sudden closing of the spin gap. Coming from the magnetically ordered side, the computation of the spin stiffness within Schwinger boson theory predicts the instability of the spiral magnetic order toward a magnetically disordered phase with one-dimensional features at (J'/J) c˜0.43 . The agreement of these complementary methods, along with the strong difference found between the intra- and the interchain DMRG short spin-spin correlations for sufficiently large values of the interchain coupling, suggests that the interplay between the quantum fluctuations and the dimensional crossover effects gives rise to the one-dimensionalization phenomenon in this frustrated spin-1 Hamiltonian.

Philtral columns and nostril shapes in nigerian children: a morphometric and aesthetic analysis.

PubMed

Abdulrasheed, Ibrahim; Eneye, Asuku Malachy

2013-01-01

Background. The upper lip-nose complex contributes significantly to the concept of symmetry and proportion of the face. A study of the morphology and aesthetic preferences of the lip-nose complex will provide a database that will serve as a guide for reconstruction. Subjects and Methods. Hundred Nigerian children participated in this study. Demographic data and standard photographs of the philtral column and nostrils were obtained. Sixty volunteers were recruited to evaluate the photographs. Each volunteer was asked to rank the photographs based on their aesthetic preference. Results. The morphology of the philtral columns was classified into four groups: (1) triangular, (2) concave, (3) flat, and (4) parallel. The nostril shape was also classified into four groups: (1) triangular, (2) round, (3) teardrop, and (4) rectangular. In both genders, the triangular shape of philtral column was the most common. There are significant age differences in the aesthetic rankings of philtral columns and nostril shapes. Conclusion. Our study establishes the basal values for the morphometric and aesthetic parameters of the lip-nose complex of 5- and 6-year-old children in Nigeria. We hope our results and reconstructive surgery will intersect at a point to treat disfigurements of the philtrum and nostrils successfully.

Surface sampling techniques for 3D object inspection

NASA Astrophysics Data System (ADS)

Shih, Chihhsiong S.; Gerhardt, Lester A.

1995-03-01

While the uniform sampling method is quite popular for pointwise measurement of manufactured parts, this paper proposes three novel sampling strategies which emphasize 3D non-uniform inspection capability. They are: (a) the adaptive sampling, (b) the local adjustment sampling, and (c) the finite element centroid sampling techniques. The adaptive sampling strategy is based on a recursive surface subdivision process. Two different approaches are described for this adaptive sampling strategy. One uses triangle patches while the other uses rectangle patches. Several real world objects were tested using these two algorithms. Preliminary results show that sample points are distributed more closely around edges, corners, and vertices as desired for many classes of objects. Adaptive sampling using triangle patches is shown to generally perform better than both uniform and adaptive sampling using rectangle patches. The local adjustment sampling strategy uses a set of predefined starting points and then finds the local optimum position of each nodal point. This method approximates the object by moving the points toward object edges and corners. In a hybrid approach, uniform points sets and non-uniform points sets, first preprocessed by the adaptive sampling algorithm on a real world object were then tested using the local adjustment sampling method. The results show that the initial point sets when preprocessed by adaptive sampling using triangle patches, are moved the least amount of distance by the subsequently applied local adjustment method, again showing the superiority of this method. The finite element sampling technique samples the centroids of the surface triangle meshes produced from the finite element method. The performance of this algorithm was compared to that of the adaptive sampling using triangular patches. The adaptive sampling with triangular patches was once again shown to be better on different classes of objects.

Interpretive Overview of Cultural Resources in Saylorville Lake, Iowa. Volume 1,

DTIC Science & Technology

1985-09-01

Rice Corner Notched variety; CN9, Turin variety). Similar side notched points were found in horizons I and II at the Cherokee Sewer site (Anderson...1980) and in the Middle Archaic levels at Koster (Brown and Vierra 1983:182-4) and the Pigeon Roost Creek site (O’Brien and Warren 1983). The Rice ...triangular blades are like the Rice Corner Notched style of the Archaic periods. Slightly smaller Manker Corner Notched points (Figures A.6, A.13) are

New similarity of triangular fuzzy number and its application.

PubMed

Zhang, Xixiang; Ma, Weimin; Chen, Liping

2014-01-01

The similarity of triangular fuzzy numbers is an important metric for application of it. There exist several approaches to measure similarity of triangular fuzzy numbers. However, some of them are opt to be large. To make the similarity well distributed, a new method SIAM (Shape's Indifferent Area and Midpoint) to measure triangular fuzzy number is put forward, which takes the shape's indifferent area and midpoint of two triangular fuzzy numbers into consideration. Comparison with other similarity measurements shows the effectiveness of the proposed method. Then, it is applied to collaborative filtering recommendation to measure users' similarity. A collaborative filtering case is used to illustrate users' similarity based on cloud model and triangular fuzzy number; the result indicates that users' similarity based on triangular fuzzy number can obtain better discrimination. Finally, a simulated collaborative filtering recommendation system is developed which uses cloud model and triangular fuzzy number to express users' comprehensive evaluation on items, and result shows that the accuracy of collaborative filtering recommendation based on triangular fuzzy number is higher.

ARTEMIS Mission Overview: From Concept to Operations

NASA Technical Reports Server (NTRS)

Folta, David; Sweetser, Theodore

2011-01-01

ARTEMIS (Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon's Interaction with the Sun) repurposed two spacecraft to extend their useful science (Angelopoulos, 2010) by moving them via lunar gravity assists from elliptical Earth orbits to L1 and L2 Earth-Moon libration orbits and then to lunar orbits by exploiting the Earth-Moon-Sun dynamical environment. This paper describes the complete design from conceptual plans using weak stability transfer options and lunar gravity assist to the implementation and operational support of the Earth-Moon libration and lunar orbits. The two spacecraft of the ARTEMIS mission will have just entered lunar orbit at this paper's presentation.

Regular Motions of Resonant Asteroids

NASA Astrophysics Data System (ADS)

Ferraz-Mello, S.

1990-11-01

RESUMEN. Se revisan resultados analiticos relativos a soluciones regulares del problema asteroidal eliptico promediados en la vecindad de una resonancia con jupiten Mencionamos Ia ley de estructura para libradores de alta excentricidad, la estabilidad de los centros de liberaci6n, las perturbaciones forzadas por la excentricidad de jupiter y las 6rbitas de corotaci6n. ABSTRAC This paper reviews analytical results concerning the regular solutions of the elliptic asteroidal problem averaged in the neighbourhood of a resonance with jupiter. We mention the law of structure for high-eccentricity librators, the stability of the libration centers, the perturbations forced by the eccentricity ofjupiter and the corotation orbits. Key words: ASThROIDS

Collective excitations and ultrafast dipolar solvation dynamics in water-ethanol binary mixture

NASA Astrophysics Data System (ADS)

Hazra, Milan K.; Bagchi, Biman

2018-03-01

In order to understand the intermolecular vibrational spectrum and the collective excitations of water-ethanol binary mixture, we investigate the density of states and the power spectrum using computer simulations aided by theory. We investigate in particular the spectra at intermediate to low frequencies (a few hundreds to few tens of cm-1) by calculating (i) the density of states from quenched normal modes, (ii) the power spectrum from velocity time correlation function, and (iii) the far infrared and dielectric spectra (that is, the Cole-Cole plot) from the total dipole moment time correlation function. The different spectra are in broad agreement with each other and at the same time reveal unique characteristics of the water-ethanol mixture. Inverse participation ratio reveals several interesting features. Libration of pure ethanol is more localized than that of pure water. With increasing ethanol content, we observe localization of the collective libration mode as well as of the hindered translational and rotational mode. An interesting mixing between the libration of water and ethanol is observed. Solvation dynamics of tryptophan measured by equilibrium energy fluctuation time correlation function show surprisingly strong non-linear dependence on composition that can be tested against experiments.

Collective excitations and ultrafast dipolar solvation dynamics in water-ethanol binary mixture.

PubMed

Hazra, Milan K; Bagchi, Biman

2018-03-21

In order to understand the intermolecular vibrational spectrum and the collective excitations of water-ethanol binary mixture, we investigate the density of states and the power spectrum using computer simulations aided by theory. We investigate in particular the spectra at intermediate to low frequencies (a few hundreds to few tens of cm -1 ) by calculating (i) the density of states from quenched normal modes, (ii) the power spectrum from velocity time correlation function, and (iii) the far infrared and dielectric spectra (that is, the Cole-Cole plot) from the total dipole moment time correlation function. The different spectra are in broad agreement with each other and at the same time reveal unique characteristics of the water-ethanol mixture. Inverse participation ratio reveals several interesting features. Libration of pure ethanol is more localized than that of pure water. With increasing ethanol content, we observe localization of the collective libration mode as well as of the hindered translational and rotational mode. An interesting mixing between the libration of water and ethanol is observed. Solvation dynamics of tryptophan measured by equilibrium energy fluctuation time correlation function show surprisingly strong non-linear dependence on composition that can be tested against experiments.

What's the matter with Enceladus' gravity?

NASA Astrophysics Data System (ADS)

Rivoldini, A.; Beuthe, M.; Trinh, A.

2016-12-01

Isostasy is clearly at work on Enceladus: long-wavelength gravity is positively correlated with topography, but also well compensated. If the influence of Enceladus' fast spin is taken into account, Airy isostasy implies a very thick crust (50 km) above a very thin ocean, in flat contradiction of the thin crust (20 km) implied by librations. In a desperate attempt to solve the problem, it was recently proposed to substitute flexural isostasy to Airy isostasy, using librations as a constraint on the crust thickness. However the huge lithospheric stresses required to support the load result in complete lithospheric failure. Here we propose a new isostatic model based on the sound physical principle of minimum crustal stress. We demonstrate that gravity combined with topography predicts a 20 km thick crust agreeing with - but independent from - the libration constraint. A consistent picture finally emerges from gravity-topography analysis, confirming that the south polar crust is only a few kilometres thick. Enceladus' resonant companion, Dione, is in a similar state of minimum stress isostasy. Its gravity and topography can be explained in terms of a 100 km thick isostatic crust overlying a 60 km thick global ocean, thus providing the first clear evidence for a present-day ocean within Dione.

Dynamic Portrait of the Retrograde 1:1 Mean Motion Resonance

NASA Astrophysics Data System (ADS)

Huang, Yukun; Li, Miao; Li, Junfeng; Gong, Shengping

2018-06-01

Asteroids in mean motion resonances with giant planets are common in the solar system, but it was not until recently that several asteroids in retrograde mean motion resonances with Jupiter and Saturn were discovered. A retrograde co-orbital asteroid of Jupiter, 2015 BZ509 is confirmed to be in a long-term stable retrograde 1:1 mean motion resonance with Jupiter, which gives rise to our interests in its unique resonant dynamics. In this paper, we investigate the phase-space structure of the retrograde 1:1 resonance in detail within the framework of the circular restricted three-body problem. We construct a simple integrable approximation for the planar retrograde resonance using canonical contact transformation and numerically employ the averaging procedure in closed form. The phase portrait of the retrograde 1:1 resonance is depicted with the level curves of the averaged Hamiltonian. We thoroughly analyze all possible librations in the co-orbital region and uncover a new apocentric libration for the retrograde 1:1 resonance inside the planet’s orbit. We also observe the significant jumps in orbital elements for outer and inner apocentric librations, which are caused by close encounters with the perturber.

Triangular Resection of the Upper Lateral Cartilage for Middle Vault Deviation.

PubMed

Ryu, Gwanghui; Seo, Min Young; Lee, Kyung Eun; Hong, Sang Duk; Chung, Seung-Kyu; Dhong, Hun-Jong; Kim, Hyo Yeol

2018-06-02

Middle vault deviation has a significant effect on the aesthetic and functional aspects of the nose, and its management continues to be a challenge. Spreader graft and its modification techniques have been focused, but there has been scarce consideration for removing surplus portion and balancing the upper lateral cartilage (ULC). This study aimed to report the newly invented triangular-shaped resection technique ("triangular resection") of the ULC and to evaluate its efficacy for correcting middle vault deviation. A retrospective study included 17 consecutive patients who presented with middle vault deviation and underwent septorhinoplasty by using triangular resection at a tertiary academic hospital from February 2014 and March 2016. Their outcomes were evaluated pre- and postoperatively including medical photographs, acoustic rhinometry and subjective nasal obstruction using a 7-point Likert scale. The immediate outcomes were evaluated around 1 month after surgery, and long-term outcomes were available in 12 patients; the mean follow-up period was 9.1 months. Nasal tip deviation angle was reduced from 5.66º to 2.37º immediately (P<0.001). Middle vault deviation also improved from 169.50º to 177.24º (P<0.001). Long-term results were 2.49º (P=0.015) for nasal tip deviation and 178.68º (P=0.002) for middle vault deviation. The aesthetic outcome involved a complete correction in eight patients (47.1%), a minimally visible deviation in seven patients (41.2%) and a remaining residual deviation in two patients (11.8%). Pre- and postoperative minimal cross-sectional areas (summation of the right and left sides) were 0.86 and 1.07, respectively (P=0.021). Fifteen patients answered about their nasal obstruction symptoms and the median symptom score had alleviated from 6.0 to 3.0 (P=0.004). Triangular resection of the ULC is a simple and effective method for correcting middle vault deviation and balancing the ULCs without complications as internal nasal valve narrowing.

Advances in understanding quiescent H-mode plasmas in DIII-Da)

NASA Astrophysics Data System (ADS)

Burrell, K. H.; West, W. P.; Doyle, E. J.; Austin, M. E.; Casper, T. A.; Gohil, P.; Greenfield, C. M.; Groebner, R. J.; Hyatt, A. W.; Jayakumar, R. J.; Kaplan, D. H.; Lao, L. L.; Leonard, A. W.; Makowski, M. A.; McKee, G. R.; Osborne, T. H.; Snyder, P. B.; Solomon, W. M.; Thomas, D. M.; Rhodes, T. L.; Strait, E. J.; Wade, M. R.; Wang, G.; Zeng, L.

2005-05-01

Recent QH-mode research on DIII-D [J. L. Luxon et al., Plasma Physics and Controlled Nuclear Fusion Research 1996 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] has used the peeling-ballooning modes model of edge magnetohydrodynamic stability as a working hypothesis to organize the data; several predictions of this theory are consistent with the experimental results. Current ramping results indicate that QH modes operate near the edge current limit set by peeling modes. This operating point explains why QH mode is easier to get at lower plasma currents. Power scans have shown a saturation of edge pressure with increasing power input. This allows QH-mode plasmas to remain stable to edge localized modes (ELMs) to the highest powers used in DIII-D. At present, the mechanism for this saturation is unknown; if the edge harmonic oscillation (EHO) is playing a role here, the physics is not a simple amplitude dependence. The increase in edge stability with plasma triangularity predicted by the peeling-ballooning theory is consistent with the substantial improvement in pedestal pressure achieved by changing the plasma shape from a single null divertor to a high triangularity double null. Detailed ELITE calculations for the high triangularity plasmas have demonstrated that the plasma operating point is marginally stable to peeling-ballooning modes. Comparison of ELMing, coinjected and quiescent, counterinjected discharges with the same shape, current, toroidal field, electron density, and electron temperature indicates that the edge radial electric field or the edge toroidal rotation are also playing a role in edge stability. The EHO produces electron, main ion, and impurity particle transport at the plasma edge which is more rapid than that produced by ELMs under similar conditions. The EHO also decreases the edge rotation while producing little change in the edge electron and ion temperatures. Other edge electromagnetic modes also produce particle transport; this includes the incoherent, broadband activity seen at high triangularity. Pedestal values of ν* and βT bracketing, those required for International Experimental Thermonuclear Reactor [Nucl. Fusion 39, 2137 (1999)] have been achieved in DIII-D, demonstrating the QH-mode edge densities are sufficient for future devices.

Advances in understanding quiescent H-mode plasmas in DIII-D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burrell, K.H.; West, W.P.; Gohil, P.

2005-05-15

Recent QH-mode research on DIII-D [J. L. Luxon et al., Plasma Physics and Controlled Nuclear Fusion Research 1996 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] has used the peeling-ballooning modes model of edge magnetohydrodynamic stability as a working hypothesis to organize the data; several predictions of this theory are consistent with the experimental results. Current ramping results indicate that QH modes operate near the edge current limit set by peeling modes. This operating point explains why QH mode is easier to get at lower plasma currents. Power scans have shown a saturation of edge pressure with increasingmore » power input. This allows QH-mode plasmas to remain stable to edge localized modes (ELMs) to the highest powers used in DIII-D. At present, the mechanism for this saturation is unknown; if the edge harmonic oscillation (EHO) is playing a role here, the physics is not a simple amplitude dependence. The increase in edge stability with plasma triangularity predicted by the peeling-ballooning theory is consistent with the substantial improvement in pedestal pressure achieved by changing the plasma shape from a single null divertor to a high triangularity double null. Detailed ELITE calculations for the high triangularity plasmas have demonstrated that the plasma operating point is marginally stable to peeling-ballooning modes. Comparison of ELMing, coinjected and quiescent, counterinjected discharges with the same shape, current, toroidal field, electron density, and electron temperature indicates that the edge radial electric field or the edge toroidal rotation are also playing a role in edge stability. The EHO produces electron, main ion, and impurity particle transport at the plasma edge which is more rapid than that produced by ELMs under similar conditions. The EHO also decreases the edge rotation while producing little change in the edge electron and ion temperatures. Other edge electromagnetic modes also produce particle transport; this includes the incoherent, broadband activity seen at high triangularity. Pedestal values of {nu}{sub *} and {beta}{sub T} bracketing, those required for International Experimental Thermonuclear Reactor [Nucl. Fusion 39, 2137 (1999)] have been achieved in DIII-D, demonstrating the QH-mode edge densities are sufficient for future devices.« less

An algorithm for propagating the square-root covariance matrix in triangular form

NASA Technical Reports Server (NTRS)

Tapley, B. D.; Choe, C. Y.

1976-01-01

A method for propagating the square root of the state error covariance matrix in lower triangular form is described. The algorithm can be combined with any triangular square-root measurement update algorithm to obtain a triangular square-root sequential estimation algorithm. The triangular square-root algorithm compares favorably with the conventional sequential estimation algorithm with regard to computation time.

Toward a New Method of Decoding Algebraic Codes Using Groebner Bases

DTIC Science & Technology

1993-10-01

variables over GF(2m). A celebrated algorithm by Buchberger produces a reduced Groebner basis of that ideal. It tums out that, since the common roots of...all the polynomials in the ideal are a set of isolated points, this reduced Groebner basis is in triangular form, and the univariate polynomial in that

Triangular arbitrage in the foreign exchange market

NASA Astrophysics Data System (ADS)

Aiba, Yukihiro; Hatano, Naomichi

2004-12-01

We first review our previous work, showing what is the triangular arbitrage transaction and how to quantify the triangular arbitrage opportunity. Next we explain that the correlation of the foreign exchange rates can appear without actual triangular arbitrage transaction.

Magnetic and magnetocaloric properties of the exactly solvable mixed-spin Ising model on a decorated triangular lattice in a magnetic field

NASA Astrophysics Data System (ADS)

Gálisová, Lucia; Strečka, Jozef

2018-05-01

The ground state, zero-temperature magnetization process, critical behaviour and isothermal entropy change of the mixed-spin Ising model on a decorated triangular lattice in a magnetic field are exactly studied after performing the generalized decoration-iteration mapping transformation. It is shown that both the inverse and conventional magnetocaloric effect can be found near the absolute zero temperature. The former phenomenon can be found in a vicinity of the discontinuous phase transitions and their crossing points, while the latter one occurs in some paramagnetic phases due to a spin frustration to be present at zero magnetic field. The inverse magnetocaloric effect can also be detected slightly above continuous phase transitions following the power-law dependence | - ΔSisomin | ∝hn, where n depends basically on the ground-state spin ordering.

The Evolution of Mission Architectures for Human Lunar Exploration

NASA Technical Reports Server (NTRS)

Everett, S. F.

1995-01-01

Defining transportation architectures for the human exploration of the Moon is a complex task due to the multitude of mission scenarios available. The mission transportation architecture recently proposed for the First Lunar Outpost (FLO) was not designed from carefully predetermined mission requirements and goals, but evolved from an initial set of requirements, which were continually modified as studies revealed that some early assumptions were not optimal. This paper focuses on the mission architectures proposed for FLO and investigates how these transportation architectures evolved. A comparison of the strengths and weaknesses of the three distinct mission architectures are discussed, namely (1) Lunar Orbit Rendezvous, (2) staging from the Cislunar Libration Point, and (3) direct to the lunar surface. In addition, several new and revolutionary architectures are discussed.

Applying the OTV to lunar logistics

NASA Technical Reports Server (NTRS)

Willcockson, W. H.

1988-01-01

The Orbit Transfer Vehicle (OTV), representing the next generation of upper stages, has recently been studied in a Phase A concept definition study managed by NASA's Marshall Space Flight Center. The vehicle has been previously defined as strictly an orbit-to-orbit type transfer device. Recently its application to the task of lunar surface logistics was investigated. Transfer options to the surface were considered which included direct transfer, and transfer via lunar orbit as well as the L1 libration point. The subsystem modifications required to enable lunar landings were established for the following elements: aerobrake, main propulsion system, landing legs, primary structure, and avionics. It is concluded that the majority of the basic systems required for efficient transfer to the lunar surface are already contained in the OTV.

Trajectory design for Saturnian Ocean Worlds orbiters using multidimensional Poincaré maps

NASA Astrophysics Data System (ADS)

Davis, Diane Craig; Phillips, Sean M.; McCarthy, Brian P.

2018-02-01

Missions based on low-energy orbits in the vicinity of planetary moons, such as Titan or Enceladus, involve significant end-to-end trajectory design challenges due to the gravitational effects of the distant larger primary. To address these challenges, the current investigation focuses on the visualization and use of multidimensional Poincaré maps to perform preliminary design of orbits with significant out-of-plane components, including orbits that provide polar coverage. Poincaré maps facilitate the identification of families of solutions to a given orbit problem and provide the ability to easily respond to changing inputs and requirements. A visual-based design process highlights a variety of trajectory options near Saturn's ocean worlds, including both moon-centered orbits and libration point orbits.

On some labelings of triangular snake and central graph of triangular snake graph

NASA Astrophysics Data System (ADS)

Agasthi, P.; Parvathi, N.

2018-04-01

A Triangular snake Tn is obtained from a path u 1 u 2 … u n by joining ui and u i+1 to a new vertex wi for 1≤i≤n‑1. A Central graph of Triangular snake C(T n ) is obtained by subdividing each edge of Tn exactly once and joining all the non adjacent vertices of Tn . In this paper the ways to construct square sum, square difference, Root Mean square, strongly Multiplicative, Even Mean and Odd Mean labeling for Triangular Snake and Central graph of Triangular Snake graphs are reported.

Strong-coupling analysis of two-dimensional O({ital N}) {sigma} models with {ital N}{le}2 on square, triangular, and honeycomb lattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campostrini, M.; Pelissetto, A.; Rossi, P.

1996-09-01

The critical behavior of two-dimensional (2D) O({ital N}) {sigma} models with {ital N}{le}2 on square, triangular, and honeycomb lattices is investigated by an analysis of the strong-coupling expansion of the two-point fundamental Green{close_quote}s function {ital G}({ital x}), calculated up to 21st order on the square lattice, 15th order on the triangular lattice, and 30th order on the honeycomb lattice. For {ital N}{lt}2 the critical behavior is of power-law type, and the exponents {gamma} and {nu} extracted from our strong-coupling analysis confirm exact results derived assuming universality with solvable solid-on-solid models. At {ital N}=2, i.e., for the 2D {ital XY} model,more » the results from all lattices considered are consistent with the Kosterlitz-Thouless exponential approach to criticality, characterized by an exponent {sigma}=1/2, and with universality. The value {sigma}=1/2 is confirmed within an uncertainty of few percent. The prediction {eta}=1/4 is also roughly verified. For various values of {ital N}{le}2, we determine some ratios of amplitudes concerning the two-point function {ital G}({ital x}) in the critical limit of the symmetric phase. This analysis shows that the low-momentum behavior of {ital G}({ital x}) in the critical region is essentially Gaussian at all values of {ital N}{le}2. Exact results for the long-distance behavior of {ital G}({ital x}) when {ital N}=1 (Ising model in the strong-coupling phase) confirm this statement. {copyright} {ital 1996 The American Physical Society.}« less

Evaluation of the AFWA WRF 4-KM Moving Nest Model Predictions for Western North Pacific Tropical Cyclones

DTIC Science & Technology

2006-03-01

16 3. Typhoon Mawar ..................................................................... 19 4. Typhoon Talim...From: Digital Typhoon website) Infrared satellite image of Tropical Storm Mawar (center) and the seedling convection of what would become...Typhoon Mawar . The red triangular points represent the period covered by the two 72-h ARW integrations. The large red dot indicates the ending time of

33 CFR 334.1330 - Bering Strait, Alaska; naval restricted area off Cape Prince of Wales.

Code of Federal Regulations, 2010 CFR

2010-07-01

... restricted area off Cape Prince of Wales. 334.1330 Section 334.1330 Navigation and Navigable Waters CORPS OF....1330 Bering Strait, Alaska; naval restricted area off Cape Prince of Wales. (a) The area. An area 2,000 feet wide extending from a point on Cape Prince of Wales marked by a triangular cable marker located...

Bone Pose Estimation in the Presence of Soft Tissue Artifact Using Triangular Cosserat Point Elements.

PubMed

Solav, Dana; Rubin, M B; Cereatti, Andrea; Camomilla, Valentina; Wolf, Alon

2016-04-01

Accurate estimation of the position and orientation (pose) of a bone from a cluster of skin markers is limited mostly by the relative motion between the bone and the markers, which is known as the soft tissue artifact (STA). This work presents a method, based on continuum mechanics, to describe the kinematics of a cluster affected by STA. The cluster is characterized by triangular cosserat point elements (TCPEs) defined by all combinations of three markers. The effects of the STA on the TCPEs are quantified using three parameters describing the strain in each TCPE and the relative rotation and translation between TCPEs. The method was evaluated using previously collected ex vivo kinematic data. Femur pose was estimated from 12 skin markers on the thigh, while its reference pose was measured using bone pins. Analysis revealed that instantaneous subsets of TCPEs exist which estimate bone position and orientation more accurately than the Procrustes Superimposition applied to the cluster of all markers. It has been shown that some of these parameters correlate well with femur pose errors, which suggests that they can be used to select, at each instant, subsets of TCPEs leading an improved estimation of the underlying bone pose.

Thermal Entanglement in XXZ Heisenberg Model for Coupled Spin-Half and Spin-One Triangular Cell

NASA Astrophysics Data System (ADS)

Najarbashi, Ghader; Balazadeh, Leila; Tavana, Ali

2018-01-01

In this paper, we investigate the thermal entanglement of two-spin subsystems in an ensemble of coupled spin-half and spin-one triangular cells, (1/2, 1/2, 1/2), (1/2, 1, 1/2), (1, 1/2, 1) and (1, 1, 1) with the XXZ anisotropic Heisenberg model subjected to an external homogeneous magnetic field. We adopt the generalized concurrence as the measure of entanglement which is a good indicator of the thermal entanglement and the critical points in the mixed higher dimensional spin systems. We observe that in the near vicinity of the absolute zero, the concurrence measure is symmetric with respect to zero magnetic field and changes abruptly from a non-null to null value for a critical magnetic field that can be signature of a quantum phase transition at finite temperature. The analysis of concurrence versus temperature shows that there exists a critical temperature, that depends on the type of the interaction, i.e. ferromagnetic or antiferromagnetic, the anisotropy parameter and the strength of the magnetic field. Results show that the pairwise thermal entanglement depends on the third spin which affects the maximum value of the concurrence at absolute zero and at quantum critical points.

Investigation of a Structural Phase Transition and Magnetic Structure of Na 2BaFe(VO 4) 2: A Triangular Magnetic Lattice with a Ferromagnetic Ground State

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sanjeewa, Liurukara D.; Garlea, Vasile O.; McGuire, Michael A.

The structural and magnetic properties of a glaserite-type Na 2BaFe(VO 4) 2 compound, featuring a triangular magnetic lattice of Fe 2+ (S = 2), are reported. Temperature dependent X-ray single crystal studies indicate that at room temperature the system adopts a trigonal Pmore » $$\\bar{3}$$ m1 structure and undergoes a structural phase transition to a C2/c monoclinic phase slightly below room temperature (T s = 288 K). This structural transition involves a tilting of Fe–O–V bond angles and strongly influences the magnetic correlation within the Fe triangular lattice. The magnetic susceptibility measurements reveal a ferromagnetic transition near 7 K. Single crystal neutron diffraction confirms the structural distortion and the ferromagnetic spin ordering in Na 2BaFe(VO 4) 2. The magnetic structure of the ordered state is modeled in the magnetic space group C2'/c' that implies a ferromagnetic order of the a and c moment components and antiferromagnetic arrangement for the b components. Altogether, the Fe magnetic moments form ferromagnetic layers that are stacked along the c-axis, where the spins point along one of the (111) facets of the FeO 6 octahedron.« less

Absence of Long-Range Order in a Triangular Spin System with Dipolar Interactions

NASA Astrophysics Data System (ADS)

Keleş, Ahmet; Zhao, Erhai

2018-05-01

The antiferromagnetic Heisenberg model on the triangular lattice is perhaps the best known example of frustrated magnets, but it orders at low temperatures. Recent density matrix renormalization group (DMRG) calculations find that the next nearest neighbor interaction J2 enhances the frustration, and it leads to a spin liquid for J2/J1∈(0.08 ,0.15 ). In addition, a DMRG study of a dipolar Heisenberg model with longer range interactions gives evidence for a spin liquid at a small dipole tilting angle θ ∈[0 ,1 0 ° ). In both cases, the putative spin liquid region appears to be small. Here, we show that for the triangular lattice dipolar Heisenberg model, a robust quantum paramagnetic phase exists in a surprisingly wide region, θ ∈[0 ,5 4 ° ) , for dipoles tilted along the lattice diagonal direction. We obtain the phase diagram of the model by functional renormalization group (RG), which treats all magnetic instabilities on equal footing. The quantum paramagnetic phase is characterized by a smooth continuous flow of vertex functions and spin susceptibility down to the lowest RG scale, in contrast to the apparent breakdown of RG flow in phases with stripe or spiral order. Our finding points to a promising direction to search for quantum spin liquids in ultracold dipolar molecules.

Investigation of a Structural Phase Transition and Magnetic Structure of Na 2BaFe(VO 4) 2: A Triangular Magnetic Lattice with a Ferromagnetic Ground State

DOE PAGES

Sanjeewa, Liurukara D.; Garlea, Vasile O.; McGuire, Michael A.; ...

2017-12-07

The structural and magnetic properties of a glaserite-type Na 2BaFe(VO 4) 2 compound, featuring a triangular magnetic lattice of Fe 2+ (S = 2), are reported. Temperature dependent X-ray single crystal studies indicate that at room temperature the system adopts a trigonal Pmore » $$\\bar{3}$$ m1 structure and undergoes a structural phase transition to a C2/c monoclinic phase slightly below room temperature (T s = 288 K). This structural transition involves a tilting of Fe–O–V bond angles and strongly influences the magnetic correlation within the Fe triangular lattice. The magnetic susceptibility measurements reveal a ferromagnetic transition near 7 K. Single crystal neutron diffraction confirms the structural distortion and the ferromagnetic spin ordering in Na 2BaFe(VO 4) 2. The magnetic structure of the ordered state is modeled in the magnetic space group C2'/c' that implies a ferromagnetic order of the a and c moment components and antiferromagnetic arrangement for the b components. Altogether, the Fe magnetic moments form ferromagnetic layers that are stacked along the c-axis, where the spins point along one of the (111) facets of the FeO 6 octahedron.« less

Numerical approach to constructing the lunar physical libration: results of the initial stage

NASA Astrophysics Data System (ADS)

Zagidullin, A.; Petrova, N.; Nefediev, Yu.; Usanin, V.; Glushkov, M.

2015-10-01

So called "main problem" it is taken as a model to develop the numerical approach in the theory of lunar physical libration. For the chosen model, there are both a good methodological basis and results obtained at the Kazan University as an outcome of the analytic theory construction. Results of the first stage in numerical approach are presented in this report. Three main limitation are taken to describe the main problem: -independent consideration of orbital and rotational motion of the Moon; - a rigid body model for the lunar body is taken and its dynamical figure is described by inertia ellipsoid, which gives us the mass distribution inside the Moon. - only gravitational interaction with the Earth and the Sun is considered. Development of selenopotential is limited on this stage by the second harmonic only. Inclusion of the 3-rd and 4-th order harmonics is the nearest task for the next stage.The full solution of libration problem consists of removing the below specified limitations: consideration of the fine effects, caused by planet perturbations, by visco-elastic properties of the lunar body, by the presence of a two-layer lunar core, by the Earth obliquity, by ecliptic rotation, if it is taken as a reference plane.

Innovations in mission architectures for exploration beyond low Earth orbit

NASA Technical Reports Server (NTRS)

Cooke, D. R.; Joosten, B. J.; Lo, M. W.; Ford, K. M.; Hansen, R. J.

2003-01-01

Through the application of advanced technologies and mission concepts, architectures for missions beyond Earth orbit have been dramatically simplified. These concepts enable a stepping stone approach to science driven; technology enabled human and robotic exploration. Numbers and masses of vehicles required are greatly reduced, yet the pursuit of a broader range of science objectives is enabled. The scope of human missions considered range from the assembly and maintenance of large aperture telescopes for emplacement at the Sun-Earth libration point L2, to human missions to asteroids, the moon and Mars. The vehicle designs are developed for proof of concept, to validate mission approaches and understand the value of new technologies. The stepping stone approach employs an incremental buildup of capabilities, which allows for future decision points on exploration objectives. It enables testing of technologies to achieve greater reliability and understanding of costs for the next steps in exploration. c2003 American Institute of Aeronautics and Astronautics. Published by Elsevier Science Ltd. All rights reserved.

Generalizing boundaries for triangular designs, and efficacy estimation at extended follow-ups.

PubMed

Allison, Annabel; Edwards, Tansy; Omollo, Raymond; Alves, Fabiana; Magirr, Dominic; E Alexander, Neal D

2015-11-16

Visceral leishmaniasis (VL) is a parasitic disease transmitted by sandflies and is fatal if left untreated. Phase II trials of new treatment regimens for VL are primarily carried out to evaluate safety and efficacy, while pharmacokinetic data are also important to inform future combination treatment regimens. The efficacy of VL treatments is evaluated at two time points, initial cure, when treatment is completed and definitive cure, commonly 6 months post end of treatment, to allow for slow response to treatment and detection of relapses. This paper investigates a generalization of the triangular design to impose a minimum sample size for pharmacokinetic or other analyses, and methods to estimate efficacy at extended follow-up accounting for the sequential design and changes in cure status during extended follow-up. We provided R functions that generalize the triangular design to impose a minimum sample size before allowing stopping for efficacy. For estimation of efficacy at a second, extended, follow-up time, the performance of a shrinkage estimator (SHE), a probability tree estimator (PTE) and the maximum likelihood estimator (MLE) for estimation was assessed by simulation. The SHE and PTE are viable approaches to estimate an extended follow-up although the SHE performed better than the PTE: the bias and root mean square error were lower and coverage probabilities higher. Generalization of the triangular design is simple to implement for adaptations to meet requirements for pharmacokinetic analyses. Using the simple MLE approach to estimate efficacy at extended follow-up will lead to biased results, generally over-estimating treatment success. The SHE is recommended in trials of two or more treatments. The PTE is an acceptable alternative for one-arm trials or where use of the SHE is not possible due to computational complexity. NCT01067443 , February 2010.

Hierarchically triangular prism structured Co3O4: Self-supported fabrication and photocatalytic property

EPA Science Inventory

The formation of ammonium cobalt (II) phosphate was utilized to synthesize unprecedented 3D structures of Co3O4, triangular prisms and trunk-like structures, via a self-supported and organics-free method. The length of a triangular side of the prepared 3D triangular prisms is ~1...

Static and dynamical properties of the spin-1/2 equilateral triangular-lattice antiferromagnet Ba 3CoSb 2O 9

DOE PAGES

Ma, Jie; Kamiya, Yoshitomo; Hong, Tao; ...

2016-02-24

We present single-crystal neutron scattering measurements of the spin-1/2 equilateral triangular-lattice antiferromagnet Ba 3CoSb 2O 9. Besides confirming that the Co 2+ magnetic moments lie in the ab plane for zero magnetic field and then determining all the exchange parameters of the minimal quasi-2D spin Hamiltonian, we provide conclusive experimental evidence of magnon decay through observation of intrinsic line broadening. Through detailed comparisons with the linear and nonlinear spin-wave theories, we also point out that the large-S approximation, which is conventionally employed to predict magnon decay in noncollinear magnets, is inadequate to explain our experimental observation. Hence, our results callmore » for a new theoretical framework for describing excitation spectra in low-dimensional frustrated magnets under strong quantum effects.« less

An adaptive optics package designed for astronomical use with a laser guide star tuned to an absorption line of atomic sodium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Salmon, J.T.; Avicola, K.; Brase, J.M.

1994-04-11

We present the design and implementation of a very compact adaptive optic system that senses the return light from a sodium guide-star and controls a deformable mirror and a pointing mirror to compensate atmospheric perturbations in the wavefront. The deformable mirror has 19 electrostrictive actuators and triangular subapertures. The wavefront sensor is a Hartmann sensor with lenslets on triangular centers. The high-bandwidth steering mirror assembly incorporates an analog controller that samples the tilt with an avalanche photodiode quad cell. An {line_integral}/25 imaging leg focuses the light into a science camera that can either obtain long-exposure images or speckle data. Inmore » laboratory tests overall Strehl ratios were improved by a factor of 3 when a mylar sheet was used as an aberrator. The crossover frequency at unity gain is 30 Hz.« less

Bell inequalities stronger than the Clauser-Horne-Shimony-Holt inequality for three-level isotropic states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ito, Tsuyoshi; Imai, Hiroshi; ERATO-SORST Quantum Computation and Information Project, Japan Science and Technology Agency, 5-28-3 Hongo, Bunkyo-ku, Tokyo, 113-0033

2006-04-15

We show that some two-party Bell inequalities with two-valued observables are stronger than the CHSH inequality for 3x3 isotropic states in the sense that they are violated by some isotropic states in the 3x3 system that do not violate the CHSH inequality. These Bell inequalities are obtained by applying triangular elimination to the list of known facet inequalities of the cut polytope on nine points. This gives a partial solution to an open problem posed by Collins and Gisin. The results of numerical optimization suggest that they are candidates for being stronger than the I{sub 3322} Bell inequality for 3x3more » isotropic states. On the other hand, we found no Bell inequalities stronger than the CHSH inequality for 2x2 isotropic states. In addition, we illustrate an inclusion relation among some Bell inequalities derived by triangular elimination.« less

Implicit Contractive Mappings in Modular Metric and Fuzzy Metric Spaces

PubMed Central

Hussain, N.; Salimi, P.

2014-01-01

The notion of modular metric spaces being a natural generalization of classical modulars over linear spaces like Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, and Calderon-Lozanovskii spaces was recently introduced. In this paper we investigate the existence of fixed points of generalized α-admissible modular contractive mappings in modular metric spaces. As applications, we derive some new fixed point theorems in partially ordered modular metric spaces, Suzuki type fixed point theorems in modular metric spaces and new fixed point theorems for integral contractions. In last section, we develop an important relation between fuzzy metric and modular metric and deduce certain new fixed point results in triangular fuzzy metric spaces. Moreover, some examples are provided here to illustrate the usability of the obtained results. PMID:25003157

Distant magnetic field effects associated with Birkeland currents /made possible by the evaluation of TRIAD's attitude oscillations/

NASA Astrophysics Data System (ADS)

Gustafsson, G.; Potemra, T. A.; Favin, S.; Saflekos, N. A.

1981-10-01

Principal oscillations of the TRIAD satellite are studied in 150 passes and are identified as the librations of a gravity-stabilized satellite. The libration periods are T(O)/2 and T(O)/(3) exp 1/2, where T(O) is the orbit period of about 100 min. The amplitude and phase change over periods of a few days, sometimes vanishing altogether, and these attitude changes are numerically evaluated and removed. Data from three consecutive passes spanning over three hours show a magnetic profile which extends as far as 10 deg in latitude from a single region 1 Birkeland current sheet, confirming the permanent and global nature of large-scale Birkeland currents.

ACOSS Eleven (Active Control of Space Structures). Volume 1

DTIC Science & Technology

1983-12-01

Influence Function ................. 19 3.4 Mirror Deformations. ........................... o............. 23 3.5 Selection of Point Objects...to simulate errors in the knowledge of influence function . 5) The influence function for edge actuators may be different from that for interior... Influence Function Each of the three mirrors has 37 actuators distributed on an equi- lateral triangular lattice as shown in Figure 3-3. In consultation with

Space manufacturing facilities: Space colonies; Proceedings of the Princeton Conference, Princeton University, Princeton, N.J., May 7-9, 1975

NASA Technical Reports Server (NTRS)

Grey, J.

1977-01-01

Reports submitted to the conference encompass: administration and law relating to inhabited space facilities and colonies; space manufacturing and processing; organization and construction of space habitats and management of space colony farms; winning and acquisition of lunar and asteroidal materials for sustaining autonomous space colonies. Attention is given to trajectories between earth, low earth orbit, earth-moon libration points (specifically L5), circumlunar parking orbits, and trajectories in translunar space; effects of low gravity and zero gravity on human physiology and on materials processing; architecture and landscaping for space colonies; closed ecosystems of space colonies. Varieties of human cultures and value hierarchies around the earth are examined for broader perspectives on the social organization of space colonies.

Contingency plans for the ISEE-3 libration-point mission

NASA Technical Reports Server (NTRS)

Dunham, D. W.

1979-01-01

During the planning stage of the International Sun-Earth Explorer-3 (ISEE-3) mission, a recovery strategy was developed in case the Delta rocket underperformed during the launch phase. If a large underburn had occurred, the ISEE-3 spacecraft would have been allowed to complete one revolution of its highly elliptical earth orbit. The recovery plan called for a maneuver near perigee to increase the energy of the off-nominal orbit; a relatively small second maneuver would then insert the spacecraft into a new transfer trajectory toward the desired halo orbit target, and a third maneuver would place the spacecraft in the halo orbit. Results of the study showed that a large range of underburns could be corrected for a total nominal velocity deviation cost within the ISEE-3 fuel budget.

The capture of lunar materials in low lunar orbit

NASA Technical Reports Server (NTRS)

Floyd, M. A.

1981-01-01

A scenario is presented for the retrieval of lunar materials sent into lunar orbit to be used as raw materials in space manufacturing operations. The proposal is based on the launch of material from the lunar surface by an electromagnetic mass driver and the capture of this material in low lunar orbit by a fleet of mass catchers which ferry the material to processing facilities when full. Material trajectories are analyzed using the two-body equations of motion, and intercept requirements and the sensitivity of the system to launch errors are determined. The present scenario is shown to be superior to scenarios that place a single mass catcher at the L2 libration point due to increased operations flexibility, decreased mass driver performance requirements and centralized catcher servicing.

High Fidelity Modeling of SRP and Its Effect on the Relative Motion of Starshade and WFIRST

NASA Technical Reports Server (NTRS)

Farres, Ariadna; Webster, Cassandra; Folta, Dave

2018-01-01

In this paper we perform a detailed analysis of how Solar Radiation Pressure (SRP) affects the relative motion of two spacecrafts, the Wide-Field Infrared Survey Telescope (WFIRST) and Starshade, orbiting in the vicinity of the Sun-Earth L2. While WFIRST orbits about its own Libration Point Orbit (LPO), Starshade will fly a specific trajectory to align with WFIRST and observe a Design Reference Mission of pre-determined target stars. In this analysis, we focus on the transfer orbit for Starshade from one observation to the other. We will describe how SRP affects the dynamics of the Starshade relative to WFIRSTand how relevant this effect is in order to get an accurate estimate of the total difference in velocity (delta v).

Contingency study for the third international Sun-Earth Explorer (ISEE-3) satellite

NASA Technical Reports Server (NTRS)

Dunham, D. W.

1979-01-01

The third satellite of the international Sun-Earth Explorer program was inserted into a periodic halo orbit about L sub 1, the collinear libration point between the Sun and the Earth-Moon barycenter. A plan is presented that was developed to enable insertion into the halo orbit in case there was a large underperformance of the Delta second or third stage during the maneuver to insert the spacecraft into the transfer trajectory. After one orbit of the Earth, a maneuver would be performed near perigee to increase the energy of the orbit. A relatively small second maneuver would put the spacecraft in a transfer trajectory to the halo orbit, into which it could be inserted for a total cost within the fuel budget. Overburns (hot transfer trajectory insertions) were also studied.

Earth Shadows and the SEV Angle of MAP's Lissajous Orbit At L2

NASA Technical Reports Server (NTRS)

Edery, Ariel

2002-01-01

The Microwave Anisotropy Probe (MAP) launched successfully on June 30, 2001 and is presently in a Lissajous orbit about the Sun-Earth libration point L2. To avoid Earth shadows at L2, the Sun-Earth-Vehicle (SEV) angle of MAP has to be greater than 0.5 deg for an extended mission of four years. An equation is derived for the SEV angle in terms of the phase angle, frequencies and amplitudes of the Lissajous. The SEV angle is shown to oscillate with a period of 90.4 days within an amplitude envelope of period 13.9 years. A range of phase angles that avoids shadows is identified. MAP'S present phase angle is within this range and will avoid shadows for approximately 5.8 years.

Investigation of dynamic noise affecting geodynamics information in a tethered subsatellite

NASA Technical Reports Server (NTRS)

Gullahorn, G. E.

1984-01-01

The effects of a tethered satellite system's internal dynamics on the subsatellite were calculated including both overall motions (libration and attitude oscillations) and internal tether oscillations. The SKYHOOK tether simulation program was modified to operate with atmospheric density variations and to output quantities of interest. Techniques and software for analyzing the results were developed including noise spectral analysis. A program was begun for computing a stable configuration of a tether system subject to air drag. These configurations will be of use as initial conditions for SKYHOOK and, through linearized analysis, directly for stability and dynamical studies. A case study in which the subsatellite traverses an atmospheric density enhancement confirmed some theoretical calculations, and pointed out some aspects of the interaction with the tether system dynamics.

The correlation of initial radiographic characteristics of distal radius fractures and injuries of the triangular fibrocartilage complex.

PubMed

Kasapinova, K; Kamiloski, V

2016-06-01

Our purpose was to determine the correlation of initial radiographic parameters of a distal radius fracture with an injury of the triangular fibrocartilage complex. In a prospective study, 85 patients with surgically treated distal radius fractures were included. Wrist arthroscopy was used to identify and classify triangular fibrocartilage complex lesions. The initial radial length and angulation, dorsal angulation, ulnar variance and distal radioulnar distance were measured. Wrist arthroscopy identified a triangular fibrocartilage complex lesion in 45 patients. Statistical analysis did not identify a correlation with any single radiographic parameter of the distal radius fractures with the associated triangular fibrocartilage complex injuries. The initial radiograph of a distal radius fracture does not predict a triangular fibrocartilage complex injury. III. © The Author(s) 2016.

Dynamic Kerr effect study on six-membered-ring molecular liquids: benzene, 1,3-cyclohexadiene, 1,4-cyclohexadiene, cyclohexene, and cyclohexane.

PubMed

Kakinuma, Shohei; Shirota, Hideaki

2015-04-02

The intermolecular dynamics of five six-membered-ring molecular liquids having different aromaticities-benzene, 1,3-cyclohexadiene, 1,4-cyclohexadiene, cyclohexene, and cyclohexane-measured by femtosecond Raman-induced Kerr effect spectroscopy have been compared in this study. The line shapes of the Fourier transform low-frequency spectra, which arise from the intermolecular vibrational dynamics, are trapezoidal for benzene and 1,3-cyclohexadiene, triangular for 1,4-cyclohexadiene and cyclohexene, and monomodal for cyclohexane. The trapezoidal shapes of the low-frequency spectra of benzene and 1,3-cyclohexadiene are due to the librational motions of their aromatic planar structures, which cause damped nuclear response features. The time integrals of the nuclear responses of the five liquids correlate to the squares of the polarizability anisotropies of the molecules calculated on the basis of density functional theory. The first moments of the low-frequency spectra roughly linearly correlate to the bulk parameters of the square roots of the surface tensions divided by the densities and the square roots of the surface tensions divided by the molecular weights, but the plots for cyclohexene deviate slightly from the correlations. The picosecond overdamped transients of the liquids are well fitted by a biexponential function. The fast time constants of all of the liquids are approximately 1.1-1.4 ps, and they do not obey the Stokes-Einstein-Debye hydrodynamic model. On the other hand, the slow time constants are roughly linearly proportional to the products of the shear viscosities and the molar volumes. The observed intramolecular vibrational modes at less than 700 cm(-1) for all of the liquids are also assigned on the basis of quantum chemistry calculations.

Hesitant triangular fuzzy information aggregation operators based on Bonferroni means and their application to multiple attribute decision making.

PubMed

Wang, Chunyong; Li, Qingguo; Zhou, Xiaoqiang; Yang, Tian

2014-01-01

We investigate the multiple attribute decision-making (MADM) problems with hesitant triangular fuzzy information. Firstly, definition and some operational laws of hesitant triangular fuzzy elements are introduced. Then, we develop some hesitant triangular fuzzy aggregation operators based on Bonferroni means and discuss their basic properties. Some existing operators can be viewed as their special cases. Next, we apply the proposed operators to deal with multiple attribute decision-making problems under hesitant triangular fuzzy environment. Finally, an illustrative example is given to show the developed method and demonstrate its practicality and effectiveness.

Hesitant Triangular Fuzzy Information Aggregation Operators Based on Bonferroni Means and Their Application to Multiple Attribute Decision Making

PubMed Central

Zhou, Xiaoqiang; Yang, Tian

2014-01-01

We investigate the multiple attribute decision-making (MADM) problems with hesitant triangular fuzzy information. Firstly, definition and some operational laws of hesitant triangular fuzzy elements are introduced. Then, we develop some hesitant triangular fuzzy aggregation operators based on Bonferroni means and discuss their basic properties. Some existing operators can be viewed as their special cases. Next, we apply the proposed operators to deal with multiple attribute decision-making problems under hesitant triangular fuzzy environment. Finally, an illustrative example is given to show the developed method and demonstrate its practicality and effectiveness. PMID:25140338

Series of Reciprocal Triangular Numbers

ERIC Educational Resources Information Center

Bruckman, Paul; Dence, Joseph B.; Dence, Thomas P.; Young, Justin

2013-01-01

Reciprocal triangular numbers have appeared in series since the very first infinite series were summed. Here we attack a number of subseries of the reciprocal triangular numbers by methodically expressing them as integrals.

A Generalization of the Formula for the Triangular Number of the Sum and Product of Natural Numbers

ERIC Educational Resources Information Center

Asiru, M. A.

2008-01-01

This note generalizes the formula for the triangular number of the sum and product of two natural numbers to similar results for the triangular number of the sum and product of "r" natural numbers. The formula is applied to derive formula for the sum of an odd and an even number of consecutive triangular numbers.

Formation Control of the MAXIM L2 Libration Orbit Mission

NASA Technical Reports Server (NTRS)

Folta, David; Hartman, Kate; Howell, Kathleen; Marchand, Belinda

2004-01-01

The Micro-Arcsecond Imaging Mission (MAXIM), a proposed concept for the Structure and Evolution of the Universe (SEU) Black Hole Imaging mission, is designed to make a ten million-fold improvement in X-ray image clarity of celestial objects by providing better than 0.1 microarcsecond imaging. To achieve mission requirements, MAXIM will have to improve on pointing by orders of magnitude. This pointing requirement impacts the control and design of the formation. Currently the architecture is comprised of 25 spacecraft, which will form the sparse apertures of a grazing incidence X-ray interferometer covering the 0.3-10 keV bandpass. This configuration will deploy 24 spacecraft as optics modules and one as the detector. The formation must allow for long duration continuous science observations and also for reconfiguration that permits re-pointing of the formation. In this paper, we provide analysis and trades of several control efforts that are dependent upon the pointing requirements and the configuration and dimensions of the MAXIM formation. We emphasize the utilization of natural motions in the Lagrangian regions that minimize the control efforts and we address both continuous and discrete control via LQR and feedback linearization. Results provide control cost, configuration options, and capabilities as guidelines for the development of this complex mission.

Biostereometric Data Processing In ERGODATA: Choice Of Human Body Models

NASA Astrophysics Data System (ADS)

Pineau, J. C.; Mollard, R.; Sauvignon, M.; Amphoux, M.

1983-07-01

The definition of human body models was elaborated with anthropometric data from ERGODATA. The first model reduces the human body into a series of points and lines. The second model is well adapted to represent volumes of each segmentary element. The third is an original model built from the conventional anatomical points. Each segment is defined in space by a tri-angular plane located with its 3-D coordinates. This new model can answer all the processing possibilities in the field of computer-aided design (C.A.D.) in ergonomy but also biomechanics and orthopaedics.

Effect of mass variation on dynamics of tethered system in orbital maneuvering

NASA Astrophysics Data System (ADS)

Sun, Liang; Zhao, Guowei; Huang, Hai

2018-05-01

In orbital maneuvering, the mass variation due to fuel consumption has an obvious impact on the dynamics of tethered system, which cannot be neglected. The contributions of the work are mainly shown in two aspects: 1) the improvement of the model; 2) the analysis of dynamics characteristics. As the mass is variable, and the derivative of the mass is directly considered in the traditional Lagrange equation, the expression of generalized force is complicated. To solve this problem, the coagulated derivative is adopted in the paper; besides, the attitude dynamics equations derived in this paper take into account the effect of mass variation and the drift of orbital trajectory at the same time. The bifurcation phenomenon, the pendular motion angular frequency, and amplitudes of tether vibration revealed in this paper can provide a reference for the parameters and controller design in practical engineering. In the article, a dumbbell model is adopted to analyze the dynamics of tethered system, in which the mass variation of base satellite is fully considered. Considering the practical application, the case of orbital transfer under a transversal thrust is mainly studied. Besides, compared with the analytical solutions of librational angles, the effects of mass variation on stability and librational characteristic are studied. Finally, in order to make an analysis of the effect on vibrational characteristic, a lumped model is introduced, which reveals a strong coupling of librational and vibrational characteristics.

Variations in Rotation Rate and Polar Motion of a Non-hydrostatic Titan

NASA Astrophysics Data System (ADS)

Van Hoolst, T.; Coyette, A.; Baland, R. M.

2017-12-01

Observations of the rotation of large synchronously rotating satellites such as Titan can help to probe their interior. Previous studies (Van Hoolst et al. 2013, Richard et al. 2014, Coyette et al. 2016) mostly assume that Titan is in hydrostatic equilibrium, although several measurements indicate that it deviates from such a state. Here we investigate the effect of non-hydrostatic equilibrium and of flow in the subsurface ocean on the rotation of Titan. We consider (1) the periodic changes in Titan's rotation rate with a period equal to Titan's orbital period (diurnal librations) as a result of the gravitational torque exerted by Saturn, (2) the periodic changes in Titan's rotation rate with a main period equal to half the orbital period of Saturn (seasonal librations) and due to the dynamic variations in the atmosphere of Titan and (3) the periodic changes of the axis of rotation with respect to the figure axis of Titan (polar motion) with a main period equal to the orbital period of Saturn and due to the dynamic variations in the atmosphere of Titan. The non-hydrostatic mass distribution significantly influences the amplitude of the diurnal and seasonal librations. It is less important for polar motion, which is sensitive to flow in the subsurface ocean. The smaller than synchronous rotation rate measured by Cassini (Meriggiola 2016) can be explained by the atmospheric forcing.

The structure of non-hierarchical triple system stability regions

NASA Astrophysics Data System (ADS)

Martynova, A. I.; Orlov, V. V.; Rubinov, A. V.

2009-08-01

A detailed study of the two-dimensional initial conditions region section in the planar three-body problem is performed. The initial conditions for the three well-known stable periodic orbits (the Schubart’s orbit, the Broucke’s orbit and the eight-like orbit) belong to this section. Continuous stability regions (for the fixed integration interval) generated by these periodic orbits are found. Zones of the quick stability violation are outlined. The analysis of some concrete trajectories coming from various stability regions is performed. In particular, trajectories possessing varying number of “eights” formed by moving triple system components are discovered. Orbits with librations are also found. The new periodic orbit originated from the zone siding with the Schubart’s orbit region is discovered. This orbit has reversibility points (each of the outer bodies possess a reversibility point) and two points of close double approach of the central body to each of the outer bodies. The influence of the numerical integration accuracy on the results is studied. The stability regions structure is preserved during calculations with different values of the precision parameter, numerical integration methods and regularization algorithms of the equations of motion.

Control of asteroid retrieval trajectories to libration point orbits

NASA Astrophysics Data System (ADS)

Ceriotti, Matteo; Sanchez, Joan Pau

2016-09-01

The fascinating idea of shepherding asteroids for science and resource utilization is being considered as a credible concept in a not too distant future. Past studies identified asteroids which could be efficiently injected into manifolds which wind onto periodic orbits around collinear Lagrangian points of the Sun-Earth system. However, the trajectories are unstable, and errors in the capture maneuver would lead to complete mission failure, with potential danger of collision with the Earth, if uncontrolled. This paper investigates the controllability of some asteroids along the transfers and the periodic orbits, assuming the use of a solar-electric low-thrust system shepherding the asteroid. Firstly, an analytical approach is introduced to estimate the stability of the trajectories from a dynamical point of view; then, a numerical control scheme based on a linear quadratic regulator is proposed, where the gains are optimized for each trajectory through a genetic algorithm. A stochastic simulation with a Monte Carlo approach is used to account for different perturbed initial conditions and the epistemic uncertainty on the asteroid mass. Results show that only a small subset of the considered combinations of trajectories/asteroids are reliably controllable, and therefore controllability must be taken into account in the selection of potential targets.

Autonomous Navigation Using Celestial Objects

NASA Technical Reports Server (NTRS)

Folta, David; Gramling, Cheryl; Leung, Dominic; Belur, Sheela; Long, Anne

1999-01-01

In the twenty-first century, National Aeronautics and Space Administration (NASA) Enterprises envision frequent low-cost missions to explore the solar system, observe the universe, and study our planet. Satellite autonomy is a key technology required to reduce satellite operating costs. The Guidance, Navigation, and Control Center (GNCC) at the Goddard Space Flight Center (GSFC) currently sponsors several initiatives associated with the development of advanced spacecraft systems to provide autonomous navigation and control. Autonomous navigation has the potential both to increase spacecraft navigation system performance and to reduce total mission cost. By eliminating the need for routine ground-based orbit determination and special tracking services, autonomous navigation can streamline spacecraft ground systems. Autonomous navigation products can be included in the science telemetry and forwarded directly to the scientific investigators. In addition, autonomous navigation products are available onboard to enable other autonomous capabilities, such as attitude control, maneuver planning and orbit control, and communications signal acquisition. Autonomous navigation is required to support advanced mission concepts such as satellite formation flying. GNCC has successfully developed high-accuracy autonomous navigation systems for near-Earth spacecraft using NASA's space and ground communications systems and the Global Positioning System (GPS). Recently, GNCC has expanded its autonomous navigation initiative to include satellite orbits that are beyond the regime in which use of GPS is possible. Currently, GNCC is assessing the feasibility of using standard spacecraft attitude sensors and communication components to provide autonomous navigation for missions including: libration point, gravity assist, high-Earth, and interplanetary orbits. The concept being evaluated uses a combination of star, Sun, and Earth sensor measurements along with forward-link Doppler measurements from the command link carrier to autonomously estimate the spacecraft's orbit and reference oscillator's frequency. To support autonomous attitude determination and control and maneuver planning and control, the orbit determination accuracy should be on the order of kilometers in position and centimeters per second in velocity. A less accurate solution (one hundred kilometers in position) could be used for acquisition purposes for command and science downloads. This paper provides performance results for both libration point orbiting and high Earth orbiting satellites as a function of sensor measurement accuracy, measurement types, measurement frequency, initial state errors, and dynamic modeling errors.

Solar sail trajectory design in the Earth-Moon circular restricted three body problem

NASA Astrophysics Data System (ADS)

Das, Ashwati

The quest to explore the Moon has helped resolve scientific questions, has spurred leaps in technology development, and has revealed Earth's celestial companion to be a gateway to other destinations. With a renewed focus on returning to the Moon in this decade, alternatives to chemical propulsion systems are becoming attractive methods to efficiently use scarce resources and support extended mission durations. Thus, an investigation is conducted to develop a general framework, that facilitates propellant-free Earth-Moon transfers by exploiting sail dynamics in combination with advantageous transfer options offered in the Earth-Moon circular restricted multi-body dynamical model. Both periodic orbits in the vicinity of the Earth-Moon libration points, and lunar-centric long-term capture orbits are incorporated as target destinations to demonstrate the applicability of the general framework to varied design scanarios, each incorporating a variety of complexities and challenges. The transfers are comprised of three phases - a spiral Earth escape, a transit period, and, finally, the capture into a desirable orbit in the vicinity of the Moon. The Earth-escape phase consists of spiral trajectories constructed using three different sail steering strategies - locally optimal, on/off and velocity tangent. In the case of the Earth-libration point transfers, naturally occurring flow structures (e.g., invariant manifolds) arising from the mutual gravitational interaction of the Earth and Moon are exploited to link an Earth departure spiral with a destination orbit. In contrast, sail steering alone is employed to establish a link between the Earth-escape phase and capture orbits about the Moon due to a lack of applicable natural structures for the required connection. Metrics associated with the transfers including flight-time and the influence of operational constraints, such as occultation events, are investigated to determine the available capabilities for Earth-Moon transfers given current sail technology levels. Although the implemented steering laws suffice to generate baseline paths, infeasible turn rate demands placed on the sail are also investigated to explore the technical hurdles in designing Earth-Moon transfers. The methodologies are suitable for a variety of mission scenarios and sail configurations, rendering the resulting trajectories valuable for a diverse range of applications.

Development of non-bonded interaction parameters between graphene and water using particle swarm optimization.

PubMed

Bejagam, Karteek K; Singh, Samrendra; Deshmukh, Sanket A

2018-05-05

New Lennard-Jones parameters have been developed to describe the interactions between atomistic model of graphene, represented by REBO potential, and five commonly used all-atom water models, namely SPC, SPC/E, SPC/Fw, SPC/Fd, and TIP3P/Fs by employing particle swarm optimization (PSO) method. These new parameters were optimized to reproduce the macroscopic contact angle of water on a graphene sheet. The calculated line tension was in the order of 10 -11 J/m for the droplets of all water models. Our molecular dynamics simulations indicate the preferential orientation of water molecules near graphene-water interface with one OH bond pointing toward the graphene surface. Detailed analysis of simulation trajectories reveals the presence of water molecules with ≤∼1, ∼2, and ∼4 hydrogen bonds at the surface of air-water interface, graphene-water interface, and bulk region of the water droplet, respectively. Presence of water molecules with ≤∼1 and ∼2 hydrogen bonds suggest the existence of water clusters of different sizes at these interfaces. The trends observed in the libration, bending, and stretching bands of the vibrational spectra are closely associated with these structural features of water. The inhomogeneity in hydrogen bond network of water at the air-water and graphene-water interface is manifested by broadening of the peaks in the libration band for water present at these interfaces. The stretching band for the molecules in water droplet shows a blue shift as compared to the pure bulk water, which conjecture the presence of weaker hydrogen bond network in a droplet. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

On geodynamo integrations conserving momentum flux

NASA Astrophysics Data System (ADS)

Wu, C.; Roberts, P. H.

2012-12-01

The equations governing the geodynamo are most often integrated by representing the magnetic field and fluid velocity by toroidal and poloidal scalars (for example, MAG code [1]). This procedure does not automatically conserve the momentum flux. The results can, particularly for flows with large shear, introduce significant errors, unless the viscosity is artificially increased. We describe a method that evades this difficulty, by solving the momentum equation directly while properly conserving momentum. It finds pressure by FFT and cyclic reduction, and integrates the governing equations on overlapping grids so avoiding the pole problem. The number of operations per time step is proportional to N3 where N is proportional to the number of grid points in each direction. This contrasts with the order N4 operations of standard spectral transform methods. The method is easily parallelized. It can also be easily adapted to schemes such as the Weighted Essentially Non-Oscillatory (WENO) method [2], a flux based procedure based on upwinding that is numerically stable even for zero explicit viscosity. The method has been successfully used to investigate the generation of magnetic fields by flows confined to spheroidal containers and driven by precessional and librational forcing [3, 4]. For spherical systems it satisfies dynamo benchmarks [5]. [1] MAG, http://www.geodynamics.org/cig/software/mag [2] Liu, XD, Osher, S and Chan, T, Weighted Essentially Nonoscillatory Schemes, J. Computational Physics, 115, 200-212, 1994. [3] Wu, CC and Roberts, PH, On a dynamo driven by topographic precession, Geophysical & Astrophysical Fluid Dynamics, 103, 467-501, (DOI: 10.1080/03091920903311788), 2009. [4] Wu, CC and Roberts, PH, On a dynamo driven topographically by longitudinal libration, Geophysical & Astrophysical Fluid Dynamics, DOI:10.1080/03091929.2012.682990, 2012. [5] Christensen, U, et al., A numerical dynamo benchmark, Phys. Earth Planet Int., 128, 25-34, 2001.

Establishing the moon as a spectral radiance standard

USGS Publications Warehouse

Kieffer, H.H.; Wildey, R.L.

1996-01-01

A new automated observatory dedicated to the radiometry of the moon has been constructed to provide new radiance information for calibration of earth-orbiting imaging instruments, particularly Earth Observing System instruments. Instrumentation includes an imaging photometer with 4.5-in. resolution on a fully digital mount and a full-aperture radiance calibration source. Interference filters within 0.35-0.95 ??m correspond to standard stellar magnitude systems, accommodate wavelengths of lunar spectral contrast, and approximate some band-passes of planned earth-orbiting instruments (ASTER, Landsat-7 ETM, MISR, MODIS, and SeaWIFS). The same equipment is used for lunar and stellar observations, with the use of an aperture stop in lunar imaging to comply with Nyquist's theorem and lengthen exposure times to avoid scintillation effects. A typical robotic night run involves observation of about 60 photometric standard stars and the moon; about 10 of the standard stars are observed repeatedly to determine atmospheric extinction, and the moon is observed several times. Observations are to be made on every photometric night during the bright half of the month for at least 4.5 years to adequately cover phase and libration variation. Each lunar image is reduced to absolute exoatmospheric radiance and reprojected to a fixed selenographic grid system. The collection of these images at various librations and phase angles will be reduced to photometric models for each of the approximately 120 000 points in the lunar grid for each filter. Radiance models of the moon can then be produced for the precise geometry of an orbiting instrument observation. Expected errors are under 1% relative and 2.5% absolute. A second telescope operating from 1.0 to 2.5 ??m is planned.

Life History and Environmental Requirements of Loggerhead Turtles

DTIC Science & Technology

1988-08-01

NOMENCLATURE/TAXONOMY/RANGE Scientific name ........ .................... Caretta caretta Preferred common name ........ ................. Loggerhead...Green 51-105 113-140 Broad, oval Olive , dark- White- Small round 15(90)’ (100)a brown mottled yellowish Loggerhead 79-125 77-140 Heart-shaped Reddish...Cream- Very large 25 (110)8 (105)8 brown yellow triangular Kemp’s ridey 59-73 36-45 Circular Olive -green Yellow Medium 13 (70)a (42)’ pointed

An interactive display system for large-scale 3D models

NASA Astrophysics Data System (ADS)

Liu, Zijian; Sun, Kun; Tao, Wenbing; Liu, Liman

2018-04-01

With the improvement of 3D reconstruction theory and the rapid development of computer hardware technology, the reconstructed 3D models are enlarging in scale and increasing in complexity. Models with tens of thousands of 3D points or triangular meshes are common in practical applications. Due to storage and computing power limitation, it is difficult to achieve real-time display and interaction with large scale 3D models for some common 3D display software, such as MeshLab. In this paper, we propose a display system for large-scale 3D scene models. We construct the LOD (Levels of Detail) model of the reconstructed 3D scene in advance, and then use an out-of-core view-dependent multi-resolution rendering scheme to realize the real-time display of the large-scale 3D model. With the proposed method, our display system is able to render in real time while roaming in the reconstructed scene and 3D camera poses can also be displayed. Furthermore, the memory consumption can be significantly decreased via internal and external memory exchange mechanism, so that it is possible to display a large scale reconstructed scene with over millions of 3D points or triangular meshes in a regular PC with only 4GB RAM.

Ordering phenomena in a heterostructure of frustrated and unfrustrated triangular-lattice Ising layers

NASA Astrophysics Data System (ADS)

Žukovič, Milan; Tomita, Yusuke; Kamiya, Y.

2017-07-01

We study critical and magnetic properties of a bilayer Ising system consisting of two triangular planes A and B, with the antiferromagnetic (AF) coupling JA and the ferromagnetic (FM) one JB for the respective layers, which are coupled by the interlayer interaction JAB by using Monte Carlo simulations. When JA and JB are of the same order, the unfrustrated FM plane orders first at a high temperature Tc 1˜JB . The spontaneous FM order then exerts influence on the other frustrated AF plane as an effective magnetic field, which subsequently induces a ferrimagnetic order in this plane at low temperatures below Tc 2. When short-range order is developed in the AF plane while the influence of the FM plane is still small, there appears a preemptive Berezinskii-Kosterlitz-Thouless-type pseudocritical crossover regime just above the ferrimagnetic phase transition point, where the short-distance behavior up to a rather large length scale exponentially diverging in ∝JA/T is controlled by a line of Gaussian fixed points at T =0 . In the crossover region, a continuous variation in the effective critical exponent 4/9 ≲ηeff≲1/2 is observed. The phase diagram by changing the ratio JA/JB is also investigated.

Libration of arguments of circumbinary-planet orbits at resonance

NASA Astrophysics Data System (ADS)

Schubart, Joachim

2017-06-01

The paper refers to fictitious resonant orbits of planet type that surround both components of a binary system. In case of 16 studied examples a suitable choice of the starting values leads to a process of libration of special angular arguments and to an evolution with an at least temporary stay of the planet in the resonant orbit. The ratio of the periods of revolution of the binary and a planet is equal to 1:5. Eight orbits depend on the ratio 1:5 of the masses of the binary components, but two other ratios appear as well. The basis of this study is the planar, elliptic or circular restricted problem of three bodies, but remarks at the end of the text refer to a four-body problem.

Methodologies for Development of Patient Specific Bone Models from Human Body CT Scans

NASA Astrophysics Data System (ADS)

Chougule, Vikas Narayan; Mulay, Arati Vinayak; Ahuja, Bharatkumar Bhagatraj

2016-06-01

This work deals with development of algorithm for physical replication of patient specific human bone and construction of corresponding implants/inserts RP models by using Reverse Engineering approach from non-invasive medical images for surgical purpose. In medical field, the volumetric data i.e. voxel and triangular facet based models are primarily used for bio-modelling and visualization, which requires huge memory space. On the other side, recent advances in Computer Aided Design (CAD) technology provides additional facilities/functions for design, prototyping and manufacturing of any object having freeform surfaces based on boundary representation techniques. This work presents a process to physical replication of 3D rapid prototyping (RP) physical models of human bone from various CAD modeling techniques developed by using 3D point cloud data which is obtained from non-invasive CT/MRI scans in DICOM 3.0 format. This point cloud data is used for construction of 3D CAD model by fitting B-spline curves through these points and then fitting surface between these curve networks by using swept blend techniques. This process also can be achieved by generating the triangular mesh directly from 3D point cloud data without developing any surface model using any commercial CAD software. The generated STL file from 3D point cloud data is used as a basic input for RP process. The Delaunay tetrahedralization approach is used to process the 3D point cloud data to obtain STL file. CT scan data of Metacarpus (human bone) is used as the case study for the generation of the 3D RP model. A 3D physical model of the human bone is generated on rapid prototyping machine and its virtual reality model is presented for visualization. The generated CAD model by different techniques is compared for the accuracy and reliability. The results of this research work are assessed for clinical reliability in replication of human bone in medical field.

Mathematical model of parking space unit for triangular parking area

NASA Astrophysics Data System (ADS)

Syahrini, Intan; Sundari, Teti; Iskandar, Taufiq; Halfiani, Vera; Munzir, Said; Ramli, Marwan

2018-01-01

Parking space unit (PSU) is an effective measure for the area size of a vehicle, including the free space and the width of the door opening of the vehicle (car). This article discusses a mathematical model for parking space of vehicles in triangular shape area. An optimization model for triangular parking lot is developed. Integer Linear Programming (ILP) method is used to determine the maximum number of the PSU. The triangular parking lot is in isosceles and equilateral triangles shape and implements four possible rows and five possible angles for each field. The vehicles which are considered are cars and motorcycles. The results show that the isosceles triangular parking area has 218 units of optimal PSU, which are 84 units of PSU for cars and 134 units of PSU for motorcycles. Equilateral triangular parking area has 688 units of optimal PSU, which are 175 units of PSU for cars and 513 units of PSU for motorcycles.

Exploration of the region near the sun-earth collinear libration points for the control of large formations

NASA Astrophysics Data System (ADS)

Heritier, Aurelie

Spacecraft formations possess many applications in the future of space exploration. During the last decade, due to the detection of a large number of extrasolar planets, new studies on formation flying in multi-body regimes have emerged to support searches for Earth-like planets in other solar systems. The L2 Sun-Earth libration point region has been a popular destination in creating an architecture for astronomical missions. It is a relatively cold environment, far from the disturbances of the Sun and, therefore, ideal for astronomical instruments. However, controlling multiple spacecraft in a multi-body environment is challenging and a good understanding of the natural dynamics in this regime is essential. The current investigation explores the dynamical environment near the L2 Sun-Earth libration point to aid in the control of formations of spacecraft. By exploiting the natural dynamics in the circular restricted three-body model (CR3BP), natural regions are determined that are particularly suitable for maintaining formations of spacecraft. The natural dynamics at small distances from a given reference trajectory are initially investigated for the placement of small formations of spacecraft. Some regions with low relative drift represent suitable locations to maintain small formations and are derived analytically using variational equations. Spacecraft located in such regions avoid large variations in their mutual distances while maintaining the orientation of the formation. These regions represent quadric surfaces, and the type of quadric surfaces, either ellipsoids or elliptic cylinders, depends on the eigenstructure reflecting the phase space along the given reference trajectory. The natural flow at large distances from a given reference trajectory is explored next to characterize regions that are suitable to maintain large formations, i.e., when the mutual distances between the spacecraft reaches tens of thousands of kilometers. Spheres of points at various locations along the reference orbit are constructed to classify the space, and regions of low natural drift on the spheres are numerically identified when the distance between two vehicles is large. These low drift regions are examined in detail, and a correspondance with the quadric surfaces that are derived for small formations is established. In particular, the orientation of these low drift zones along a given reference orbit are investigated as some parameters vary, such as the size of the formation as well as the reference orbit. Using the low natural drift regions, control strategies are then developed for large formations. Traditional controllers, such as impulsive maneuvers and linear quadratic regulators (LQR), are employed to quantify the level of control that is required to maintain large formations along specific directions in the CR3BP. Designs of new controllers are also investigated to produce some set of desired relative motions between two spacecraft placed at large mutual distances. In a potential formation option investigated in this analysis, a deputy vehicle maintains a fixed circular motion in a plane relative to a chief spacecraft moving along its reference trajectory. Finally, the effectiveness of using the low natural drift regions as derived for large formations is tested for the New Worlds Observer mission concept. This scenario involves a large telescope-occulter formation for star observations, to detect and characterize habitable terrestrial exoplanets. The low drift zones are employed to reduce the control effort to maintain a large telescope-occulter formation during the observation of inertially-fixed target stars. In particular, the occulter is maintained via a linear quadratic regulator during star observations. Given a set of inertially-fixed target stars, an automatic star sequence design process is proposed with observation and reconfiguration phases using the low drift regions. This design creates star sequences that lead to relatively small overall maneuver costs for this particular mission concept.

The triangular kagomé lattices revisited

NASA Astrophysics Data System (ADS)

Liu, Xiaoyun; Yan, Weigen

2013-11-01

The dimer problem, Ising spins and bond percolation on the triangular kagomé lattice have been studied extensively by physicists. In this paper, based on the fact the triangular kagomé lattice with toroidal boundary condition can be regarded as the line graph of 3.12.12 lattice with toroidal boundary condition, we derive the formulae of the number of spanning trees, the energy, and the Kirchhoff index of the triangular kagomé lattice with toroidal boundary condition.

Classification of ulnar triangular fibrocartilage complex tears. A treatment algorithm for Palmer type IB tears.

PubMed

Atzei, A; Luchetti, R; Garagnani, L

2017-05-01

The classical definition of 'Palmer Type IB' triangular fibrocartilage complex tear, includes a spectrum of clinical conditions. This review highlights the clinical and arthroscopic criteria that enable us to categorize five classes on a treatment-oriented classification system of triangular fibrocartilage complex peripheral tears. Class 1 lesions represent isolated tears of the distal triangular fibrocartilage complex without distal radio-ulnar joint instability and are amenable to arthroscopic suture. Class 2 tears include rupture of both the distal triangular fibrocartilage complex and proximal attachments of the triangular fibrocartilage complex to the fovea. Class 3 tears constitute isolated ruptures of the proximal attachment of the triangular fibrocartilage complex to the fovea; they are not visible at radio-carpal arthroscopy. Both Class 2 and Class 3 tears are diagnosed with a positive hook test and are typically associated with distal radio-ulnar joint instability. If required, treatment is through reattachment of the distal radio-ulnar ligament insertions to the fovea. Class 4 lesions are irreparable tears due to the size of the defect or to poor tissue quality and, if required, treatment is through distal radio-ulnar ligament reconstruction with tendon graft. Class 5 tears are associated with distal radio-ulnar joint arthritis and can only be treated with salvage procedures. This subdivision of type IB triangular fibrocartilage complex tear provides more insights in the pathomechanics and treatment strategies. II.

A novel method of the image processing on irregular triangular meshes

NASA Astrophysics Data System (ADS)

Vishnyakov, Sergey; Pekhterev, Vitaliy; Sokolova, Elizaveta

2018-04-01

The paper describes a novel method of the image processing based on irregular triangular meshes implementation. The triangular mesh is adaptive to the image content, least mean square linear approximation is proposed for the basic interpolation within the triangle. It is proposed to use triangular numbers to simplify using of the local (barycentric) coordinates for the further analysis - triangular element of the initial irregular mesh is to be represented through the set of the four equilateral triangles. This allows to use fast and simple pixels indexing in local coordinates, e.g. "for" or "while" loops for access to the pixels. Moreover, representation proposed allows to use discrete cosine transform of the simple "rectangular" symmetric form without additional pixels reordering (as it is used for shape-adaptive DCT forms). Furthermore, this approach leads to the simple form of the wavelet transform on triangular mesh. The results of the method application are presented. It is shown that advantage of the method proposed is a combination of the flexibility of the image-adaptive irregular meshes with the simple form of the pixel indexing in local triangular coordinates and the using of the common forms of the discrete transforms for triangular meshes. Method described is proposed for the image compression, pattern recognition, image quality improvement, image search and indexing. It also may be used as a part of video coding (intra-frame or inter-frame coding, motion detection).

Rotational Properties of Jupiter Trojan 1173 Anchises

NASA Astrophysics Data System (ADS)

Chatelain, Joseph; Henry, Todd; French, Linda; Trilling, David

2015-11-01

Anchises (1173) is a large Trojan asteroid librating about Jupiter’s L5 Lagrange point. Here we examine its rotational and lightcurve properties by way of data collected over a 3.5 year observing campaign. The length of the campaign means that data were gathered for more than a quarter of Anchises' full orbital revolution which allows for accurate determinations of pole orientation and bulk shape properties for the asteroid that can then be compared to results of previous work (i.e. French 1987, Horner et al. 2012). In addition to light curves, photometric data taken during this campaign could potentially detect color differences between hemispheres as the viewing geometry changes over time. Understanding these details about a prominent member of the Jupiter Trojans may help us better understand the history of this fascinating and important group of asteroids.

Trajectory design strategies that incorporate invariant manifolds and swingby

NASA Technical Reports Server (NTRS)

Guzman, J. J.; Cooley, D. S.; Howell, K. C.; Folta, D. C.

1998-01-01

Libration point orbits serve as excellent platforms for scientific investigations involving the Sun as well as planetary environments. Trajectory design in support of such missions is increasingly challenging as more complex missions are envisioned in the next few decades. Software tools for trajectory design in this regime must be further developed to incorporate better understanding of the solution space and, thus, improve the efficiency and expand the capabilities of current approaches. Only recently applied to trajectory design, dynamical systems theory now offers new insights into the natural dynamics associated with the multi-body problem. The goal of this effort is the blending of analysis from dynamical systems theory with the well established NASA Goddard software program SWINGBY to enhance and expand the capabilities for mission design. Basic knowledge concerning the solution space is improved as well.

The Mercury Laser Altimeter Instrument for the MESSENGER Mission

NASA Technical Reports Server (NTRS)

Cavanaugh, John F.; Smith, James C.; Sun, Xiaoli; Bartels, Arlin E.; Ramos-Izquierdo, Luis; Krebs, Danny J.; Novo-Gradac, Anne marie; McGarry, Jan F.; Trunzo, Raymond; Britt, Jamie L.

2006-01-01

The Mercury Laser Altimeter (MLA) is one of the payload science instruments on the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) mission, which launched on 3 August 2004. The altimeter will measure the round trip time-of-flight of transmitted laser pulses reflected from the surface of the planet that, in combination with the spacecraft orbit position and pointing data, gives a high-precision measurement of surface topography referenced to Mercury's center of mass. The altimeter measurements will be used to determine the planet's forced librations by tracking the motion of large-scale topographic features as a function of time. MLA's laser pulse energy monitor and the echo pulse energy estimate will provide an active measurement of the surface reflectivity at 1064 nm. This paper describes the instrument design, prelaunch testing, calibration, and results of post-launch testing.

Contingency Planning for the Microwave Anisotropy Probe Mission

NASA Technical Reports Server (NTRS)

Mesarch, Michael A.; Rohrbaugh, David; Schiff, Conrad; Bauer, Frank (Technical Monitor)

2002-01-01

The Microwave Anisotropy Probe (MAP) utilized a phasing loop/lunar encounter strategy to achieve a small amplitude Lissajous orbit about the Sun-Earth/Moon L2 libration point. The use of phasing loops was key in minimizing MAP's overall deltaV needs while also providing ample opportunities for contingency resolution. This paper will discuss the different contingencies and responses studied for MAP. These contingencies included accommodating excessive launch vehicle errors (beyond 3 sigma), splitting perigee maneuvers to achieve ground station coverage through the Deep Space Network (DSN), delaying the start of a perigee maneuver, aborting a perigee maneuver in the middle of execution, missing a perigee maneuver altogether, and missing the lunar encounter (crucial to achieving the final Lissajous orbit). It is determined that using a phasing loop approach permits many opportunities to correct for a majority of these contingencies.

Spectroscopic properties of triangular silver nanoplates immobilized on polyelectrolyte multilayer-modified glass substrates

NASA Astrophysics Data System (ADS)

Rabor, Janice B.; Kawamura, Koki; Muko, Daiki; Kurawaki, Junichi; Niidome, Yasuro

2017-07-01

Fabrication of surface-immobilized silver nanostructures with reproducible plasmonic properties by dip-coating technique is difficult due to shape alteration. To address this challenge, we used a polyelectrolyte multilayer to promote immobilization of as-received triangular silver nanoplates (TSNP) on a glass substrate through electrostatic interaction. The substrate-immobilized TSNP were characterized by absorption spectrophotometry and scanning electron microscopy. The bandwidth and peak position of localized surface plasmon resonance (LSPR) bands can be tuned by simply varying the concentration of the colloidal solution and immersion time. TSNP immobilized from a higher concentration of colloidal solution with longer immersion time produced broadened LSPR bands in the near-IR region, while a lower concentration with shorter immersion time produced narrower bands in the visible region. The shape of the nanoplates was retained even at long immersion time. Analysis of peak positions and bandwidths also revealed the point at which the main species of the immobilization had been changed from isolates to aggregates.

Fall Down Detection Under Smart Home System.

PubMed

Juang, Li-Hong; Wu, Ming-Ni

2015-10-01

Medical technology makes an inevitable trend for the elderly population, therefore the intelligent home care is an important direction for science and technology development, in particular, elderly in-home safety management issues become more and more important. In this research, a low of operation algorithm and using the triangular pattern rule are proposed, then can quickly detect fall-down movements of humanoid by the installation of a robot with camera vision at home that will be able to judge the fall-down movements of in-home elderly people in real time. In this paper, it will present a preliminary design and experimental results of fall-down movements from body posture that utilizes image pre-processing and three triangular-mass-central points to extract the characteristics. The result shows that the proposed method would adopt some characteristic value and the accuracy can reach up to 90 % for a single character posture. Furthermore the accuracy can be up to 100 % when a continuous-time sampling criterion and support vector machine (SVM) classifier are used.

Rendezvous missions to temporarily captured near Earth asteroids

NASA Astrophysics Data System (ADS)

Brelsford, S.; Chyba, M.; Haberkorn, T.; Patterson, G.

2016-04-01

Missions to rendezvous with or capture an asteroid present significant interest both from a geophysical and safety point of view. They are key to the understanding of our solar system and are stepping stones for interplanetary human flight. In this paper, we focus on a rendezvous mission with 2006 RH120, an asteroid classified as a Temporarily Captured Orbiter (TCO). TCOs form a new population of near Earth objects presenting many advantages toward that goal. Prior to the mission, we consider the spacecraft hibernating on a Halo orbit around the Earth-Moon's L2 libration point. The objective is to design a transfer for the spacecraft from the parking orbit to rendezvous with 2006 RH120 while minimizing the fuel consumption. Our transfers use indirect methods, based on the Pontryagin Maximum Principle, combined with continuation techniques and a direct method to address the sensitivity of the initialization. We demonstrate that a rendezvous mission with 2006 RH120 can be accomplished with low delta-v. This exploratory work can be seen as a first step to identify good candidates for a rendezvous on a given TCO trajectory.

Optical transmission for the James Webb Space Telescope

NASA Astrophysics Data System (ADS)

Lightsey, Paul A.; Gallagher, Benjamin B.; Nickles, Neal; Copp, Tracy

2012-09-01

The fabrication and coating of the mirrors for the James Webb Space Telescope has been completed. The spectral reflectivity of the protected gold coated beryllium mirrors has been measured. The predicted end-of-life transmission through the telescope builds from these values. The additional phenomena that have been analyzed are contamination effects and effects of the environment for the JWST operation about the Earth-Sun L2 Lagrange libration point. The L2 environment analysis has been based on radiation testing of mirror samples and hypervelocity testing to assess the micrometeoroid impact effects. The mirror showed no change in reflectance over the VIS-SWIR wavelengths after exposure to 6-9 Grad (Si) that simulated 6 years orbiting the L2 Lagrange point. The effects of hypervelocity particle impacts on the mirrors from test data has been extrapolated to the to the anticipated flux characteristics for micrometeoroids at the L2 environment. The results show that the micrometeoroid effects are orders of magnitude below the particulate contamination effects. The final end-of-life transmission for the mirrors including all of these phenomena will meet the performance requirements for JWST.

Systems Engineering Challenges for GSFC Space Science Mission Operations

NASA Technical Reports Server (NTRS)

Thienel, Julie; Harman, Richard R.

2017-01-01

The NASA Goddard Space Flight Center Space Science Mission Operations (SSMO) project currently manages19 missions for the NASA Science Mission Directorate, within the Planetary, Astrophysics, and Heliophysics Divisions. The mission lifespans range from just a few months to more than20 years. The WIND spacecraft, the oldest SSMO mission, was launched in 1994. SSMO spacecraft reside in low earth, geosynchronous,highly elliptical, libration point, lunar, heliocentric,and Martian orbits. SSMO spacecraft range in size from 125kg (Aeronomy of Ice in the Mesosphere (AIM)) to over 4000kg (Fermi Gamma-Ray Space Telescope (Fermi)). The attitude modes include both spin and three-axis stabilized, with varying requirements on pointing accuracy. The spacecraft are operated from control centers at Goddard and off-site control centers;the Lunar Reconnaissance Orbiter (LRO), the Solar Dynamics Observatory (SDO) and Magnetospheric MultiScale (MMS)mission were built at Goddard. The Advanced Composition Explorer (ACE) and Wind are operated out of a multi-mission operations center, which will also host several SSMO-managed cubesats in 2017. This paper focuses on the systems engineeringchallenges for such a large and varied fleet of spacecraft.

Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics

NASA Astrophysics Data System (ADS)

Koon, Wang Sang; Lo, Martin W.; Marsden, Jerrold E.; Ross, Shane D.

2000-06-01

In this paper we apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted three-body problem. These related phenomena have been of concern for some time in topics such as the capture of comets and asteroids and with the design of trajectories for space missions such as the Genesis Discovery Mission. The main new technical result in this paper is the numerical demonstration of the existence of a heteroclinic connection between pairs of periodic orbits: one around the libration point L1 and the other around L2, with the two periodic orbits having the same energy. This result is applied to the resonance transition problem and to the explicit numerical construction of interesting orbits with prescribed itineraries. The point of view developed in this paper is that the invariant manifold structures associated to L1 and L2 as well as the aforementioned heteroclinic connection are fundamental tools that can aid in understanding dynamical channels throughout the solar system as well as transport between the ``interior'' and ``exterior'' Hill's regions and other resonant phenomena.

The Effect of a Soap Film on a Catenary: Measurement of Surface Tension from the Triangular Configuration

ERIC Educational Resources Information Center

Behroozi, F.; Behroozi, P. S.

2011-01-01

A chain assumes the well-known shape known as a catenary when it hangs loosely from two points in a gravitational field. The correct solution of the catenary was one of the early triumphs of the newly invented calculus of variations at the end of the 17th century. Here we revisit the catenary and show that, for a chain hanging from a horizontal…

Characterization of Martian Rock Shape for MER Airbag Drop Tests

NASA Astrophysics Data System (ADS)

Dimaggio, E. N.; Schroeder, R.; Castle, N.; Golombek, M.

2002-12-01

Rock distributions for the final platforms used in airbag drop tests are currently being designed for the Mars Exploration Rovers (MER) scheduled to launch in 2003. Like Mars Pathfinder (MPF), launched in 1996, MER will use a series of airbags to cushion its landing on the surface of Mars. Previous MER airbag drop tests have shown that sharp, angular (triangular) rocks >20 cm high may be hazardous. To aid in defining the rock distributions for the final airbag tests, images from the Viking Landers 1 and 2 and MPF were used to identify rocks that are >20 cm high, and characterize them as triangular, square or round. Approximately 33% of all rocks analyzed are triangular. Of the rocks analyzed that are ~20-60 cm high, ~14% are triangular. Most of these triangular rocks are small, ~20-30 cm high. Rock distributions of previous airbag platforms were similarly classified and show a greater percentage of triangular and square rocks that are ~20-60 cm high than at the landing sites. The burial of a rock (perched, partially buried or buried) was also considered because perched rocks may pose less of a threat to the airbags than those buried because perched rocks can be dislodged and roll during impact. Approximately 19% of all rocks analyzed, and ~19% of rocks that are ~20-60 cm high, are triangular and partially buried or buried. These data suggest that the platform rock distributions appropriately represented the risks to the airbags associated with triangular rocks. A similar percentage of >20 cm high triangular rocks will be added to the drop test platforms to represent landing site rock distributions.

Magnetoresistance measurement of permalloy thin film rings with triangular fins

NASA Astrophysics Data System (ADS)

Lai, Mei-Feng; Hsu, Chia-Jung; Liao, Chun-Neng; Chen, Ying-Jiun; Wei, Zung-Hang

2010-01-01

Magnetization reversals in permalloy rings controlled by nucleation sites using triangular fins at the same side and diagonal with respect to the field direction are demonstrated by magnetoresistance measurement and micromagnetic simulation. In the ring with triangular fins at the same side, there exists two-step reversal from onion to flux-closure state (or vortex state) and then from flux-closure (or vortex state) to reverse onion state; in the ring with diagonal triangular fins, one-step reversal occurs directly from onion to reverse onion state. The reversal processes are repeatable and controllable in contrast to an ideal ring without triangular fins where one-step and two-step reversals occur randomly in sweep-up and sweep-down processes.

Benchmarks of simple, generic, shaped plates for validation of low-frequency electromagnetic computational codes

NASA Technical Reports Server (NTRS)

Deshpande, M. D.; Cockrell, C. R.; Beck, F. B.; Nguyen, T. X.

1993-01-01

The validation of low-frequency measurements and electromagnetic (EM) scattering computations for several simple, generic shapes, such as an equilateral-triangular plate, an equilateral-triangular plate with a concentric equilateral-triangular hole, and diamond- and hexagonal-shaped plates, is discussed. The plates were constructed from a thin aluminum sheet with a thickness of 0.08 cm. EM scattering by the planar plates was measured in the experimental test range (ETR) facility of NASA Langley Research Center. The dimensions of the plates were selected such that, over the frequency range of interest, the dimensions were in the range of lambda0 to 3(lambda0). In addition, the triangular plate with a triangular hole was selected to study internal-hole resonances.

Low mass planet migration in magnetically torqued dead zones - I. Static migration torque

NASA Astrophysics Data System (ADS)

McNally, Colin P.; Nelson, Richard P.; Paardekooper, Sijme-Jan; Gressel, Oliver; Lyra, Wladimir

2017-12-01

Motivated by models suggesting that the inner planet forming regions of protoplanetary discs are predominantly lacking in viscosity-inducing turbulence, and are possibly threaded by Hall-effect generated large-scale horizontal magnetic fields, we examine the dynamics of the corotation region of a low-mass planet in such an environment. The corotation torque in an inviscid, isothermal, dead zone ought to saturate, with the libration region becoming both symmetrical and of a uniform vortensity, leading to fast inward migration driven by the Lindblad torques alone. However, in such a low viscosity situation, the material on librating streamlines essentially preserves its vortensity. If there is relative radial motion between the disc gas and the planet, the librating streamlines will no longer be symmetrical. Hence, if the gas is torqued by a large-scale magnetic field so that it undergoes a net inflow or outflow past the planet, driving evolution of the vortensity and inducing asymmetry of the corotation region, the corotation torque can grow, leading to a positive torque. In this paper, we treat this effect by applying a symmetry argument to the previously studied case of a migrating planet in an inviscid disc. Our results show that the corotation torque due to a laminar Hall-induced magnetic field in a dead zone behaves quite differently from that studied previously for a viscous disc. Furthermore, the magnetic field induced corotation torque and the dynamical corotation torque in a low viscosity disc can be regarded as one unified effect.

Creating unconventional geometric beams with large depth of field using double freeform-surface optics.

PubMed

Feng, Zexin; Froese, Brittany D; Huang, Chih-Yu; Ma, Donglin; Liang, Rongguang

2015-07-10

We consider here creation of an unconventional flattop beam with a large depth of field by employing double freeform optical surfaces. The output beam is designed with continuous variations from the flattop to almost zero near the edges to resist the influence of diffraction on its propagation. We solve this challenging problem by naturally incorporating an optimal transport map computation scheme for unconventional boundary conditions with a simultaneous point-by-point double surface construction procedure. We demonstrate experimentally the generation of a long-range propagated triangular beam through a plano-freeform lens pair fabricated by a diamond-tuning machine.

7 CFR 810.1002 - Definition of other terms.

Code of Federal Regulations, 2014 CFR

2014-01-01

... seeds. All matter that passes through a 5/64 triangular-hole sieve after sieving according to procedures..., rye, safflower, sorghum, soybeans, spelt, sunflower seed, sweet corn, triticale, and wheat. (e) Sieves—(1) 5/64 triangular-hole sieve. A metal sieve 0.032 inch thick with equilateral triangular...

7 CFR 810.1002 - Definition of other terms.

Code of Federal Regulations, 2012 CFR

2012-01-01

... seeds. All matter that passes through a 5/64 triangular-hole sieve after sieving according to procedures..., rye, safflower, sorghum, soybeans, spelt, sunflower seed, sweet corn, triticale, and wheat. (e) Sieves—(1) 5/64 triangular-hole sieve. A metal sieve 0.032 inch thick with equilateral triangular...

7 CFR 810.1002 - Definition of other terms.

Code of Federal Regulations, 2013 CFR

2013-01-01

... seeds. All matter that passes through a 5/64 triangular-hole sieve after sieving according to procedures..., rye, safflower, sorghum, soybeans, spelt, sunflower seed, sweet corn, triticale, and wheat. (e) Sieves—(1) 5/64 triangular-hole sieve. A metal sieve 0.032 inch thick with equilateral triangular...

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Jiang, Yi-Tsann

1993-01-01

A general solution adaptive scheme-based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

ASICs Approach for the Implementation of a Symmetric Triangular Fuzzy Coprocessor and Its Application to Adaptive Filtering

NASA Technical Reports Server (NTRS)

Starks, Scott; Abdel-Hafeez, Saleh; Usevitch, Bryan

1997-01-01

This paper discusses the implementation of a fuzzy logic system using an ASICs design approach. The approach is based upon combining the inherent advantages of symmetric triangular membership functions and fuzzy singleton sets to obtain a novel structure for fuzzy logic system application development. The resulting structure utilizes a fuzzy static RAM to store the rule-base and the end-points of the triangular membership functions. This provides advantages over other approaches in which all sampled values of membership functions for all universes must be stored. The fuzzy coprocessor structure implements the fuzzification and defuzzification processes through a two-stage parallel pipeline architecture which is capable of executing complex fuzzy computations in less than 0.55us with an accuracy of more than 95%, thus making it suitable for a wide range of applications. Using the approach presented in this paper, a fuzzy logic rule-base can be directly downloaded via a host processor to an onchip rule-base memory with a size of 64 words. The fuzzy coprocessor's design supports up to 49 rules for seven fuzzy membership functions associated with each of the chip's two input variables. This feature allows designers to create fuzzy logic systems without the need for additional on-board memory. Finally, the paper reports on simulation studies that were conducted for several adaptive filter applications using the least mean squared adaptive algorithm for adjusting the knowledge rule-base.

Designing Tripodal and Triangular Gadolinium Oxide Nanoplates and Self-Assembled Nanofibrils as Potential Multimodal Bioimaging Probes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Paik, T; Gordon, TR; Prantner, AM

2013-03-01

Here, we report the shape-controlled synthesis of tripodal and triangular gadolinium oxide (Gd2O3) nanoplates. In the presence of lithium ions, the shape of the nanocrystals is readily controlled by tailoring reaction parameters such as temperature and time. We observe that the morphology transforms from an initial tripodal shape to a triangular shape with increasing reaction time or elevated temperatures. Highly uniform Gd2O3 nanoplates are self-assembled into nanofibril-like liquid-crystalline superlattices with long-range orientational and positional order. In addition, shape-directed self-assemblies are investigated by tailoring the aspect ratio of the arms of the Gd2O3 nanoplates. Due to a strong paramagnetic response, Gd2O3more » nanocrystals are excellent candidates for MRI contrast agents and also can be doped with rare-earth ions to form nanophosphors, pointing to their potential in multimodal imaging. In this work, we investigate the MR relaxometry at high magnetic fields (9,4 and 14.1 T) and the optical properties including near-IR to visible upconversion luminescence and X-ray excited optical luminescence of doped Gd2O3 nanoplates. The complex shape of Gd2O3 nanoplates, coupled with their magnetic properties and their ability to phosphoresce under NIR or X-ray excitation which penetrate deep into tissue, makes these nanoplates a promising platform for multimodal imaging in biomedical applications.« less

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Jiang, Yi-Tsann; Usab, William J., Jr.

1993-01-01

A general solution adaptive scheme based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Triangular Diagrams Teach Steady and Dynamic Behaviour of Catalytic Reactions.

ERIC Educational Resources Information Center

Klusacek, K.; And Others

1989-01-01

Illustrates how triangular diagrams can aid in presenting some of the rather complex transient interactions that occur among gas and surface species during heterogeneous catalytic reactions. The basic equations and numerical examples are described. Classroom use of the triangular diagram is discussed. Several diagrams and graphs are provided. (YP)

On Certain Topological Indices of Boron Triangular Nanotubes

NASA Astrophysics Data System (ADS)

Aslam, Adnan; Ahmad, Safyan; Gao, Wei

2017-08-01

The topological index gives information about the whole structure of a chemical graph, especially degree-based topological indices that are very useful. Boron triangular nanotubes are now replacing usual carbon nanotubes due to their excellent properties. We have computed general Randić (Rα), first Zagreb (M1) and second Zagreb (M2), atom-bond connectivity (ABC), and geometric-arithmetic (GA) indices of boron triangular nanotubes. Also, we have computed the fourth version of atom-bond connectivity (ABC4) and the fifth version of geometric-arithmetic (GA5) indices of boron triangular nanotubes.

Adaptive non-predictor control of lower triangular uncertain nonlinear systems with an unknown time-varying delay in the input

NASA Astrophysics Data System (ADS)

Koo, Min-Sung; Choi, Ho-Lim

2018-01-01

In this paper, we consider a control problem for a class of uncertain nonlinear systems in which there exists an unknown time-varying delay in the input and lower triangular nonlinearities. Usually, in the existing results, input delays have been coupled with feedforward (or upper triangular) nonlinearities; in other words, the combination of lower triangular nonlinearities and input delay has been rare. Motivated by the existing controller for input-delayed chain of integrators with nonlinearity, we show that the control of input-delayed nonlinear systems with two particular types of lower triangular nonlinearities can be done. As a control solution, we propose a newly designed feedback controller whose main features are its dynamic gain and non-predictor approach. Three examples are given for illustration.

Formation Control of the MAXIM L2 Libration Orbit Mission

NASA Technical Reports Server (NTRS)

Folta, David; Hartman, Kate; Howell, Kathleen; Marchand, Belinda

2004-01-01

The Micro-Arcsecond X-ray Imaging Mission (MAXIM), a proposed concept for the Structure and Evolution of the Universe (SEU) Black Hole Imager mission, is designed to make a ten million-fold improvement in X-ray image clarity of celestial objects by providing better than 0.1 micro-arcsecond imaging. Currently the mission architecture comprises 25 spacecraft, 24 as optics modules and one as the detector, which will form sparse sub-apertures of a grazing incidence X-ray interferometer covering the 0.3-10 keV bandpass. This formation must allow for long duration continuous science observations and also for reconfiguration that permits re-pointing of the formation. To achieve these mission goals, the formation is required to cooperatively point at desired targets. Once pointed, the individual elements of the MAXIM formation must remain stable, maintaining their relative positions and attitudes below a critical threshold. These pointing and formation stability requirements impact the control and design of the formation. In this paper, we provide analysis of control efforts that are dependent upon the stability and the configuration and dimensions of the MAXIM formation. We emphasize the utilization of natural motions in the Lagrangian regions to minimize the control efforts and we address continuous control via input feedback linearization (IFL). Results provide control cost, configuration options, and capabilities as guidelines for the development of this complex mission.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuprat, A.P.; Glasser, A.H.

The authors discuss unstructured grids for application to transport in the tokamak edge SOL. They have developed a new metric with which to judge element elongation and resolution requirements. Using this method, the authors apply a standard moving finite element technique to advance the SOL equations while inserting/deleting dynamically nodes that violate an elongation criterion. In a tokamak plasma, this method achieves a more uniform accuracy, and results in highly stretched triangular finite elements, except near separatrix X-point where transport is more isotropic.

Computational Fluid Dynamics (CFD) Simulations of a Finned Projectile with Microflaps for Flow Control

DTIC Science & Technology

2016-04-01

fields associated with these control mechanisms for US Army weapons are complex, involving 3-dimensional (3-D) shock- boundary layer interactions...distribution over the rear finned section and thus produce control forces and moments. Dykes et al.6 used a flat - plate fin interaction design of...cells—tetrahedrals, triangular prisms, and pyramids—were used in the mesh. Grid points shown in Fig. 3a were clustered in the boundary layer region

Anomalous finite-size effect due to quasidegenerate phases in triangular antiferromagnets with long-range interactions and mapping to the generalized six-state clock model

NASA Astrophysics Data System (ADS)

Nishino, Masamichi; Miyashita, Seiji

2016-11-01

The effect of long-range (LR) interactions on frustrated-spin models is an interesting problem, which provides rich ordering processes. We study the effect of LR interactions on triangular Ising antiferromagnets with the next-nearest-neighbor ferromagnetic interaction (TIAFF). In the thermodynamic limit, the LRTIAFF model should reproduce the corresponding mean-field results, in which successive phase transitions occur among various phases, i.e., the disordered paramagnetic phase, so-called partially disordered phase, three-sublattice ferrimagnetic phase, and two-sublattice ferrimagnetic phase. In the present paper we focus on the magnetic susceptibility at the transition point between the two-sublattice ferrimagnetic and the disordered paramagnetic phases at relatively large ferromagnetic interactions. In the mean-field analysis, the magnetic susceptibility shows no divergence at the transition point. In contrast, a divergencelike enhancement of the susceptibility is observed in Monte Carlo simulations in finite-size systems. We investigate the origin of this difference and find that it is attributed to a virtual degeneracy of the free energies of the partially disordered and 2-FR phases. We also exploit a generalized six-state clock model with an LR interaction, which is a more general system with Z6 symmetry. We discuss the phase diagram of this model and find that it exhibits richer transition patterns and contains the physics of the LRTIAFF model.

Heat transfer and pressure drop characteristics of the tube bank fin heat exchanger with fin punched with flow redistributors and curved triangular vortex generators

NASA Astrophysics Data System (ADS)

Liu, Song; Jin, Hua; Song, KeWei; Wang, LiangChen; Wu, Xiang; Wang, LiangBi

2017-10-01

The heat transfer performance of the tube bank fin heat exchanger is limited by the air-side thermal resistance. Thus, enhancing the air-side heat transfer is an effective method to improve the performance of the heat exchanger. A new fin pattern with flow redistributors and curved triangular vortex generators is experimentally studied in this paper. The effects of the flow redistributors located in front of the tube stagnation point and the curved vortex generators located around the tube on the characteristics of heat transfer and pressure drop are discussed in detail. A performance comparison is also carried out between the fins with and without flow redistributors. The experimental results show that the flow redistributors stamped out from the fin in front of the tube stagnation points can decrease the friction factor at the cost of decreasing the heat transfer performance. Whether the combination of the flow redistributors and the curved vortex generators will present a better heat transfer performance depends on the size of the curved vortex generators. As for the studied two sizes of vortex generators, the heat transfer performance is promoted by the flow redistributors for the fin with larger size of vortex generators and the performance is suppressed by the flow redistributors for the fin with smaller vortex generators.

Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Youshan, E-mail: ysliu@mail.iggcas.ac.cn; Teng, Jiwen, E-mail: jwteng@mail.iggcas.ac.cn; Xu, Tao, E-mail: xutao@mail.iggcas.ac.cn

2017-05-01

The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate newmore » cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant–Friedrichs–Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational efficiency, the OTSEM is more efficient than the Fekete-based TSEM, although it is slightly costlier than the QSEM when a comparable numerical accuracy is required. - Highlights: • Higher-order cubature points for degrees 7 to 9 are developed. • The effects of quadrature rule on the mass and stiffness matrices has been conducted. • The cubature points have always positive integration weights. • Freeing from the inversion of a wide bandwidth mass matrix. • The accuracy of the TSEM has been improved in about one order of magnitude.« less

7 CFR 810.802 - Definition of other terms.

Code of Federal Regulations, 2012 CFR

2012-01-01

... and fines. All matter other than whole flaxseed that passes through a 5/64 triangular-hole sieve, and... established under the Act, that are materially discolored and damaged by heat. (e) Sieve— 5/64 triangular-hole sieve. A metal sieve 0.032 inch thick with equilateral triangular perforations the inscribed circles of...

7 CFR 810.802 - Definition of other terms.

Code of Federal Regulations, 2013 CFR

2013-01-01

... and fines. All matter other than whole flaxseed that passes through a 5/64 triangular-hole sieve, and... established under the Act, that are materially discolored and damaged by heat. (e) Sieve— 5/64 triangular-hole sieve. A metal sieve 0.032 inch thick with equilateral triangular perforations the inscribed circles of...

7 CFR 810.802 - Definition of other terms.

Code of Federal Regulations, 2011 CFR

2011-01-01

... and fines. All matter other than whole flaxseed that passes through a 5/64 triangular-hole sieve, and... established under the Act, that are materially discolored and damaged by heat. (e) Sieve— 5/64 triangular-hole sieve. A metal sieve 0.032 inch thick with equilateral triangular perforations the inscribed circles of...

7 CFR 810.802 - Definition of other terms.

Code of Federal Regulations, 2014 CFR

2014-01-01

... and fines. All matter other than whole flaxseed that passes through a 5/64 triangular-hole sieve, and... established under the Act, that are materially discolored and damaged by heat. (e) Sieve— 5/64 triangular-hole sieve. A metal sieve 0.032 inch thick with equilateral triangular perforations the inscribed circles of...

Sorption of Triangular Silver Nanoplates on Polyurethane Foam

NASA Astrophysics Data System (ADS)

Furletov, A. A.; Apyari, V. V.; Garshev, A. V.; Volkov, P. A.; Tolmacheva, V. V.; Dmitrienko, S. G.

2018-02-01

The sorption of triangular silver nanoplates on polyurethane foam is investigated as a procedure for creating a nanocomposite sensing material for subsequent use in optical means of chemical analysis. Triangular silver nanoplates are synthesized and characterized, and a simple sorption technique for the formation of a composite material based on these nanoplates is proposed.

Properties of plane discrete Poisson-Voronoi tessellations on triangular tiling formed by the Kolmogorov-Johnson-Mehl-Avrami growth of triangular islands

NASA Astrophysics Data System (ADS)

Korobov, A.

2011-08-01

Discrete uniform Poisson-Voronoi tessellations of two-dimensional triangular tilings resulting from the Kolmogorov-Johnson-Mehl-Avrami (KJMA) growth of triangular islands have been studied. This shape of tiles and islands, rarely considered in the field of random tessellations, is prompted by the birth-growth process of Ir(210) faceting. The growth mode determines a triangular metric different from the Euclidean metric. Kinetic characteristics of tessellations appear to be metric sensitive, in contrast to area distributions. The latter have been studied for the variant of nuclei growth to the first impingement in addition to the conventional case of complete growth. Kiang conjecture works in both cases. The averaged number of neighbors is six for all studied densities of random tessellations, but neighbors appear to be mainly different in triangular and Euclidean metrics. Also, the applicability of the obtained results for simulating birth-growth processes when the 2D nucleation and impingements are combined with the 3D growth in the particular case of similar shape and the same orientation of growing nuclei is briefly discussed.

Properties of plane discrete Poisson-Voronoi tessellations on triangular tiling formed by the Kolmogorov-Johnson-Mehl-Avrami growth of triangular islands.

PubMed

Korobov, A

2011-08-01

Discrete uniform Poisson-Voronoi tessellations of two-dimensional triangular tilings resulting from the Kolmogorov-Johnson-Mehl-Avrami (KJMA) growth of triangular islands have been studied. This shape of tiles and islands, rarely considered in the field of random tessellations, is prompted by the birth-growth process of Ir(210) faceting. The growth mode determines a triangular metric different from the Euclidean metric. Kinetic characteristics of tessellations appear to be metric sensitive, in contrast to area distributions. The latter have been studied for the variant of nuclei growth to the first impingement in addition to the conventional case of complete growth. Kiang conjecture works in both cases. The averaged number of neighbors is six for all studied densities of random tessellations, but neighbors appear to be mainly different in triangular and Euclidean metrics. Also, the applicability of the obtained results for simulating birth-growth processes when the 2D nucleation and impingements are combined with the 3D growth in the particular case of similar shape and the same orientation of growing nuclei is briefly discussed.

A Ranking Analysis/An Interlinking Approach of New Triangular Fuzzy Cognitive Maps and Combined Effective Time Dependent Matrix

NASA Astrophysics Data System (ADS)

Adiga, Shreemathi; Saraswathi, A.; Praveen Prakash, A.

2018-04-01

This paper aims an interlinking approach of new Triangular Fuzzy Cognitive Maps (TrFCM) and Combined Effective Time Dependent (CETD) matrix to find the ranking of the problems of Transgenders. Section one begins with an introduction that briefly describes the scope of Triangular Fuzzy Cognitive Maps (TrFCM) and CETD Matrix. Section two provides the process of causes of problems faced by Transgenders using Fuzzy Triangular Fuzzy Cognitive Maps (TrFCM) method and performs the calculations using the collected data among the Transgender. In Section 3, the reasons for the main causes for the problems of the Transgenders. Section 4 describes the Charles Spearmans coefficients of rank correlation method by interlinking of Triangular Fuzzy Cognitive Maps (TrFCM) Method and CETD Matrix. Section 5 shows the results based on our study.

Mapping the stability field of Jupiter Trojans

NASA Technical Reports Server (NTRS)

Levison, H. F.; Shoemaker, E. M.; Wolfe, R. F.

1991-01-01

Jupiter Trojans are a remnant of outer solar system planetesimals captured into stable or quasistable libration about the 1:1 resonance with the mean motion of Jupiter. The observed swarms of Trojans may provide insight into the original mass of condensed solids in the zone from which the Jovian planets accumulated, provided that the mechanisms of capture can be understood. As the first step toward this understanding, the stability field of Trojans were mapped in the coordinate proper eccentricity, e(sub p), and libration amplitude, D. To accomplish this mapping, the orbits of 100 particles with e(sub p) in the range of 0 to 0.8 and D in the range 0 to 140 deg were numerically integrated. Orbits of the Sun, the four Jovian planets, and the massless particles were integrated as a full N-body system, in a barycentric frame using fourth order symplectic scheme.

Evolution of triangular topographic facets along active normal faults

NASA Astrophysics Data System (ADS)

Balogun, A.; Dawers, N. H.; Gasparini, N. M.; Giachetta, E.

2011-12-01

Triangular shaped facets, which are generally formed by the erosion of fault - bounded mountain ranges, are arguably one of the most prominent geomorphic features on active normal fault scarps. Some previous studies of triangular facet development have suggested that facet size and slope exhibit a strong linear dependency on fault slip rate, thus linking their growth directly to the kinematics of fault initiation and linkage. Other studies, however, generally conclude that there is no variation in triangular facet geometry (height and slope) with fault slip rate. The landscape of the northeastern Basin and Range Province of the western United States provides an opportunity for addressing this problem. This is due to the presence of well developed triangular facets along active normal faults, as well as spatial variations in fault scale and slip rate. In addition, the Holocene climatic record for this region suggests a dominant tectonic regime, as the faulted landscape shows little evidence of precipitation gradients associated with tectonic uplift. Using GIS-based analyses of USGS 30 m digital elevation data (DEMs) for east - central Idaho and southwestern Montana, we analyze triangular facet geometries along fault systems of varying number of constituent segments. This approach allows us to link these geometries with established patterns of along - strike slip rate variation. For this study, we consider major watersheds to include only catchments with upstream and downstream boundaries extending from the drainage divide to the mapped fault trace, respectively. In order to maintain consistency in the selection criteria for the analyzed triangular facets, only facets bounded on opposite sides by major watersheds were considered. Our preliminary observations reflect a general along - strike increase in the surface area, average slope, and relief of triangular facets from the tips of the fault towards the center. We attribute anomalies in the along - strike geometric measurements of the triangular facets to represent possible locations of fault segment linkage associated with normal fault evolution.

Model Estimated GCR Particle Flux Variation - Assessment with CRIS Data

NASA Astrophysics Data System (ADS)

Saganti, Premkumar

We present model calculated particle flux as a function of time during the current solar cycle along with the comparisons from the ACE/CRIS data and the Mars/MARIE data. In our model calculations we make use of the NASA's HZETRN (High Z and Energy Transport) code along with the nuclear fragmentation cross sections that are described by the quantum multiple scattering (QMSFRG) model. The time dependant variation of the GCR environment is derived making use of the solar modulation potential, phi. For the past ten years, Advanced Composition Explorer (ACE) has been in orbit at the Sun- Earth libration point (L1). Data from the Cosmic Ray Isotope Spectrometer (CRIS) instrument onboard the ACE spacecraft has been available from 1997 through the present time. Our model calculated particle flux showed high degree of correlation during the earlier phase of the current solar cycle (2003) in the lower Z region within 15

A Nonlinear, Six-Degree of Freedom Precision Formation Control Algorithm, Based on Restricted Three Body Dynamics

NASA Technical Reports Server (NTRS)

Bauer, Frank (Technical Monitor); Luquette, Richard J.; Sanner, Robert M.

2003-01-01

Precision Formation Flying is an enabling technology for a variety of proposed space-based observatories, including the Micro-Arcsecond X-ray Imaging Mission (MAXIM), the associated MAXIM pathfinder mission, and the Stellar Imager. An essential element of the technology is the control algorithm. This paper discusses the development of a nonlinear, six-degree of freedom (6DOF) control algorithm for maintaining the relative position and attitude of a spacecraft within a formation. The translation dynamics are based on the equations of motion for the restricted three body problem. The control law guarantees the tracking error convergences to zero, based on a Lyapunov analysis. The simulation, modelled after the MAXIM Pathfinder mission, maintains the relative position and attitude of a Follower spacecraft with respect to a Leader spacecraft, stationed near the L2 libration point in the Sun-Earth system.

Space Trajectory Error Analysis Program (STEAP) for halo orbit missions. Volume 2: Programmer's manual

NASA Technical Reports Server (NTRS)

Byrnes, D. V.; Carney, P. C.; Underwood, J. W.; Vogt, E. D.

1974-01-01

The six month effort was responsible for the development, test, conversion, and documentation of computer software for the mission analysis of missions to halo orbits about libration points in the earth-sun system. The software consisting of two programs called NOMNAL and ERRAN is part of the Space Trajectories Error Analysis Programs. The program NOMNAL targets a transfer trajectory from earth on a given launch date to a specified halo orbit on a required arrival date. Either impulsive or finite thrust insertion maneuvers into halo orbit are permitted by the program. The transfer trajectory is consistent with a realistic launch profile input by the user. The second program ERRAN conducts error analyses of the targeted transfer trajectory. Measurements including range, doppler, star-planet angles, and apparent planet diameter are processed in a Kalman-Schmidt filter to determine the trajectory knowledge uncertainty.

Advanced Materials and Component Development for Lithium-ion Cells for NASA Missions

NASA Technical Reports Server (NTRS)

Reid, Concha M.

2012-01-01

Human missions to Near Earth Objects, such as asteroids, planets, moons, libration points, and orbiting structures, will require safe, high specific energy, high energy density batteries to provide new or extended capabilities than are possible with today s state-of-the-art aerospace batteries. The National Aeronautics and Space Administration is developing advanced High Energy and Ultra High Energy lithium-ion cells to address these needs. In order to meet the performance goals, advanced, high-performing materials are required to provide improved performance at the component-level that contributes to performance at the integrated cell level. This paper will provide an update on the performance of experimental materials through the completion of two years of development. The progress of materials development, remaining challenges, and an outlook for the future of these materials in near term cell products will be discussed.

Linear State-Space Representation of the Dynamics of Relative Motion, Based on Restricted Three Body Dynamics

NASA Technical Reports Server (NTRS)

Luquette,Richard J.; Sanner, Robert M.

2004-01-01

Precision Formation Flying is an enabling technology for a variety of proposed space-based observatories, including the Micro-Arcsecond X-ray Imaging Mission (MAXIM) , the associated MAXIM pathfinder mission, Stellar Imager (SI) and the Terrestrial Planet Finder (TPF). An essential element of the technology is the control algorithm, requiring a clear understanding of the dynamics of relative motion. This paper examines the dynamics of relative motion in the context of the Restricted Three Body Problem (RTBP). The natural dynamics of relative motion are presented in their full nonlinear form. Motivated by the desire to apply linear control methods, the dynamics equations are linearized and presented in state-space form. The stability properties are explored for regions in proximity to each of the libration points in the Earth/Moon - Sun rotating frame. The dynamics of relative motion are presented in both the inertial and rotating coordinate frames.

Towards measuring quantum electrodynamic torque with a levitated nanorod

NASA Astrophysics Data System (ADS)

Xu, Zhujing; Bang, Jaehoon; Ahn, Jonghoon; Hoang, Thai M.; Li, Tongcang

2017-04-01

According to quantum electrodynamics, quantum fluctuations of electromagnetic fields give rise to a zero-point energy that never vanishes, even in the absence of electromagnetic sources. The interaction energy will not only lead to the well-known Casimir force but will also contribute to the Casimir torque for anisotropic materials. We propose to use an optically levitated nanorod in vacuum and a birefringent substrate to experimentally investigate the QED torque. We have previously observed the libration of an optically levitated non-spherical nanoparticle in vacuum and found it to be an ultrasensitive torque sensor. A nanorod with a long axis of 300nm and a diameter of 60nm levitated in vacuum at 10 (- 8) torr will have a remarkable torque detection sensitivity on the order of 10 (- 28) Nm/ √Hz, which will be sufficient to detect the Casimir torque. This work is partially supported by the National Science Foundation under Grant No.1555035-PHY.

Development of a Two-Wheel Contingency Mode for the MAP Spacecraft

NASA Technical Reports Server (NTRS)

Starin, Scott R.; ODonnell, James R., Jr.; Bauer, Frank (Technical Monitor)

2002-01-01

The Microwave Anisotropy Probe (MAP) is a follow-on mission to the Cosmic Background Explorer (COBE), and is currently collecting data from its orbit near the second Sun-Earth libration point. Due to limited mass, power, and financial resources, a traditional reliability concept including fully redundant components was not feasible for MAP. Instead, the MAP design employs selective hardware redundancy in tandem with contingency software modes and algorithms to improve the odds of mission success. One direction for such improvement has been the development of a two-wheel backup control strategy. This strategy would allow MAP to position itself for maneuvers and collect science data should one of its three reaction wheels fail. Along with operational considerations, the strategy includes three new control algorithms. These algorithms would use the remaining attitude control actuators-thrusters and two reaction wheels-in ways that achieve control goals while minimizing adverse impacts on the functionality of other subsystems and software.

X-ray and simulation studies of water

NASA Astrophysics Data System (ADS)

Nilsson, A.; Schlesinger, D.; G. M. Pettersson, L.

Here we present a picture that combines discussions regarding the thermodynamic anomalies in ambient and supercooled water with recent interpretations of X-ray spectroscopy and scattering data of water. At ambient temperatures most molecules favor a closer packing than tetrahedral, with strongly distorted hydrogen bonds, which allows the quantized librational modes to be excited and contribute to the entropy, but with enthalpically favored tetrahedrally bonded water patches appearing as fluctuations, a competition between entropy and enthalpy. Upon cooling water the amount of molecules participating in tetrahedral structures and the size of the tetrahedral patches increase. The two local structures are connected to the liquid-liquid critical point hypothesis in supercooled water corresponding to high-density liquid (HDL) and low-density liquid (LDL). We demonstrate that the HDL local structure deviates from a tetrahedral coordination not only through a collapse of the 2nd shell but also through severe distortions around the 1st coordination shell.

Triangular Arbitrage as an Interaction in Foreign Exchange Markets

NASA Astrophysics Data System (ADS)

Aiba, Yukihiro; Hatano, Naomichi

Analyzing correlation in financial time series is a topic of considerable interest [1]-[17]. In the foreign exchange market, a correlation among the exchange rates can be generated by a triangular arbitrage transaction. The purpose of this article is to review our recent study [18]-[23] on modeling the interaction generated by the triangular arbitrage.

Orbital Injection of the SEDSAT Satellite: Tethered Systems Dynamics and Flight Data Analysis

NASA Technical Reports Server (NTRS)

Lorenzini, Enrico C.; Gullahorn, Gordon E.; Cosmo, Mario L.; Ruiz, Manuel; Pelaez, Jesus

1996-01-01

This report deals with the following topics which are all related to the orbital injection of the SEDSAT satellite: Dynamics and Stability of Tether Oscillations after the First Cut. The dynamics of the tether after the first cut (i.e., without the Shuttle attached to it) is investigated. The tether oscillations with the free end are analyzed in order to assess the stability of the rectilinear configuration in between the two tether cuts; analysis of Unstable Modes. The unstable modes that appear for high libration angles are further investigated in order to determine their occurrences and the possible transition from bound librations to rotations; Orbital Release Strategies for SEDSAT. A parametric analysis of the orbital decay rate of the SEDSAT satellite after the two tether cuts has been carried out as a function of the following free parameters: libration amplitude at the end of deployment, deviation angle from LV at the first cut, and orbital anomaly at the second cut. The values of these parameters that provide a minimum orbital decay rate of the satellite (after the two cuts) have been computed; and Dynamics and Control of SEDSAT. The deployment control law has been modified to cope with the new ejection velocity of the satellite from the Shuttle cargo bay. New reference profiles have been derived as well as new control parameters. Timing errors at the satellite release as a function of the variations of the initial conditions and the tension model parameters have been estimated for the modified control law.

Variation in shape of the lingula in the adult human mandible

PubMed Central

TULI, A.; CHOUDHRY, R.; CHOUDHRY, S.; RAHEJA, S.; AGARWAL, S.

2000-01-01

The lingulae of both sides of 165 dry adult human mandibles, 131 males and 34 females of Indian origin, were classified by their shape into 4 types: 1, triangular; 2, truncated; 3, nodular; and 4, assimilated. Triangular lingulae were found in 226 (68.5%) sides, truncated in 52 (15.8%), nodular in 36 (10.9%) and assimilated in 16 (4.8%) sides. Triangular lingulae were found bilaterally in 110, truncated in 23, nodular in 17 and assimilated in 7 mandibles. Of the remaining 8 mandibles with different appearances on the 2 sides, 6 had a combination of triangular and truncated and 2 had nodular and assimilated. The incidence of triangular and assimilated types in the male and female mandibles are almost equal. In the truncated type it was double in the male mandibles while the nodular type was a little less than double in the female mandibles. PMID:11005723

Facile synthesis of microporous SiO2/triangular Ag composite nanostructures for photocatalysis

NASA Astrophysics Data System (ADS)

Sirohi, Sidhharth; Singh, Anandpreet; Dagar, Chakit; Saini, Gajender; Pani, Balaram; Nain, Ratyakshi

2017-11-01

In this article, we present a novel fabrication of microporous SiO2/triangular Ag nanoparticles for dye (methylene blue) adsorption and plasmon-mediated degradation. Microporous SiO2 nanoparticles with pore size <2 nm were synthesized using cetyltrimethylammonium bromide as a structure-directing agent and functionalized with APTMS ((3-aminopropyl) trimethoxysilane) to introduce amine groups. Amine-functionalized microporous silica was used for adsorption of triangular silver (Ag) nanoparticles. The synthesized microporous SiO2 nanostructures were investigated for adsorption of different dyes including methylene blue, congo red, direct green 26 and curcumin crystalline. Amine-functionalized microporous SiO2/triangular Ag nanostructures were used for plasmon-mediated photocatalysis of methylene blue. The experimental results revealed that the large surface area of microporous silica facilitated adsorption of dye. Triangular Ag nanoparticles, due to their better charge carrier generation and enhanced surface plasmon resonance, further enhanced the photocatalysis performance.

Molecular dynamics simulation of nonlinear spectroscopies of intermolecular motions in liquid water.

PubMed

Yagasaki, Takuma; Saito, Shinji

2009-09-15

Water is the most extensively studied of liquids because of both its ubiquity and its anomalous thermodynamic and dynamic properties. The properties of water are dominated by hydrogen bonds and hydrogen bond network rearrangements. Fundamental information on the dynamics of liquid water has been provided by linear infrared (IR), Raman, and neutron-scattering experiments; molecular dynamics simulations have also provided insights. Recently developed higher-order nonlinear spectroscopies open new windows into the study of the hydrogen bond dynamics of liquid water. For example, the vibrational lifetimes of stretches and a bend, intramolecular features of water dynamics, can be accurately measured and are found to be on the femtosecond time scale at room temperature. Higher-order nonlinear spectroscopy is expressed by a multitime correlation function, whereas traditional linear spectroscopy is given by a one-time correlation function. Thus, nonlinear spectroscopy yields more detailed information on the dynamics of condensed media than linear spectroscopy. In this Account, we describe the theoretical background and methods for calculating higher order nonlinear spectroscopy; equilibrium and nonequilibrium molecular dynamics simulations, and a combination of both, are used. We also present the intermolecular dynamics of liquid water revealed by fifth-order two-dimensional (2D) Raman spectroscopy and third-order IR spectroscopy. 2D Raman spectroscopy is sensitive to couplings between modes; the calculated 2D Raman signal of liquid water shows large anharmonicity in the translational motion and strong coupling between the translational and librational motions. Third-order IR spectroscopy makes it possible to examine the time-dependent couplings. The 2D IR spectra and three-pulse photon echo peak shift show the fast frequency modulation of the librational motion. A significant effect of the translational motion on the fast frequency modulation of the librational motion is elucidated by introducing the "translation-free" molecular dynamics simulation. The isotropic pump-probe signal and the polarization anisotropy decay show fast transfer of the librational energy to the surrounding water molecules, followed by relaxation to the hot ground state. These theoretical methods do not require frequently used assumptions and can thus be called ab initio methods; together with multidimensional nonlinear spectroscopies, they provide powerful methods for examining the inter- and intramolecular details of water dynamics.

Strong Cosserat Elasticity in a Transversely Isotropic Polymer Lattice

NASA Astrophysics Data System (ADS)

Rueger, Z.; Lakes, R. S.

2018-02-01

Large size effects are experimentally measured in lattices of triangular unit cells: about a factor of 36 in torsion rigidity and 29 in bending rigidity. This nonclassical phenomenon is consistent with Cosserat elasticity, which allows for the rotation of points and distributed moments in addition to the translation of points and force stress of classical elasticity. The Cosserat characteristic length for torsion is ℓt=9.4 mm ; for bending, it is ℓb=8.8 mm ; these values are comparable to the cell size. Nonclassical effects are much stronger than in stretch-dominated lattices with uniform straight ribs. The lattice structure provides a path to the attainment of arbitrarily large effects.

Corkscrew point spread function for far-field three-dimensional nanoscale localization of pointlike objects

PubMed Central

Lew, Matthew D.; Lee, Steven F.; Badieirostami, Majid; Moerner, W. E.

2011-01-01

We describe the corkscrew point spread function (PSF), which can localize objects in three dimensions throughout a 3.2 µm depth of field with nanometer precision. The corkscrew PSF rotates as a function of the axial (z) position of an emitter. Fisher information calculations show that the corkscrew PSF can achieve nanometer localization precision with limited numbers of photons. We demonstrate three-dimensional super-resolution microscopy with the corkscrew PSF by imaging beads on the surface of a triangular polydimethylsiloxane (PDMS) grating. With 99,000 photons detected, the corkscrew PSF achieves a localization precision of 2.7 nm in x, 2.1 nm in y, and 5.7 nm in z. PMID:21263500

Corkscrew point spread function for far-field three-dimensional nanoscale localization of pointlike objects.

PubMed

Lew, Matthew D; Lee, Steven F; Badieirostami, Majid; Moerner, W E

2011-01-15

We describe the corkscrew point spread function (PSF), which can localize objects in three dimensions throughout a 3.2 μm depth of field with nanometer precision. The corkscrew PSF rotates as a function of the axial (z) position of an emitter. Fisher information calculations show that the corkscrew PSF can achieve nanometer localization precision with limited numbers of photons. We demonstrate three-dimensional super-resolution microscopy with the corkscrew PSF by imaging beads on the surface of a triangular polydimethylsiloxane (PDMS) grating. With 99,000 photons detected, the corkscrew PSF achieves a localization precision of 2.7 nm in x, 2.1 nm in y, and 5.7 nm in z.

Development of the program visualizing the lunar physical libration with Visual Basic

NASA Astrophysics Data System (ADS)

Zagidullin, Arthur; Petrova, Natalia

Study of the Moon, of its spin-orbital characteristics and parameters of the lunar interior is one of the traditional fields of the Kazan astronomical school. However, despite the incredible successes in space investigations of the planets and of the Moon, in last years the interest to celestial mechanics, ephemerides astronomy and astrometry is significantly decreased, especially among the young scientists and students. Therefore, it is encouraging to see the work of the third-year student, which is devoted to the study of the physical libration of the Moon. This report presents the results of the first stage of the above study associated with the study of Cassini's laws in the rotation of the Moon and the visualization of these laws by means the programming language Visual Basic. The Earth moves on the Moon's orbit in selenocentric frame. Dynamic coordinate system is based on the principal axes of inertia of the Moon. The x-axis is directed along the largest principal axis of inertia A, the axis z is a dynamic pole of the Moon associated with the smallest principal axis of inertia C. According to the first Cassini’s law the lunar pole is inclined at a constant angle approximately equal to 1.5 degree. The ascending node of the orbit is coincides with descending node of the lunar equator (the second Cassini’s law) and, as a result, the ecliptic pole lies between the orbit pole and spin pole. Therefore the three vectors directed from the lunar centre of mass to orbit pole, ecliptic pole and spin pole form a single plane. The third Cassini’s law reflects the uniform rotation of the Moon synchronised with orbital motion of the Moon around the Earth (in the selenocentric frame the Earth moves around the Moon). It’s necessary a significant time to calculate the corresponding coordinates of points, which move synchronously on the orbit and on the equator. In any time t the Earth moves with the mean velocity n and forms the angle n*t in the orbit plane. At the same time, according to the third law, the axis x forms the same angle varphi = n*t in equatorial plane. In other words the longest axis of the Moon is always "looking" at the Earth. The latter action, which the developed program executes, is a demonstration of the effects of several, the most powerful, harmonics of the physical libration. Unfortunately, Visual Basic opportunities are severely limited for creating three-dimensional images. Because of this we could not to support real scale in angles and time. This work was supported by RFBR grant No. 13-02-00792.

Landing Trail in 3-D

NASA Technical Reports Server (NTRS)

2004-01-01

A three-dimensional color model created using data from the Mars Exploration Rover's panoramic camera shows images of airbag drag marks on the martian surface. The triangular rock in the upper left corner is approximately 20 centimeters (8 inches) tall. The meatball-shaped rock in the upper right corner is approximately 10 centimeters (4 inches) tall. The dark portion of the surface, or 'trough' is approximately 1 centimeter (0.4 inches) deep at its deepest point. This model is displayed using software developed by NASA's Ames Research Center.

Dynamics and Origin of the 2:1 Orbital Resonances of the GJ 876 Planets

NASA Astrophysics Data System (ADS)

Lee, Man Hoi; Peale, S. J.

2002-03-01

The discovery by Marcy and coworkers of two planets in 2:1 orbital resonance about the star GJ 876 has been supplemented by a dynamical fit to the data by Laughlin & Chambers, which places the planets in coplanar orbits deep in three resonances at the 2:1 mean-motion commensurability. The selection of this almost singular state by the dynamical fit means that the resonances are almost certainly real, and with the small amplitudes of libration of the resonance variables, indefinitely stable. Several unusual properties of the 2:1 resonances are revealed by the GJ 876 system. The libration of both lowest order mean-motion resonance variables and the secular resonance variable, θ1=λ1- 2λ2+ϖ1, θ2=λ1- 2λ2+ϖ2, and θ3=ϖ1-ϖ2, about 0° (where λ1,2 are the mean longitudes of the inner and outer planet and ϖ1,2 are the longitudes of periapse) differs from the familiar geometry of the Io-Europa pair, where θ2 and θ3 librate about 180°. By considering the condition that ϖ1=ϖ2 for stable simultaneous librations of θ1 and θ2, we show that the GJ 876 geometry results from the large orbital eccentricities ei, whereas the very small eccentricities in the Io-Europa system lead to the latter's geometry. Surprisingly, the GJ 876 configuration, with θ1, θ2, and θ3 all librating, remains stable for e1 up to 0.86 and for amplitude of libration of θ1 approaching 45° with the current eccentricities-further supporting the indefinite stability of the existing system. Any process that drives originally widely separated orbits toward each other could result in capture into the observed resonances at the 2:1 commensurability. We find that forced inward migration of the outer planet of the GJ 876 system results in certain capture into the observed resonances if initially e1<~0.06 and e2<~0.03 and the migration rate |a2/a2|<~3×10- 2(a2/AU)-3/2yr-1. Larger eccentricities lead to likely capture into higher order resonances before the 2:1 commensurability is reached. The planets are sufficiently massive to open gaps in the nebular disk surrounding the young GJ 876 and to clear the disk material between them, and the resulting planet-nebular interaction typically forces the outer planet to migrate inward on the disk viscous timescale, whose inverse is about 3 orders of magnitude less than the above upper bound on |a2/a2| for certain capture. If there is no eccentricity damping, eccentricity growth is rapid with continued migration within the resonance, with ei exceeding the observed values after a further reduction in the semimajor axes ai of only 7%. With eccentricity damping ei/ei=-K|ai/ai|, the eccentricities reach equilibrium values that remain constant for arbitrarily long migration within the resonances. The equilibrium eccentricities are close to the observed eccentricities for K~100 if there is migration and damping of the outer planet only, but for K~10 if there is also migration and damping of the inner planet. This result is independent of the magnitude or functional form of the migration rate ai as long as ei/ei=-K|ai/ai|. Although existing analytic estimates of the effects of planet-nebula interaction are consistent with this form of eccentricity damping for certain disk parameter values, it is as yet unclear that such interaction can produce the large value of K required to obtain the observed eccentricities. The alternative eccentricity damping by tidal dissipation within the star or the planets is completely negligible, so the observed dynamical properties of the GJ 876 system may require an unlikely fine-tuning of the time of resonance capture to be near the end of the nebula lifetime.

Indications, techniques, and outcomes of arthroscopic repair of scapholunate ligament and triangular fibrocartilage complex.

PubMed

Mathoulin, C L

2017-07-01

This review includes updated understanding of the roles of intrinsic and extrinsic carpal ligaments in scapholunate instability and details the author's experience of indications, arthroscopic repair methods, and outcomes of treating the instability. A classification on triangular fibrocartilage complex injuries is reviewed, followed by author's indications, methods, and outcomes of arthroscopic repair of triangular fibrocartilage complex injuries.

Localized states in a triangular set of linearly coupled complex Ginzburg-Landau equations.

PubMed

Sigler, Ariel; Malomed, Boris A; Skryabin, Dmitry V

2006-12-01

We introduce a pattern-formation model based on a symmetric system of three linearly coupled cubic-quintic complex Ginzburg-Landau equations, which form a triangular configuration. This is the simplest model of a multicore fiber laser. We identify stability regions for various types of localized patterns possible in this setting, which include stationary and breathing triangular vortices.

26 CFR 1.367(b)-14T - Acquisition of parent stock for property in triangular reorganizations (temporary).

Code of Federal Regulations, 2010 CFR

2010-04-01

... 26 Internal Revenue 4 2010-04-01 2010-04-01 false Acquisition of parent stock for property in triangular reorganizations (temporary). 1.367(b)-14T Section 1.367(b)-14T Internal Revenue INTERNAL REVENUE... § 1.367(b)-14T Acquisition of parent stock for property in triangular reorganizations (temporary). (a...

Comparative analysis of film cooling efficiency at coolant supply into a single array of triangular dimples

NASA Astrophysics Data System (ADS)

Khalatov, A. A.; Petliak, O. O.; Severin, S. D.; Panchenko, N. A.

2018-03-01

The purpose of this work is a comparative study of the physical structure and film cooling efficiency of the single array of inclined holes, placed in triangular dimples and in a trench. The software package ANSYS CFX 17.0 was used along with RANS SST turbulence model. Calculations were made in a wide range of the blowing ratio ranging from 0.5 to 2.0. Results of modeling have shown high efficiency of triangular film cooling configuration. At m ≥ 1.5, the triangular configuration is comparable with the trench configuration in terms of the film cooling efficiency.

Nonzero θ13 from the Triangular Ansatz and Leptogenesis

NASA Astrophysics Data System (ADS)

Benaoum, H. B.

2012-08-01

Recent experiments indicate a departure from the exact tri-bimaximal mixing by measure ring definitive nonzero value of θ13. Within the framework of type I seesaw mechanism, we reconstruct the triangular Dirac neutrino mass matrix from the μ - τ symmetric mass matrix. The deviation from μ - τ symmetry is then parametrized by adding dimensionless parameters yi in the triangular mass matrix. In this parametrization of the neutrino mass matrix, the nonzero value θ13 is controlled by Δy = y4 - y6. We also calculate the resulting leptogenesis and show that the triangular texture can generate the observed baryon asymmetry in the universe via leptogenesis scenario.

Influence of two different flap designs on the sequelae of mandibular third molar surgery.

PubMed

Erdogan, Ozgür; Tatlı, Ufuk; Ustün, Yakup; Damlar, Ibrahim

2011-09-01

The aim of this study was to compare the influence of triangular and envelope flaps on trismus, pain, and facial swelling after mandibular third molar surgery. Twenty healthy patients with bilateral, symmetrically impacted mandibular third molars were included in this double-blinded, prospective, cross-over, randomized study. The patients were operated with envelope flap on one side and triangular flap on the other side. Trismus was determined by measuring maximum interincisal opening, and facial swelling was evaluated using a tape measuring method. Pain was determined using visual analog scale (VAS) and recording the number of pain pills taken. The facial swelling measurements and VAS scores were lower in the envelope flap group compared to the triangular flap group. There was no significant difference between the two flap designs in operation time, maximum interincisal opening, and the number of analgesics taken. Envelope flap yields to less facial swelling and reduced VAS scores in comparison to triangular flap. There is no clinical difference in trismus between the two flap designs. Despite the higher VAS scores with triangular flap, no additional doses of analgesics were required in triangular flap.

Orbital evolution and escape of Martian Trojans due to the Yarkovsky effect

NASA Astrophysics Data System (ADS)

Christou, Apostolos

2017-06-01

Recently it was shown that the Yarkovsky effect can lead to significant orbit change for Trojans of Mars [1,2] and that the orbital distribution of observed Trojans is consistent with a negative along-track acceleration of the same functional form as seasonal yarkovsky; this feature was used to constrain the age of the Eureka family of Mars Trojan asteroids [2]. In contrast, the Yarkovsky effect appears to have a negligible role in shaping observed families of Jupiter Trojans [3].To explore the evolution and end states of Trojans evolved by the Yarkosky effect, I have numerically integrated test particles under a model of the diurnal variant and for different values of the acceleration strength up to 10-2 AU/Myr for da/dt outside the resonance. I use as a starting point the orbits of the three largest Martian Trojans: 5261 Eureka, (101429) 1998 VF31 and (121514) 1999 UJ7.I find, as in [2], that the evolution of the inclination I and the libration amplitude L depends on the sign of the acceleration and is essentially deterministic. Considering the rate of change of the Tisserand constant [5,6] leads to a simple analytical expression that reproduces well the inclination evolution of the Trojans. The evolution of e is somewhat more stochastic, probably due to chaotic diffusion [4] and/or the influence of Mars’ eccentricity [2].Trojans escape upon reaching the boundaries of stability domains mapped out in [4], demarcated by resonances with principal secular modes and the Kozai resonance. The mechanism of escape is by increasing e and/or the libration amplitude to the point of allowing close encounters with Mars.During the presentation I will describe the ensemble evolution of Trojans under Yarkovsky, how it is related to the lifetime in the 1:1 resonance and discuss the implications for Trojan stability at Earth and Jupiter.[1] Christou, A.A., 2013, Icarus, 224, 144.[2] Ćuk, M., Christou, A.A., Hamilton, D.P., 2015, Icarus, 252, 339.[3] Milani, A., Knezević, Z., Spoto, F., Cellino, A., Novaković, B., Tsirvoulis, G., 2017, Icarus, 288, 240.[4] Scholl, H., Marzari, F., Tricarico, P., 2005, Icarus, 175, 397.[5] Hamilton, D.P., 1994, Icarus, 109, 221[6] Liou, J. C., Zook, H. A., 1997, Icarus, 128, 354.

Stereo matching and view interpolation based on image domain triangulation.

PubMed

Fickel, Guilherme Pinto; Jung, Claudio R; Malzbender, Tom; Samadani, Ramin; Culbertson, Bruce

2013-09-01

This paper presents a new approach for stereo matching and view interpolation problems based on triangular tessellations suitable for a linear array of rectified cameras. The domain of the reference image is initially partitioned into triangular regions using edge and scale information, aiming to place vertices along image edges and increase the number of triangles in textured regions. A region-based matching algorithm is then used to find an initial disparity for each triangle, and a refinement stage is applied to change the disparity at the vertices of the triangles, generating a piecewise linear disparity map. A simple post-processing procedure is applied to connect triangles with similar disparities generating a full 3D mesh related to each camera (view), which are used to generate new synthesized views along the linear camera array. With the proposed framework, view interpolation reduces to the trivial task of rendering polygonal meshes, which can be done very fast, particularly when GPUs are employed. Furthermore, the generated views are hole-free, unlike most point-based view interpolation schemes that require some kind of post-processing procedures to fill holes.

Addressing the Big-Earth-Data Variety Challenge with the Hierarchical Triangular Mesh

NASA Technical Reports Server (NTRS)

Rilee, Michael L.; Kuo, Kwo-Sen; Clune, Thomas; Oloso, Amidu; Brown, Paul G.; Yu, Honfeng

2016-01-01

We have implemented an updated Hierarchical Triangular Mesh (HTM) as the basis for a unified data model and an indexing scheme for geoscience data to address the variety challenge of Big Earth Data. We observe that, in the absence of variety, the volume challenge of Big Data is relatively easily addressable with parallel processing. The more important challenge in achieving optimal value with a Big Data solution for Earth Science (ES) data analysis, however, is being able to achieve good scalability with variety. With HTM unifying at least the three popular data models, i.e. Grid, Swath, and Point, used by current ES data products, data preparation time for integrative analysis of diverse datasets can be drastically reduced and better variety scaling can be achieved. In addition, since HTM is also an indexing scheme, when it is used to index all ES datasets, data placement alignment (or co-location) on the shared nothing architecture, which most Big Data systems are based on, is guaranteed and better performance is ensured. Moreover, our updated HTM encoding turns most geospatial set operations into integer interval operations, gaining further performance advantages.

Critical frontier of the triangular Ising antiferromagnet in a field

NASA Astrophysics Data System (ADS)

Qian, Xiaofeng; Wegewijs, Maarten; Blöte, Henk W.

2004-03-01

We study the critical line of the triangular Ising antiferromagnet in an external magnetic field by means of a finite-size analysis of results obtained by transfer-matrix and Monte Carlo techniques. We compare the shape of the critical line with predictions of two different theoretical scenarios. Both scenarios, while plausible, involve assumptions. The first scenario is based on the generalization of the model to a vertex model, and the assumption that the exact analytic form of the critical manifold of this vertex model is determined by the zeroes of an O(2) gauge-invariant polynomial in the vertex weights. However, it is not possible to fit the coefficients of such polynomials of orders up to 10, such as to reproduce the numerical data for the critical points. The second theoretical prediction is based on the assumption that a renormalization mapping exists of the Ising model on the Coulomb gas, and analysis of the resulting renormalization equations. It leads to a shape of the critical line that is inconsistent with the first prediction, but consistent with the numerical data.

Exact ground states for the nearest neighbor quantum XXZ model on the kagome and other lattices with triangular motifs at Jz /Jxy = - 1 / 2

NASA Astrophysics Data System (ADS)

Changlani, Hitesh; Kumar, Krishna; Kochkov, Dmitrii; Fradkin, Eduardo; Clark, Bryan

We report the existence of a quantum macroscopically degenerate ground state manifold on the nearest neighbor XXZ model on the kagome lattice at the point Jz /Jxy = - 1 / 2 . On many lattices with triangular motifs (including the kagome, sawtooth, icosidodecahedron and Shastry-Sutherland lattice for a certain choice of couplings) this Hamiltonian is found to be frustration-free with exact ground states which correspond to three-colorings of these lattices. Several results also generalize to the case of variable couplings and to other motifs (albeit with possibly more complex Hamiltonians). The degenerate manifold on the kagome lattice corresponds to a ''many-body flat band'' of interacting hard-core bosons; and for the one boson case our results also explain the well-known non-interacting flat band. On adding realistic perturbations, state selection in this manifold of quantum many-body states is discussed along with the implications for the phase diagram of the kagome lattice antiferromagnet. supported by DE-FG02-12ER46875, DMR 1408713, DE-FG02-08ER46544.

A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations

NASA Astrophysics Data System (ADS)

Ke, Rihuan; Ng, Michael K.; Sun, Hai-Wei

2015-12-01

In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O (MNlog2 ⁡ M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method.

Distance Determination by Gated Viewing Systems Taking into Account the Illuminating Pulse Shape

NASA Astrophysics Data System (ADS)

Gorobets, V. A.; Kuntsevich, B. F.; Shabrov, D. V.

2017-11-01

For gated viewing systems with triangular and trapezoidal illuminating pulses, we have obtained the range-intensity profiles (RIPs) of the signal as the time delay was varied between the leading edges of the gate pulse and the illuminating pulse. We have established that if the duration of the illuminating pulse Δtlas is less than or equal to the duration of the gate pulse ΔtIC, then the expressions for the characteristic distances are the same as for rectangular pulses and they can be used to determine the distance to objects. When Δtlas > ΔtIC, in the case of triangular illuminating pulses the RIP is bell-shaped. For trapezoidal pulses, the RIP is bell-shaped with or without a plateau section. We propose an empirical method for determining the characteristic distances to the RIP maximum and the boundary points for the plateau section, which we then use to calculate the distance to the object. Using calibration constants, we propose a method for determining the distance to an object and we have experimentally confirmed the feasibility of this method.

Triangular Quantum Loop Topography for Machine Learning

NASA Astrophysics Data System (ADS)

Zhang, Yi; Kim, Eun-Ah

Despite rapidly growing interest in harnessing machine learning in the study of quantum many-body systems there has been little success in training neural networks to identify topological phases. The key challenge is in efficiently extracting essential information from the many-body Hamiltonian or wave function and turning the information into an image that can be fed into a neural network. When targeting topological phases, this task becomes particularly challenging as topological phases are defined in terms of non-local properties. Here we introduce triangular quantum loop (TQL) topography: a procedure of constructing a multi-dimensional image from the ''sample'' Hamiltonian or wave function using two-point functions that form triangles. Feeding the TQL topography to a fully-connected neural network with a single hidden layer, we demonstrate that the architecture can be effectively trained to distinguish Chern insulator and fractional Chern insulator from trivial insulators with high fidelity. Given the versatility of the TQL topography procedure that can handle different lattice geometries, disorder, interaction and even degeneracy our work paves the route towards powerful applications of machine learning in the study of topological quantum matters.

Fast precalculated triangular mesh algorithm for 3D binary computer-generated holograms.

PubMed

Yang, Fan; Kaczorowski, Andrzej; Wilkinson, Tim D

2014-12-10

A new method for constructing computer-generated holograms using a precalculated triangular mesh is presented. The speed of calculation can be increased dramatically by exploiting both the precalculated base triangle and GPU parallel computing. Unlike algorithms using point-based sources, this method can reconstruct a more vivid 3D object instead of a "hollow image." In addition, there is no need to do a fast Fourier transform for each 3D element every time. A ferroelectric liquid crystal spatial light modulator is used to display the binary hologram within our experiment and the hologram of a base right triangle is produced by utilizing just a one-step Fourier transform in the 2D case, which can be expanded to the 3D case by multiplying by a suitable Fresnel phase plane. All 3D holograms generated in this paper are based on Fresnel propagation; thus, the Fresnel plane is treated as a vital element in producing the hologram. A GeForce GTX 770 graphics card with 2 GB memory is used to achieve parallel computing.

Two-Year Outcomes from a Randomized Controlled Trial of Minimally Invasive Sacroiliac Joint Fusion vs. Non-Surgical Management for Sacroiliac Joint Dysfunction.

PubMed

Polly, David W; Swofford, John; Whang, Peter G; Frank, Clay J; Glaser, John A; Limoni, Robert P; Cher, Daniel J; Wine, Kathryn D; Sembrano, Jonathan N

2016-01-01

Sacroiliac joint (SIJ) dysfunction is an important and underappreciated cause of chronic low back pain. To prospectively and concurrently compare outcomes after surgical and non-surgical treatment for chronic SIJ dysfunction. One hundred and forty-eight subjects with SIJ dysfunction were randomly assigned to minimally invasive SIJ fusion with triangular titanium implants (SIJF, n = 102) or non-surgical management (NSM, n = 46). SIJ pain (measured with a 100-point visual analog scale, VAS), disability (measured with Oswestry Disability Index, ODI) and quality of life scores were collected at baseline and at scheduled visits to 24 months. Crossover from non-surgical to surgical care was allowed after the 6-month study visit was complete. Improvements in continuous measures were compared using repeated measures analysis of variance. The proportions of subjects with clinical improvement (SIJ pain improvement ≥20 points, ODI ≥15 points) and substantial clinical benefit (SIJ pain improvement ≥25 points or SIJ pain rating ≤35, ODI ≥18.8 points) were compared. In the SIJF group, mean SIJ pain improved rapidly and was sustained (mean improvement of 55.4 points) at month 24. The 6-month mean change in the NSM group (12.2 points) was substantially smaller than that in the SIJF group (by 38.3 points, p<.0001 for superiority). By month 24, 83.1% and 82.0% received either clinical improvement or substantial clinical benefit in VAS SIJ pain score. Similarly, 68.2% and 65.9% had received clinical improvement or substantial clinical benefit in ODI score at month 24. In the NSM group, these proportions were <10% with non-surgical treatment only. Parallel changes were seen for EQ-5D and SF-36, with larger changes in the surgery group at 6 months compared to NSM. The rate of adverse events related to SIJF was low and only 3 subjects assigned to SIJF underwent revision surgery within the 24-month follow-up period. In this Level 1 multicenter prospective randomized controlled trial, minimally invasive SIJF with triangular titanium implants provided larger improvements in pain, disability and quality of life compared to NSM. Improvements after SIJF persisted to 24 months. This study was approved by a local or central IRB before any subjects were enrolled. All patients provided study-specific informed consent prior to participation.

Lattice modes of the chirally pure and racemic phases of tyrosine crystals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Belyanchikov, M. A.; Gorelik, V. S., E-mail: gorelik@sci.lebedev.ru; Gorshunov, B. P.

High-Q librational modes have been found to be present in the infrared absorption and Raman spectra of chirally pure L-tyrosine. Such modes can serve as terahertz radiation detectors and generators in chirally pure biostructures.

Merging of the Dirac points in electronic artificial graphene

NASA Astrophysics Data System (ADS)

Feilhauer, J.; Apel, W.; Schweitzer, L.

2015-12-01

Theory predicts that graphene under uniaxial compressive strain in an armchair direction should undergo a topological phase transition from a semimetal into an insulator. Due to the change of the hopping integrals under compression, both Dirac points shift away from the corners of the Brillouin zone towards each other. For sufficiently large strain, the Dirac points merge and an energy gap appears. However, such a topological phase transition has not yet been observed in normal graphene (due to its large stiffness) neither in any other electronic system. We show numerically and analytically that such a merging of the Dirac points can be observed in electronic artificial graphene created from a two-dimensional electron gas by application of a triangular lattice of repulsive antidots. Here, the effect of strain is modeled by tuning the distance between the repulsive potentials along the armchair direction. Our results show that the merging of the Dirac points should be observable in a recent experiment with molecular graphene.

Site Selection and Deployment Scenarios for Servicing of Deep-Space Observatories

NASA Technical Reports Server (NTRS)

Willenberg, Harvey J.; Fruhwirth, Michael A.; Potter, Seth D.; Leete, Stephen J.; Moe, Rud V.

2001-01-01

The deep-space environment and relative transportation accessibility of the Weak Stability Boundary (WSB) region connecting the Earth-Moon and Sun-Earth libration points makes the Sun-Earth L2 an attractive operating location for future observatories. A summary is presented of key characteristics of future observatories designed to operate in this region. The ability to service observatories that operate within the region around the Lagrange points may greatly enhance their reliability, lifetime, and scientific return. The range of servicing missions might begin with initial deployment, assembly, test, and checkout. Post-assembly servicing missions might also include maintenance and repair, critical fluids resupply, and instrument upgrades. We define the range of servicing missions that can be performed with extravehicular activity, with teleoperated robots, and with autonomous robots. We then describe deployment scenarios that affect payload design. A trade study is summarized of the benefits and risks of alternative servicing sites, including at the International Space Station, at other low-Earth-orbit locations, at the Earth-Moon L1 location, and on-site at the Sun-Earth L2 location. Required technology trades and development issues for observatory servicing at each site, and with each level of autonomy, are summarized.

Astronomical aspects of cosmic threats: new problems and approaches to asteroid—comet hazard following the chelyabinsk event of February 15, 2013

NASA Astrophysics Data System (ADS)

Shustov, B. M.; Shugarov, A. S.; Naroenkov, S. A.; Prokhorov, M. E.

2015-10-01

A new definition of hazardous celestial bodies (HCBs) is introduced, in which the lower limit of the size of a HCB is reduced to 10 m. A new definition for threatening and collisional orbits of DCBs is introduced. The main astronomical factors that must be taken into account when creating systems for the detection of HCBs are analyzed. The most important of these are the uniformity of the distribution of points (regions) for the appearance of HCBs on the celestial sphere in near-Earth space and the practical limit for the velocity of approach of a HCB of 20 km/s (for 90% of bodies). It is shown that the creation of a system for the nearby detection of asteroids and comets arriving from the daytime sky requires the use of a space-based system. A concept for such a system, in which one or several optical telescopes are placed in the vicinity of the libration point L1 for the Sun—Earth system, is developed. Preliminary plans for such a system, called the System for the Detection of Daytime Asteroids (SDDA), are briefly described.

Dynamical evolution of a fictitious population of binary Neptune Trojans

NASA Astrophysics Data System (ADS)

Brunini, Adrián

2018-03-01

We present numerical simulations of the evolution of a synthetic population of Binary Neptune Trojans, under the influence of the solar perturbations and tidal friction (the so-called Kozai cycles and tidal friction evolution). Our model includes the dynamical influence of the four giant planets on the heliocentric orbit of the binary centre of mass. In this paper, we explore the evolution of initially tight binaries around the Neptune L4 Lagrange point. We found that the variation of the heliocentric orbital elements due to the libration around the Lagrange point introduces significant changes in the orbital evolution of the binaries. Collisional processes would not play a significant role in the dynamical evolution of Neptune Trojans. After 4.5 × 109 yr of evolution, ˜50 per cent of the synthetic systems end up separated as single objects, most of them with slow diurnal rotation rate. The final orbital distribution of the surviving binary systems is statistically similar to the one found for Kuiper Belt Binaries when collisional evolution is not included in the model. Systems composed by a primary and a small satellite are more fragile than the ones composed by components of similar sizes.

Mercury's spin-orbit model and signature of C/MR2

NASA Astrophysics Data System (ADS)

Rambaux, N.; Bois, E.

2003-04-01

The upcoming missions, MESSENGER (Solomon etal 2001, Planet. Space Sci 49) and Bepi Colombo (Milani etal 2001, Planet. Space Sci 49) with onboard instrumentation capable of measuring the rotational parameters stimulate the objective to reach an accurate theory of the rotational motion of Mercury. Our work deals with the physical and dynamical causes that induce librations around an equilibrium state defined by the 3:2 spin-orbit resonance of Mercury. In order to integrate the spin-orbit motion of Mercury, we have used our gravitational model of the solar System including the Moon's spin-orbit motion. This model, called SONYR (acronym of Spin-Orbit N-bodY Relativistic model), was previously built by Bois, Journet and Vokrouhlicky in accordance with the requirements of the Lunar Laser Ranging observational accuracy (see for instance a review by Bois 2000, C. R. Acad. Sci. Série IV, or Bois and Vokrouhlický 1995). Using the model, the present study is devoted to the main perturbations acting on the spin-orbit motion of Mercury such as the planetary interactions (and their hierarchy) and the dynamical figure of the planet. The effect of the torque of Venus is 105 times smaller in magnitude than the one due to the Sun. Moreover, the complete rotation of Mercury exhibits two proper frequencies, namely 15.825 and 1089 years, and one secular variation of 271043 years which is due to the nodal precession between the equatorial plane of Mercury and its orbital plane. It is the second synchronism of Mercury mentioned by Beletski in 1986. We have made into evidence that the 3:2 resonance of Mercury is preserved by this second synchronism, which can be understood as a spin-orbit secular resonance. We have shown that the secular resonance variable ψ - Ω librates with a frequency of 1089 years. Our model integration starts with an initial obliquity of 1.65 arcminute (re-evaluate from the Cassini state) and gives an amplitude of libration in longitude of the order of 20 arcseconds, which is in agreement with Balogh and Giamperi (2002, Rep. Prog. Phys. 65). Besides, we have computed in the Hermean librations the impact of the variation of the greatest principal moment of inertia, cm2. The maximal signature on the obliquity is then 1.4 mas (milliarsecond) on the 176 day period, and the one on the libration in longitude is 0.4 mas on the 87.9 day period, resulting from an increase of the cm2 value of 1%. These values have to be understood as upper bounds of such signatures. These two effects permit to contribute to precise the relationship between the cm2 coefficient and the internal structure of Mercury. References : Balog, A., and Giamperi, G., 2002, Rep. Prog. Phys. 65, 529-560. Beletski, V, 1986, "Essais sur le Mouvement des Corps Cosmiques", Mir (ed), Moscou. Bois, E., 2000, C. R. Acad. Sci. Paris, t. 1, Série IV, 809-823. Bois, E., and Vokrouhlický, D., 1995, Astronomy and Astrophysics 300, 559-567. Milani, A., Vokrouhlicky, D., and Bonanno, C., 2001, Planet. Space Sci 49, 1579. Solomon, etal, 2001, Planet. Space Sci 49, 1445.

Diagnosing central lesions of the triangular fibrocartilage as traumatic or degenerative: a review of clinical accuracy.

PubMed

Löw, S; Erne, H; Pillukat, T; Mühldorfer-Fodor, M; Unglaub, F; Spies, C K

2017-05-01

This study examined the reliability of surgeons' estimations as to whether central lesions of the triangular fibrocartilage complex were traumatic or degenerative. A total of 50 consecutive central triangular fibrocartilage complex lesions were independently rated by ten experienced wrist surgeons viewing high-quality arthroscopy videos. The videos were reassessed after intervals of 3 months; at the second assessment surgeons were given the patient's history, radiographs and both, each in a randomized order. Finally, the surgeons assessed the histories and radiographs without the videos. Kappa statistics revealed fair interrater agreement when the histories were added to the videos. The other four modalities demonstrated moderate agreement, with lower Kappa values for the assessment without videos. Intra-rater reliability showed fair agreement for three surgeons, moderate agreement for two surgeons and substantial agreement for five surgeons. It appears that classification of central triangular fibrocartilage complex lesions depends on the information provided upon viewing the triangular fibrocartilage complex at arthroscopy. II.

Patients with triangular fibrocartilage complex injuries and distal radioulnar joint instability have reduced rotational torque in the forearm.

PubMed

Andersson, J K; Axelsson, P; Strömberg, J; Karlsson, J; Fridén, J

2016-09-01

A total of 20 patients scheduled for wrist arthroscopy, all with clinical signs of rupture to the triangular fibrocartilage complex and distal radioulnar joint instability, were tested pre-operatively by an independent observer for strength of forearm rotation. During surgery, the intra-articular pathology was documented by photography and also subsequently individually analysed by another independent hand surgeon. Arthroscopy revealed a type 1-B injury to the triangular fibrocartilage complex in 18 of 20 patients. Inter-rater reliability between the operating surgeon and the independent reviewer showed absolute agreement in all but one patient (95%) in terms of the injury to the triangular fibrocartilage complex and its classification. The average pre-operative torque strength was 71% of the strength of the non-injured contralateral side in pronation and supination. Distal radioulnar joint instability with an arthroscopically verified injury to the triangular fibrocartilage complex is associated with a significant loss of both pronation and supination torque. Case series, Level IV. © The Author(s) 2015.

Anisotropic magnetic properties of the triangular plane lattice material TmMgGaO 4

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cevallos, F. Alex; Stolze, Karoline; Kong, Tai

Here, the crystal growth, structure, and basic magnetic properties of TmMgGaO 4 are reported. The Tm ions are located in a planar triangular lattice consisting of distorted TmO6 octahedra, while the Mg and Ga atoms randomly occupy intermediary bilayers of M-O triangular bipyramids. The Tm ions are positionally disordered. The material displays an antiferromagnetic Curie Weiss theta of ~ -20 -25 K, with no clear ordering visible in the magnetic susceptibility down to 1.8 K; the structure and magnetic properties suggest that ordering of the magnetic moments is frustrated by both structural disorder and the triangular magnetic motif. Single crystalmore » magnetization measurements indicate that the magnetic properties are highly anisotropic, with large moments measured perpendicular to the triangular planes. At 2 K, a broad step-like feature is seen in the field-dependent magnetization perpendicular to the plane on applied field near 2 Tesla.« less

[Fluorescence Resonance Energy Transfer Detection of Cobalt Ions by Silver Triangular Nanoplates and Rhodamine 6G].

PubMed

Zhang, Xiu-qing; Peng, Jun; Ling, Jian; Liu, Chao-juan; Cao, Qiu-e; Ding, Zhong-tao

2015-04-01

In the present paper, the authors studied fluorescence resonance energy transfer (FRET) phenomenon between silver triangular nanoplates and bovine serum albumin (BSA)/Rhodamine 6G fluorescence complex, and established a fluorescence method for the detection of cobalt ions. We found that when increasing the silver triangular nanoplates added to certain concentrations of fluorescent bovine serum albumin (BSA)/Rhodamine 6G complex, the fluorescence of Rhodamine 6G would be quenched up to 80% due to the FRET between the quencher and donor. However, in the presence of cobalt ions, the disassociation of the fluorescent complex from silver triangular nanoplates occurred and the fluorescence of the Rhodamine 6G recovered. The recovery of fluorescence intensity rate (I/I0) has a good relationship with the cobalt ion concentration (cCO2+) added. Thus, the authors developed a fluorescence method for the detection of cobalt ions based on the FRET of silver triangular nanoplates and Rhodamine 6G.

Simultaneous travel time tomography for updating both velocity and reflector geometry in triangular/tetrahedral cell model

NASA Astrophysics Data System (ADS)

Bai, Chao-ying; He, Lei-yu; Li, Xing-wang; Sun, Jia-yu

2018-05-01

To conduct forward and simultaneous inversion in a complex geological model, including an irregular topography (or irregular reflector or velocity anomaly), we in this paper combined our previous multiphase arrival tracking method (referred as triangular shortest-path method, TSPM) in triangular (2D) or tetrahedral (3D) cell model and a linearized inversion solver (referred to as damped minimum norms and constrained least squares problem solved using the conjugate gradient method, DMNCLS-CG) to formulate a simultaneous travel time inversion method for updating both velocity and reflector geometry by using multiphase arrival times. In the triangular/tetrahedral cells, we deduced the partial derivative of velocity variation with respective to the depth change of reflector. The numerical simulation results show that the computational accuracy can be tuned to a high precision in forward modeling and the irregular velocity anomaly and reflector geometry can be accurately captured in the simultaneous inversion, because the triangular/tetrahedral cell can be easily used to stitch the irregular topography or subsurface interface.

Simultaneous travel time tomography for updating both velocity and reflector geometry in triangular/tetrahedral cell model

NASA Astrophysics Data System (ADS)

Bai, Chao-ying; He, Lei-yu; Li, Xing-wang; Sun, Jia-yu

2017-12-01

To conduct forward and simultaneous inversion in a complex geological model, including an irregular topography (or irregular reflector or velocity anomaly), we in this paper combined our previous multiphase arrival tracking method (referred as triangular shortest-path method, TSPM) in triangular (2D) or tetrahedral (3D) cell model and a linearized inversion solver (referred to as damped minimum norms and constrained least squares problem solved using the conjugate gradient method, DMNCLS-CG) to formulate a simultaneous travel time inversion method for updating both velocity and reflector geometry by using multiphase arrival times. In the triangular/tetrahedral cells, we deduced the partial derivative of velocity variation with respective to the depth change of reflector. The numerical simulation results show that the computational accuracy can be tuned to a high precision in forward modeling and the irregular velocity anomaly and reflector geometry can be accurately captured in the simultaneous inversion, because the triangular/tetrahedral cell can be easily used to stitch the irregular topography or subsurface interface.

Solution of Volterra and Fredholm Classes of Equations via Triangular Orthogonal Function (A Combination of Right Hand Triangular Function and Left Hand Triangular Function) and Hybrid Orthogonal Function (A Combination of Sample Hold Function and Right Hand Triangular Function)

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Anirban; Ganguly, Anindita; Chatterjee, Saumya Deep

2018-04-01

In this paper the authors have dealt with seven kinds of non-linear Volterra and Fredholm classes of equations. The authors have formulated an algorithm for solving the aforementioned equation types via Hybrid Function (HF) and Triangular Function (TF) piecewise-linear orthogonal approach. In this approach the authors have reduced integral equation or integro-differential equation into equivalent system of simultaneous non-linear equation and have employed either Newton's method or Broyden's method to solve the simultaneous non-linear equations. The authors have calculated the L2-norm error and the max-norm error for both HF and TF method for each kind of equations. Through the illustrated examples, the authors have shown that the HF based algorithm produces stable result, on the contrary TF-computational method yields either stable, anomalous or unstable results.

Logical spin-filtering in a triangular network of quantum nanorings with a Rashba spin-orbit interaction

NASA Astrophysics Data System (ADS)

Dehghan, E.; Sanavi Khoshnoud, D.; Naeimi, A. S.

2018-01-01

The spin-resolved electron transport through a triangular network of quantum nanorings is studied in the presence of Rashba spin-orbit interaction (RSOI) and a magnetic flux using quantum waveguide theory. This study illustrates that, by tuning Rashba constant, magnetic flux and incoming electron energy, the triangular network of quantum rings can act as a perfect logical spin-filtering with high efficiency. By changing in the energy of incoming electron, at a proper value of the Rashba constant and magnetic flux, a reverse in the direction of spin can take place in the triangular network of quantum nanorings. Furthermore, the triangular network of quantum nanorings can be designed as a device and shows several simultaneous spintronic properties such as spin-splitter and spin-inverter. This spin-splitting is dependent on the energy of the incoming electron. Additionally, different polarizations can be achieved in the two outgoing leads from an originally incoming spin state that simulates a Stern-Gerlach apparatus.

Anisotropic magnetic properties of the triangular plane lattice material TmMgGaO 4

DOE PAGES

Cevallos, F. Alex; Stolze, Karoline; Kong, Tai; ...

2018-04-30

Here, the crystal growth, structure, and basic magnetic properties of TmMgGaO 4 are reported. The Tm ions are located in a planar triangular lattice consisting of distorted TmO6 octahedra, while the Mg and Ga atoms randomly occupy intermediary bilayers of M-O triangular bipyramids. The Tm ions are positionally disordered. The material displays an antiferromagnetic Curie Weiss theta of ~ -20 -25 K, with no clear ordering visible in the magnetic susceptibility down to 1.8 K; the structure and magnetic properties suggest that ordering of the magnetic moments is frustrated by both structural disorder and the triangular magnetic motif. Single crystalmore » magnetization measurements indicate that the magnetic properties are highly anisotropic, with large moments measured perpendicular to the triangular planes. At 2 K, a broad step-like feature is seen in the field-dependent magnetization perpendicular to the plane on applied field near 2 Tesla.« less

The rotation of Titan and Ganymede

NASA Astrophysics Data System (ADS)

Van Hoolst, Tim; Coyette, Alexis; Baland, Rose-Marie; Trinh, Antony

2016-10-01

The rotation rates of Titan and Ganymede, the largest satellites of Saturn and Jupiter, are on average equal to their orbital mean motion. Here we discuss small deviations from the average rotation for both satellites and evaluate the polar motion of Titan induced by its surface fluid layers. We examine different causes at various time scales and assess possible consequences and the potential of using librations and polar motion as probes of the interior structure of the satellites.The rotation rate of Titan and Ganymede cannot be constant on the orbital time scale as a result of the gravitational torque of the central planet acting on the satellites. Titan is moreover expected to show significant polar motion and additional variations in the rotation rate due to angular momentum exchange with the atmosphere, mainly at seasonal periods. Observational evidence for deviations from the synchronous state has been reported several times for Titan but is unfortunately inconclusive. The measurements of the rotation variations are based on determinations of the shift in position of Cassini radar images taken during different flybys. The ESA JUICE (JUpiter ICy moons Explorer) mission will measure the rotation variations of Ganymede during its orbital phase around the satellite starting in 2032.We report on different theoretical aspects of the librations and polar motion. We consider the influence of the rheology of the ice shell and take into account Cassini measurements of the external gravitational field and of the topography of Titan and similar Galileo data about Ganymede. We also evaluate the librations and polar motion induced by Titan's hydrocarbon seas and use the most recent results of Titan's atmosphere dynamics. We finally evaluate the potential of rotation variations to constrain the satellite's interior structure, in particular its ice shell and ocean.

Estimating Mass Parameters of Doubly Synchronous Binary Asteroids

NASA Astrophysics Data System (ADS)

Davis, Alex; Scheeres, Daniel J.

2017-10-01

The non-spherical mass distributions of binary asteroid systems lead to coupled mutual gravitational forces and torques. Observations of the coupled attitude and orbital dynamics can be leveraged to provide information about the mass parameters of the binary system. The full 3-dimensional motion has 9 degrees of freedom, and coupled dynamics require the use of numerical investigation only. In the current study we simplify the system to a planar ellipsoid-ellipsoid binary system in a doubly synchronous orbit. Three modes are identified for the system, which has 4 degrees of freedom, with one degree of freedom corresponding to an ignorable coordinate. The three modes correspond to the three major librational modes of the system when it is in a doubly synchronous orbit. The linearized periods of each mode are a function of the mass parameters of the two asteroids, enabling measurement of these parameters based on observations of the librational motion. Here we implement estimation techniques to evaluate the capabilities of this mass measurement method. We apply this methodology to the Trojan binary asteroid system 617 Patroclus and Menoetius (1906 VY), the final flyby target of the recently announced LUCY Discovery mission. This system is of interest because a stellar occultation campaign of the Patroclus and Menoetius system has suggested that the asteroids are similarly sized oblate ellipsoids moving in a doubly-synchronous orbit, making the system an ideal test for this investigation. A number of missed observations during the campaign also suggested the possibility of a crater on the southern limb of Menoetius, the presence of which could be evaluated by our mass estimation method. This presentation will review the methodology and potential accuracy of our approach in addition to evaluating how the dynamical coupling can be used to help understand light curve and stellar occultation observations for librating binary systems.

Triangular arbitrage as an interaction among foreign exchange rates

NASA Astrophysics Data System (ADS)

Aiba, Yukihiro; Hatano, Naomichi; Takayasu, Hideki; Marumo, Kouhei; Shimizu, Tokiko

2002-07-01

We first show that there are in fact triangular arbitrage opportunities in the spot foreign exchange markets, analyzing the time dependence of the yen-dollar rate, the dollar-euro rate and the yen-euro rate. Next, we propose a model of foreign exchange rates with an interaction. The model includes effects of triangular arbitrage transactions as an interaction among three rates. The model explains the actual data of the multiple foreign exchange rates well.

Field-design optimization with triangular heliostat pods

NASA Astrophysics Data System (ADS)

Domínguez-Bravo, Carmen-Ana; Bode, Sebastian-James; Heiming, Gregor; Richter, Pascal; Carrizosa, Emilio; Fernández-Cara, Enrique; Frank, Martin; Gauché, Paul

2016-05-01

In this paper the optimization of a heliostat field with triangular heliostat pods is addressed. The use of structures which allow the combination of several heliostats into a common pod system aims to reduce the high costs associated with the heliostat field and therefore reduces the Levelized Cost of Electricity value. A pattern-based algorithm and two pattern-free algorithms are adapted to handle the field layout problem with triangular heliostat pods. Under the Helio100 project in South Africa, a new small-scale Solar Power Tower plant has been recently constructed. The Helio100 plant has 20 triangular pods (each with 6 heliostats) whose positions follow a linear pattern. The obtained field layouts after optimization are compared against the reference field Helio100.

Lattice dynamics of a rotor-stator molecular crystal: Fullerene-cubane C60ṡC8H8

NASA Astrophysics Data System (ADS)

Bousige, Colin; Rols, Stéphane; Cambedouzou, Julien; Verberck, Bart; Pekker, Sándor; Kováts, Éva; Durkó, Gábor; Jalsovsky, István; Pellegrini, Éric; Launois, Pascale

2010-11-01

The dynamics of fullerene-cubane (C60ṡC8H8) cocrystal is studied combining experimental [x-ray diffuse scattering, quasielastic and inelastic neutron scattering (INS)] and simulation (molecular dynamics) investigations. Neutron scattering gives direct evidence of the free rotation of fullerenes and of the libration of cubanes in the high-temperature phase, validating the “rotor-stator” description of this molecular system. X-ray diffuse scattering shows that orientational disorder survives the order/disorder transition in the low-temperature phase, although the loss of fullerene isotropic rotational diffusion is featured by the appearance of a 2.2 meV mode in the INS spectra. The coupling between INS and simulations allows identifying a degeneracy lift of the cubane librations in the low temperature phase, which is used as a tool for probing the environment of cubane in this phase and for getting further insights into the phase transition mechanism.

Improvements on the interior structure of Mercury expected from geodesy measurements

NASA Astrophysics Data System (ADS)

Rivoldini, A.; van Hoolst, T.; Verhoeven, O.

2008-09-01

ABSTRACT We assess the improvements on the interior structure of Mercury provided by expected data from geodesy experiments to be performed with the MESSENGER and BepiColombo orbiters. The observation of obliquity will allow estimating the moment of inertia, whereas measurements of libration will determine the moment of inertia of the silicate shell (mantle and crust). Tidal measurements will constrain the Love numbers that characterize the response of Mercury to the solar tidal forcing. Here, we construct depth-dependent interior structure models of Mercury for several plausible chemical compositions of the core and of the mantle using recent data on core and mantle materials. In particular we study the core structure for different mantle mineralogies and two different temperature profiles. We investigate the influence of the core light element concentration, temperature, and melting law on core state and inner core size. We compute libration amplitude, obliquity, tidal deformation, and tidal changes in the external potential for our models.

Near-Earth asteroid satellite spins under spin-orbit coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Naidu, Shantanu P.; Margot, Jean-Luc

We develop a fourth-order numerical integrator to simulate the coupled spin and orbital motions of two rigid bodies having arbitrary mass distributions under the influence of their mutual gravitational potential. We simulate the dynamics of components in well-characterized binary and triple near-Earth asteroid systems and use surface of section plots to map the possible spin configurations of the satellites. For asynchronous satellites, the analysis reveals large regions of phase space where the spin state of the satellite is chaotic. For synchronous satellites, we show that libration amplitudes can reach detectable values even for moderately elongated shapes. The presence of chaoticmore » regions in the phase space has important consequences for the evolution of binary asteroids. It may substantially increase spin synchronization timescales, explain the observed fraction of asychronous binaries, delay BYORP-type evolution, and extend the lifetime of binaries. The variations in spin rate due to large librations also affect the analysis and interpretation of light curve and radar observations.« less

Stationkeeping Monte Carlo Simulation for the James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Dichmann, Donald J.; Alberding, Cassandra M.; Yu, Wayne H.

2014-01-01

The James Webb Space Telescope (JWST) is scheduled to launch in 2018 into a Libration Point Orbit (LPO) around the Sun-Earth/Moon (SEM) L2 point, with a planned mission lifetime of 10.5 years after a six-month transfer to the mission orbit. This paper discusses our approach to Stationkeeping (SK) maneuver planning to determine an adequate SK delta-V budget. The SK maneuver planning for JWST is made challenging by two factors: JWST has a large Sunshield, and JWST will be repointed regularly producing significant changes in Solar Radiation Pressure (SRP). To accurately model SRP we employ the Solar Pressure and Drag (SPAD) tool, which uses ray tracing to accurately compute SRP force as a function of attitude. As an additional challenge, the future JWST observation schedule will not be known at the time of SK maneuver planning. Thus there will be significant variation in SRP between SK maneuvers, and the future variation in SRP is unknown. We have enhanced an earlier SK simulation to create a Monte Carlo simulation that incorporates random draws for uncertainties that affect the budget, including random draws of the observation schedule. Each SK maneuver is planned to optimize delta-V magnitude, subject to constraints on spacecraft pointing. We report the results of the Monte Carlo simulations and discuss possible improvements during flight operations to reduce the SK delta-V budget.

Cusp repair in aortic valve reconstruction: does the technique affect stability?

PubMed

Aicher, Diana; Langer, Frank; Adam, Oliver; Tscholl, Dietmar; Lausberg, Henning; Schäfers, Hans-Joachim

2007-12-01

Cusp prolapse may be an isolated cause of aortic regurgitation or may exist in conjunction with dilatation of the proximal aorta. Prolapse can be corrected by central plication, triangular resection, or pericardial patch implantation. We retrospectively analyzed our results with these techniques. From October 1995 to December 2006, 604 patients (aged 3-86 years) underwent aortic valve repair. Cusp prolapse was found in 427 patients (246 tricuspid, 181 bicuspid). Prolapse was corrected by central plication (n = 275) or triangular resection (n = 80). A pericardial patch was implanted for pre-existing cusp defects or after excision of calcium (n = 72). One cusp was repaired in 198 patients; the remaining patients underwent repair of 2 (n = 189) or 3 cusps (n = 40). In 102 patients more than one technique was used, and the patients were allocated to the group of the assumedly more complex repair (central plication < triangular resection < pericardial patch plasty). Cumulative follow-up was 1238 patient-years (mean 35 +/- 27 months). Hospital mortality was 2.6% (11/427). Actuarial freedom from aortic regurgitation of grade II or more at 5 years was 92% (central plication), 90% (triangular resection), and 90% (pericardial patch plasty). Thirteen patients were reoperated on, with prolapse as the most common reason for failure (n = 7); 6 underwent re-repair. Freedom from reoperation at 5 years was 95% (central plication), 94% (triangular resection), and 94% (pericardial patch plasty). Freedom from valve replacement at 5 years was 97% (central plication), 99% (triangular resection), and 98% (pericardial patch plasty). In aortic valve repair, cusp prolapse can be treated reliably by central plication. In the presence of more complex disease, triangular resection or pericardial patch plasty may be used without compromising midterm durability.

Dependence of the L-Mode scrape-off layer power fall-off length on the upper triangularity in TCV

NASA Astrophysics Data System (ADS)

Faitsch, M.; Maurizio, R.; Gallo, A.; Coda, S.; Eich, T.; Labit, B.; Merle, A.; Reimerdes, H.; Sieglin, B.; Theiler, C.; the Eurofusion MST1 Team; the TCV Team

2018-04-01

This paper reports on experimental observations on TCV with a scan in upper triangularity {δ }up}, including negative triangularity, focusing on the power fall-off length {λ }{{q}} in L-Mode. The upper triangularity is scanned from -0.28 to 0.47. Smaller {λ }{{q}}out} is measured at the outer divertor target for decreasing {δ }up} together with higher edge temperature {T}{{e},{edge}} leading to increased confinement. This effect is observed for both magnetic drift directions for discharges in deuterium and helium. In helium larger {λ }{{q}} values are observed compared to deuterium. The power fall-off length at the inner divertor target {λ }{{q}}in} has a non-monotonic behaviour with changing triangularity. The largest values are around {δ }up}=0. The ratio {λ }{{q}}in}/{λ }{{q}}out} increases for decreasing {δ }up} for positive triangularity and is approximately constant for negative triangularity. {λ }{{q}}out} is compared to available scaling laws. Partial agreement is only observed for a scaling law containing a proxy for {T}{{e},{edge}} at ASDEX Upgrade (Sieglin 2016 Plasma Phys. Control. Fusion 58 055015). Extending this scaling to TCV and using {T}{{e},{edge}} at {ρ }pol}=0.95 suggests that {λ }{{q}}out} is independent of machine size {λ }{{q}}{{L} - {Mode}} ({mm}) = 165\\cdot {B}pol}{({{T}})}-0.66\\cdot A{({{u}})}-0.15\\cdot {T}{{e},{edge}}{({eV})}-0.93\\cdot R{({{m}})}-0.03. Possible explanations for smaller {λ }{{q}}out} for decreasing {δ }up} is a reduction in turbulence or a direct effect of increasing {T}{{e},{edge}}.

Modulation transfer function of a triangular pixel array detector.

PubMed

Karimzadeh, Ayatollah

2014-07-01

The modulation transfer function (MTF) is the main parameter that is used to evaluate image quality in electro-optical systems. Detector sampling MTF in most electro-optical systems determines the cutoff frequency of the system. The MTF of the detector depends on its pixel shape. In this work, we calculated the MTF of a detector with an equilateral triangular pixel shape. Some new results were found in deriving the MTF for the equilateral triangular pixel shape.

Galerkin finite difference Laplacian operators on isolated unstructured triangular meshes by linear combinations

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.

1990-01-01

The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formulae in Cartesian coordinates for the Laplacian operator on isolated unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator along with linear combinations of the residual equations are used to develop the algorithm. The algorithm was tested for a wide variety of unstructured meshes and found to give satisfactory results.

Unitary Root Music and Unitary Music with Real-Valued Rank Revealing Triangular Factorization

DTIC Science & Technology

2010-06-01

AFRL-RY-WP-TP-2010-1213 UNITARY ROOT MUSIC AND UNITARY MUSIC WITH REAL-VALUED RANK REVEALING TRIANGULAR FACTORIZATION (Postprint) Nizar...DATES COVERED (From - To) June 2010 Journal Article Postprint 08 September 2006 – 31 August 2009 4. TITLE AND SUBTITLE UNITARY ROOT MUSIC AND...UNITARY MUSIC WITH REAL-VALUED RANK REVEALING TRIANGULAR FACTORIZATION (Postprint) 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA8650-05-D-1912-0007 5c

Are the Color Gamuts of CRT and LCD Triangular? An Experimental Study

DTIC Science & Technology

2000-07-01

UNCLASSIFIED Defense Technical Information Center Compilation Part Notice ADPO113 31 TITLE: Are the Color Gamuts of CRT and LCD Triangular? An...ADP011297 thru ADP011332 UNCLASSIFIED Are the Color Gamuts of CRT and LCD Triangular? An Experimental Study Guan-wei Leea and Chao-hua Wenb aDepartment of...Tube) display. This study describes the difference of color gamuts in different luminance level and the accuracy of color between CRT and LCD. In the

Comparison of two-transsacral-screw fixation versus triangular osteosynthesis for transforaminal sacral fractures.

PubMed

Min, Kyong S; Zamorano, David P; Wahba, George M; Garcia, Ivan; Bhatia, Nitin; Lee, Thay Q

2014-09-01

Transforaminal pelvic fractures are high-energy injuries that are translationally and rotationally unstable. This study compared the biomechanical stability of triangular osteosynthesis vs 2-transsacral-screw fixation in the repair of a transforaminal pelvic fracture model. A transforaminal fracture model was created in 10 cadaveric lumbopelvic specimens. Five of the specimens were stabilized with triangular osteosynthesis, which consisted of unilateral L5-to-ilium lumbopelvic fixation and ipsilateral iliosacral screw fixation. The remaining 5 were stabilized with a 2-transsacral-screw fixation technique that consisted of 2 transsacral screws inserted across S1. All specimens were loaded cyclically and then loaded to failure. Translation and rotation were measured using the MicroScribe 3D digitizing system (Revware Inc, Raleigh, North Carolina). The 2-transsacral-screw group showed significantly greater stiffness than the triangular osteosynthesis group (2-transsacral-screw group, 248.7 N/mm [standard deviation, 73.9]; triangular osteosynthesis group, 125.0 N/mm [standard deviation, 66.9]; P=.02); however, ultimate load and rotational stiffness were not statistically significant. Compared with triangular osteosynthesis fixation, the use of 2 transsacral screws provides a comparable biomechanical stability profile in both translation and rotation. This newly revised 2-transsacral-screw construct offers the traumatologist an alternative method of repair for vertical shear fractures that provides biplanar stability. It also offers the advantage of percutaneous placement in either the prone or supine position. Copyright 2014, SLACK Incorporated.

On the Use of the Beta Distribution in Probabilistic Resource Assessments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Olea, Ricardo A., E-mail: olea@usgs.gov

2011-12-15

The triangular distribution is a popular choice when it comes to modeling bounded continuous random variables. Its wide acceptance derives mostly from its simple analytic properties and the ease with which modelers can specify its three parameters through the extremes and the mode. On the negative side, hardly any real process follows a triangular distribution, which from the outset puts at a disadvantage any model employing triangular distributions. At a time when numerical techniques such as the Monte Carlo method are displacing analytic approaches in stochastic resource assessments, easy specification remains the most attractive characteristic of the triangular distribution. Themore » beta distribution is another continuous distribution defined within a finite interval offering wider flexibility in style of variation, thus allowing consideration of models in which the random variables closely follow the observed or expected styles of variation. Despite its more complex definition, generation of values following a beta distribution is as straightforward as generating values following a triangular distribution, leaving the selection of parameters as the main impediment to practically considering beta distributions. This contribution intends to promote the acceptance of the beta distribution by explaining its properties and offering several suggestions to facilitate the specification of its two shape parameters. In general, given the same distributional parameters, use of the beta distributions in stochastic modeling may yield significantly different results, yet better estimates, than the triangular distribution.« less

Triangular-shaped landforms reveal subglacial drainage routes in SW Finland

NASA Astrophysics Data System (ADS)

Mäkinen, J.; Kajuutti, K.; Palmu, J.-P.; Ojala, A.; Ahokangas, E.

2017-05-01

The aim of this study is to present the first evidence of triangular-shaped till landforms and related erosional features indicative of subglacial drainage within the ice stream bed of the Scandinavian ice sheet in Finland. Previously unidentified grouped patterns of Quaternary deposits with triangular landforms can be recognized from LiDAR-based DEMs. The triangular landforms occur as segments within geomorphologically distinguishable routes that are associated with eskers. The morphological and sedimentological characteristics as well as the distribution of the triangular landforms are interpreted to involve the creep of saturated deforming till, flow and pressure fluctuations of subglacial meltwater associated with meltwater erosion. There are no existing models for the formation of this kind of large-scale drainage systems, but we claim that they represent an efficient drainage system for subglacial meltwater transfer under high pressure conditions. Our hypothesis is that the routed, large-scale subglacial drainage systems described herein form a continuum between channelized (eskers) and more widely spread small-scale distributed subglacial drainage. Moreover, the transition from the conduit dominated drainage to triangular-shaped subglacial landforms takes place about 50-60 km from the ice margin. We provide an important contribution towards a more realistic representation of ice sheet hydrological drainage systems that could be used to improve paleoglaciological models and to simulate likely responses of ice sheets to increased meltwater production.