An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. II. Thermal correlation functions.

PubMed

Liu, Jian; Miller, William H

2011-03-14

We show the exact expression of the quantum mechanical time correlation function in the phase space formulation of quantum mechanics. The trajectory-based dynamics that conserves the quantum canonical distribution-equilibrium Liouville dynamics (ELD) proposed in Paper I is then used to approximately evaluate the exact expression. It gives exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Various methods have been presented for the implementation of ELD. Numerical tests of the ELD approach in the Wigner or Husimi phase space have been made for a harmonic oscillator and two strongly anharmonic model problems, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. It suggests ELD can be a potentially useful approach for describing quantum effects for complex systems in condense phase.

Wigner phase space distribution via classical adiabatic switching

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

Bose, Amartya; Makri, Nancy; Department of Physics, University of Illinois, 1110 W. Green Street, Urbana, Illinois 61801

2015-09-21

Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if themore » perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations.« less

Geometric diffusion of quantum trajectories

PubMed Central

Yang, Fan; Liu, Ren-Bao

2015-01-01

A quantum object can acquire a geometric phase (such as Berry phases and Aharonov–Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects. PMID:26178745

Terminal Transient Phase of Chaotic Transients

NASA Astrophysics Data System (ADS)

Lilienkamp, Thomas; Parlitz, Ulrich

2018-03-01

Transient chaos in spatially extended systems can be characterized by the length of the transient phase, which typically grows quickly with the system size (supertransients). For a large class of these systems, the chaotic phase terminates abruptly, without any obvious precursors in commonly used observables. Here we investigate transient spatiotemporal chaos in two different models of this class. By probing the state space using perturbed trajectories we show the existence of a "terminal transient phase," which occurs prior to the abrupt collapse of chaotic dynamics. During this phase the impact of perturbations is significantly different from the earlier transient and particular patterns of (non)susceptible regions in state space occur close to the chaotic trajectories. We therefore hypothesize that even without perturbations proper precursors for the collapse of chaotic transients exist, which might be highly relevant for coping with spatiotemporal chaos in cardiac arrhythmias or brain functionality, for example.

Trajectory optimization for A S.S.T.O. using in-flight LOX collection

NASA Astrophysics Data System (ADS)

Saint-Mard, M.; Hendrick, P.

A key point for a space mission (launch of a satellite, earth observation,…) is the optimization of the vehicle trajectory in order to burn the smallest quantity of propelant and then maximize the payload. This is true for evay space vehicle, but especially it is a crucial point for a Single-Stage-To-Orbit (SSTO) where the choice of a bad trajectory can result in an unrealizable vehicle due to the large airbreathing part of the flight In this study, we discuss the trajectory optimization for a Vertical Take-Off and Horizontal Landing (VTOHL) SSTO using supersonic in-flight atmospheric oxygen collection during a cruise phase (constant speed & constant altitude). This collected oxygen is stored in the LOX tanks and reused in the final rocket phase. This SSTO bas a Blended Body aerodynamic configuration as the one chosen by Lockheed Martin for its new space launcher (VentureStar and X-33). This SSTO uses rocket engines from take-off to Mach 1.7 and also for the exoatmospheric flight phase (that means for an altitude higher than 30km and a Mach number evolution from 6.8 to about 20). Between these two rocket phases, the SSTO is propelled by a subsonic ramjet. To perform this study, we use 2 computer programs (running on a home Computer): the first one allows to estimate the SSTO performances (TOGW, dry weight, hydrogen and oxygen consumptions) for a fixed payload mass and the second one permits the evaluation of the payload mass for a fixed TOGW.

Mean-trajectory approximation for electronic and vibrational-electronic nonlinear spectroscopy

NASA Astrophysics Data System (ADS)

Loring, Roger F.

2017-04-01

Mean-trajectory approximations permit the calculation of nonlinear vibrational spectra from semiclassically quantized trajectories on a single electronically adiabatic potential surface. By describing electronic degrees of freedom with classical phase-space variables and subjecting these to semiclassical quantization, mean-trajectory approximations may be extended to compute both nonlinear electronic spectra and vibrational-electronic spectra. A general mean-trajectory approximation for both electronic and nuclear degrees of freedom is presented, and the results for purely electronic and for vibrational-electronic four-wave mixing experiments are quantitatively assessed for harmonic surfaces with linear electronic-nuclear coupling.

Asymptotically stable phase synchronization revealed by autoregressive circle maps

NASA Astrophysics Data System (ADS)

Drepper, F. R.

2000-11-01

A specially designed of nonlinear time series analysis is introduced based on phases, which are defined as polar angles in spaces spanned by a finite number of delayed coordinates. A canonical choice of the polar axis and a related implicit estimation scheme for the potentially underlying autoregressive circle map (next phase map) guarantee the invertibility of reconstructed phase space trajectories to the original coordinates. The resulting Fourier approximated, invertibility enforcing phase space map allows us to detect conditional asymptotic stability of coupled phases. This comparatively general synchronization criterion unites two existing generalizations of the old concept and can successfully be applied, e.g., to phases obtained from electrocardiogram and airflow recordings characterizing cardiorespiratory interaction.

Hamiltonian flow over saddles for exploring molecular phase space structures

NASA Astrophysics Data System (ADS)

Farantos, Stavros C.

2018-03-01

Despite using potential energy surfaces, multivariable functions on molecular configuration space, to comprehend chemical dynamics for decades, the real happenings in molecules occur in phase space, in which the states of a classical dynamical system are completely determined by the coordinates and their conjugate momenta. Theoretical and numerical results are presented, employing alanine dipeptide as a model system, to support the view that geometrical structures in phase space dictate the dynamics of molecules, the fingerprints of which are traced by following the Hamiltonian flow above saddles. By properly selecting initial conditions in alanine dipeptide, we have found internally free rotor trajectories the existence of which can only be justified in a phase space perspective. This article is part of the theme issue `Modern theoretical chemistry'.

Mapping quantum-classical Liouville equation: projectors and trajectories.

PubMed

Kelly, Aaron; van Zon, Ramses; Schofield, Jeremy; Kapral, Raymond

2012-02-28

The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining projection operators onto the mapping states corresponding to the physical quantum states, it is shown that the mapping quantum-classical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectory-based solution of this equation can be constructed that requires the simulation of an ensemble of entangled trajectories. An approximation to this evolution equation which retains only the Poisson bracket contribution to the evolution operator does admit a solution in an ensemble of independent trajectories but it is shown that this operator does not commute with the projection operators and the dynamics may take the system outside the physical space. The dynamical instabilities, utility, and domain of validity of this approximate dynamics are discussed. The effects are illustrated by simulations on several quantum systems.

Self-adaptive enhanced sampling in the energy and trajectory spaces: accelerated thermodynamics and kinetic calculations.

PubMed

Gao, Yi Qin

2008-04-07

Here, we introduce a simple self-adaptive computational method to enhance the sampling in energy, configuration, and trajectory spaces. The method makes use of two strategies. It first uses a non-Boltzmann distribution method to enhance the sampling in the phase space, in particular, in the configuration space. The application of this method leads to a broad energy distribution in a large energy range and a quickly converged sampling of molecular configurations. In the second stage of simulations, the configuration space of the system is divided into a number of small regions according to preselected collective coordinates. An enhanced sampling of reactive transition paths is then performed in a self-adaptive fashion to accelerate kinetics calculations.

Leaking in history space: A way to analyze systems subjected to arbitrary driving

NASA Astrophysics Data System (ADS)

Kaszás, Bálint; Feudel, Ulrike; Tél, Tamás

2018-03-01

Our aim is to unfold phase space structures underlying systems with a drift in their parameters. Such systems are non-autonomous and belong to the class of non-periodically driven systems where the traditional theory of chaos (based e.g., on periodic orbits) does not hold. We demonstrate that even such systems possess an underlying topological horseshoe-like structure at least for a finite period of time. This result is based on a specifically developed method which allows to compute the corresponding time-dependent stable and unstable foliations. These structures can be made visible by prescribing a certain type of history for an ensemble of trajectories in phase space and by analyzing the trajectories fulfilling this constraint. The process can be considered as a leaking in history space—a generalization of traditional leaking, a method that has become widespread in traditional chaotic systems, to leaks depending on time.

Fractional dynamics using an ensemble of classical trajectories

NASA Astrophysics Data System (ADS)

Sun, Zhaopeng; Dong, Hao; Zheng, Yujun

2018-01-01

A trajectory-based formulation for fractional dynamics is presented and the trajectories are generated deterministically. In this theoretical framework, we derive a new class of estimators in terms of confluent hypergeometric function (F11) to represent the Riesz fractional derivative. Using this method, the simulation of free and confined Lévy flight are in excellent agreement with the exact numerical and analytical results. In addition, the barrier crossing in a bistable potential driven by Lévy noise of index α is investigated. In phase space, the behavior of trajectories reveal the feature of Lévy flight in a better perspective.

Semiclassical propagator of the Wigner function.

PubMed

Dittrich, Thomas; Viviescas, Carlos; Sandoval, Luis

2006-02-24

Propagation of the Wigner function is studied on two levels of semiclassical propagation: one based on the Van Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator take the form of a time-dependent quantum spot. Its oscillatory structure depends on whether the underlying classical flow is elliptic or hyperbolic. It can be interpreted as the result of interference of a pair of classical trajectories, indicating how quantum coherences are to be propagated semiclassically in phase space. The phase-space path-integral approach allows for a finer resolution of the quantum spot in terms of Airy functions.

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone

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

Mauguière, Frédéric A. L., E-mail: frederic.mauguiere@bristol.ac.uk; Collins, Peter, E-mail: peter.collins@bristol.ac.uk; Wiggins, Stephen, E-mail: stephen.wiggins@mac.com

We examine the phase space structures that govern reaction dynamics in the absence of critical points on the potential energy surface. We show that in the vicinity of hyperbolic invariant tori, it is possible to define phase space dividing surfaces that are analogous to the dividing surfaces governing transition from reactants to products near a critical point of the potential energy surface. We investigate the problem of capture of an atom by a diatomic molecule and show that a normally hyperbolic invariant manifold exists at large atom-diatom distances, away from any critical points on the potential. This normally hyperbolic invariantmore » manifold is the anchor for the construction of a dividing surface in phase space, which defines the outer or loose transition state governing capture dynamics. We present an algorithm for sampling an approximate capture dividing surface, and apply our methods to the recombination of the ozone molecule. We treat both 2 and 3 degrees of freedom models with zero total angular momentum. We have located the normally hyperbolic invariant manifold from which the orbiting (outer) transition state is constructed. This forms the basis for our analysis of trajectories for ozone in general, but with particular emphasis on the roaming trajectories.« less

Toward understanding the roaming mechanism in H + MgH → Mg + HH reaction

DOE PAGES

Mauguiere, Frederic A. L.; Collins, Peter; Stamatiadis, Stamatis; ...

2016-02-26

The roaming mechanism in the reaction H + MgH →Mg + HH is investigated by classical and quantum dynamics employing an accurate ab initio threedimensional ground electronic state potential energy surface. The reaction dynamics are explored by running trajectories initialized on a four-dimensional dividing surface anchored on three-dimensional normally hyperbolic invariant manifold associated with a family of unstable orbiting periodic orbits in the entrance channel of the reaction (H + MgH). By locating periodic orbits localized in the HMgH well or involving H orbiting around the MgH diatom, and following their continuation with the total energy, regions in phase spacemore » where reactive or nonreactive trajectories may be trapped are found. In this way roaming reaction pathways are deduced in phase space. Patterns similar to periodic orbits projected into configuration space are found for the quantum bound and resonance eigenstates. Roaming is attributed to the capture of the trajectories in the neighborhood of certain periodic orbits. As a result, the complex forming trajectories in the HMgH well can either return to the radical channel or “roam” to the MgHH minimum from where the molecule may react.« less

Automated Design of Multiphase Space Missions Using Hybrid Optimal Control

ERIC Educational Resources Information Center

Chilan, Christian Miguel

2009-01-01

A modern space mission is assembled from multiple phases or events such as impulsive maneuvers, coast arcs, thrust arcs and planetary flybys. Traditionally, a mission planner would resort to intuition and experience to develop a sequence of events for the multiphase mission and to find the space trajectory that minimizes propellant use by solving…

Quasi-Airy beams along tunable propagation trajectories and directions.

PubMed

Qian, Yixian; Zhang, Site

2016-05-02

We present a theoretical and experimental exhibit that accelerates quasi-Airy beams propagating along arbitrarily appointed parabolic trajectories and directions in free space. We also demonstrate that such quasi-Airy beams can be generated by a tunable phase pattern, where two disturbance factors are introduced. The topological structures of quasi-Airy beams are readily manipulated with tunable phase patterns. Quasi-Airy beams still possess the characteristics of non-diffraction, self-healing to some extent, although they are not the solutions for paraxial wave equation. The experiments show the results are consistent with theoretical predictions. It is believed that the property of propagation along arbitrarily desired parabolic trajectories will provide a broad application in trapping atom and living cell manipulation.

Effects of reactant rotational excitation on H + O2--> OH + O reaction rate constant: quantum wave packet, quasi-classical trajectory and phase space theory calculations.

PubMed

Lin, Shi Ying; Guo, Hua; Lendvay, György; Xie, Daiqian

2009-06-21

We examine the impact of initial rotational excitation on the reactivity of the H + O(2)--> OH + O reaction. Accurate Chebyshev wave packet calculations have been carried out for the upsilon(i) = 0, j(i) = 9 initial state of O(2) and the J = 50 partial wave. In addition, we present Gaussian-weighted quasi-classical trajectory and phase space theory calculations of the integral cross section and thermal rate constant for the title reaction. These theoretical results suggest that the initial rotational excitation significantly enhances reactivity with an amount comparable to the effect of initial vibrational state excitation. The inclusion of internally excited reactants is shown to improve the agreement with experimental rate constant.

Flight Dynamics Operations: Methods and Lessons Learned from Space Shuttle Orbit Operations

NASA Technical Reports Server (NTRS)

Cutri-Kohart, Rebecca M.

2011-01-01

The Flight Dynamics Officer is responsible for trajectory maintenance of the Space Shuttle. This paper will cover high level operational considerations, methodology, procedures, and lessons learned involved in performing the functions of orbit and rendezvous Flight Dynamics Officer and leading the team of flight dynamics specialists during different phases of flight. The primary functions that will be address are: onboard state vector maintenance, ground ephemeris maintenance, calculation of ground and spacecraft acquisitions, collision avoidance, burn targeting for the primary mission, rendezvous, deorbit and contingencies, separation sequences, emergency deorbit preparation, mass properties coordination, payload deployment planning, coordination with the International Space Station, and coordination with worldwide trajectory customers. Each of these tasks require the Flight Dynamics Officer to have cognizance of the current trajectory state as well as the impact of future events on the trajectory plan in order to properly analyze and react to real-time changes. Additionally, considerations are made to prepare flexible alternative trajectory plans in the case timeline changes or a systems failure impact the primary plan. The evolution of the methodology, procedures, and techniques used by the Flight Dynamics Officer to perform these tasks will be discussed. Particular attention will be given to how specific Space Shuttle mission and training simulation experiences, particularly off-nominal or unexpected events such as shortened mission durations, tank failures, contingency deorbit, navigation errors, conjunctions, and unexpected payload deployments, have influenced the operational procedures and training for performing Space Shuttle flight dynamics operations over the history of the program. These lessons learned can then be extended to future vehicle trajectory operations.

Methodology and Results of the Near-Earth Object (NEO) Human Space Flight (HSF) Accessible Targets Study (NHATS)

NASA Technical Reports Server (NTRS)

Barbee, Brent; Mink, Ronald; Adamo, Daniel

2011-01-01

Near-Earth Asteroids (NEAs) have been identified by the current administration as potential destinations for human explorers during the mid-2020s. While the close proximity of these objects' orbits to Earth's orbit creates a risk of highly damaging or catastrophic impacts, it also makes some of these objects particularly accessible to spacecraft departing Earth, and this presents unique opportunities for solar system science and humanity's first ventures beyond cislunar space. Planning such ambitious missions first requires the selection of potentially accessible targets from the growing population of nearly 7,800 NEAs. To accomplish this, NASA is conducting the Near-Earth Object (NEO) Human Space Flight (HSF) Accessible Targets Study (NHATS). Phase I of the NHATS was executed during September of 2010, and Phase II was completed by early March of 2011. The study is ongoing because previously undetected NEAs are being discovered constantly, which has motivated an effort to automate the analysis algorithms in order to provide continuous monitoring of NEA accessibility. The NHATS analysis process consists of a trajectory filter and a minimum maximum estimated size criterion. The trajectory filter employs the method of embedded trajectory grids to compute all possible ballistic round-trip mission trajectories to every NEA in the Jet Propulsion Laboratory (JPL) Small-Body Database (SBDB) and stores all solutions that satisfy the trajectory filter criteria. An NEA must offer at least one qualifying trajectory solution to pass the trajectory filter. The Phase II NHATS filter criteria were purposely chosen to be highly inclusive, requiring Earth departure date between January 1st, 2015 and December 31st, 2040, total round-trip flight time <= 450 days, stay time at the NEA >= 8 days, Earth departure C(sub 3) energy <= 60 km(exp 2)/s(exp 2), total mission delta-v <= 12 km/s (including an Earth departure maneuver from a 400 km altitude circular parking orbit), and a maximum atmospheric re-entry speed of 12 km/s. After determining which NEAs offer at least one trajectory solution meeting the criteria, the estimated size constraint is then imposed whereby those NEAs may only be considered NHATS- qualifying NEAs if their maximum estimated size is >= 30 m. This corresponds to an absolute magnitude H <= 26.5 with an assumed albedo p = 0:05. The following is a brief high-level summary of the Phase II study results. Of the 7,665 NEAs in the SBDB as of February 3rd, 2011, 765 NEAs passed the trajectory filter and yielded a total of 79,157,604 trajectory solutions. The trajectory solutions for each NEA are post-processed into Pork Chop Contour (PCC) plots which show total mission delta-v as a function of Earth departure date and total mission duration. Although the PCC plots necessarily compress a very multi-dimensional design space into a two-dimensional plot, they permit rapid assessment of the breadth and quality of an NEA's available Earth departure season and clearly indicate the regions of the trajectory design space which warrant further analysis and optimization. The PCC plot for the NEA with the greatest number of NHATS-qualifying trajectory solutions, 2000 SG-344, is shown. Of the 765 NEAs which passed the Phase II trajectory filter, a total of 590 NEAs also satisfied the further constraint of maximum estimated size >= 30 m. The distributions of osculating heliocentric orbital semi-major axis (a), eccentricity (e), and inclination (i), for those 590 NEAs are shown. Note that the semi-latus rectum used is equal to alpha (1-e(exp 2)). To further our understanding of round-trip trajectory accessibility dynamics, it is instructive to examine the distribution of the NHATS-Qualifying NEAs according to orbit classification. NEAs are grouped into four orbit families: Atiras (aphelion < 0.983 AU), Atens (aphelion > 0.983 AU, alpha < 1.0 AU), Apollos (perihelion < 1.017 AU, alpha > 1.0 AU), and Amors (1.017 < perihelion < 1.3 AU). Of the 765 NEAhich satisfied the NHATS trajectory criteria, none are Atiras, 193 are Atens (31% of known Atens), 456 are Apollos (11% of known Apollos), and 116 are Amors (4% of known Amors). While Apollos comprise 60% of the NEAs which pass the NHATS trajectory filter and Atens comprise only 25%, the percentages according to orbit family are perhaps more relevant. Note that only 11% of known Apollos passed the trajectory filter while 31% of known Atens passed. These simple statistics alone strongly suggest that Aten orbits possess features which tend to enhance their round-trip trajectory accessibility as compared to Apollos or Amors. This is significant because Atens' orbits cause them to spend considerable time in Earth's daytime sky, making them difficult to discover and track using ground-based observing assets. In this paper we will detail the NHATS analysis algorithms, present and analyze all NHATS results to date, and discuss aspects of HSF mission architecture design for future NEA missions.

Phase space analysis for a scalar-tensor model with kinetic and Gauss-Bonnet couplings

NASA Astrophysics Data System (ADS)

Granda, L. N.; Loaiza, E.

2016-09-01

We study the phase space for a scalar-tensor string inspired model of dark energy with nonminimal kinetic and Gauss-Bonnet couplings. The form of the scalar potential and of the coupling terms is of the exponential type, which gives rise to appealing cosmological solutions. The critical points describe a variety of cosmological scenarios that go from a matter or radiation dominated universe to a dark energy dominated universe. Trajectories were found in the phase space departing from unstable or saddle fixed points and arriving at the stable scalar field dominated point corresponding to late-time accelerated expansion.

Comparison of centric and reverse-centric trajectories for highly accelerated three-dimensional saturation recovery cardiac perfusion imaging.

PubMed

Wang, Haonan; Bangerter, Neal K; Park, Daniel J; Adluru, Ganesh; Kholmovski, Eugene G; Xu, Jian; DiBella, Edward

2015-10-01

Highly undersampled three-dimensional (3D) saturation-recovery sequences are affected by k-space trajectory since the magnetization does not reach steady state during the acquisition and the slab excitation profile yields different flip angles in different slices. This study compares centric and reverse-centric 3D cardiac perfusion imaging. An undersampled (98 phase encodes) 3D ECG-gated saturation-recovery sequence that alternates centric and reverse-centric acquisitions each time frame was used to image phantoms and in vivo subjects. Flip angle variation across the slices was measured, and contrast with each trajectory was analyzed via Bloch simulation. Significant variations in flip angle were observed across slices, leading to larger signal variation across slices for the centric acquisition. In simulation, severe transient artifacts were observed when using the centric trajectory with higher flip angles, placing practical limits on the maximum flip angle used. The reverse-centric trajectory provided less contrast, but was more robust to flip angle variations. Both of the k-space trajectories can provide reasonable image quality. The centric trajectory can have higher CNR, but is more sensitive to flip angle variation. The reverse-centric trajectory is more robust to flip angle variation. © 2014 Wiley Periodicals, Inc.

Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems

NASA Astrophysics Data System (ADS)

Tobasco, Ian; Goluskin, David; Doering, Charles R.

2018-02-01

For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper bounds on time averages can be proved a priori using auxiliary functions, the optimal choice of which is a convex optimization problem. We prove that the problems of finding maximal trajectories and minimal auxiliary functions are strongly dual. Thus, auxiliary functions provide arbitrarily sharp upper bounds on time averages. Moreover, any nearly minimal auxiliary function provides phase space volumes in which all nearly maximal trajectories are guaranteed to lie. For polynomial equations, auxiliary functions can be constructed by semidefinite programming, which we illustrate using the Lorenz system.

Phase-Space Approach to the Tunnel Effect: A New Semiclassical Traversal Time

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

Xavier, A.L. Jr.; de Aguiar, M.A.

1997-11-01

We determine the semiclassical coherent-state propagator for a particle going through one-dimensional evolution in a simple barrier potential. The described semiclassical method makes use of complex trajectories which, by its turn, enables the definition of (real) traversal times in the complexified phase space. We then discuss the behavior of this time for a wave packet whose average energy is below the barrier height. {copyright} {ital 1997} {ital The American Physical Society}

Cooperative control of two active spacecraft during proximity operations. M.S. Thesis - MIT

NASA Technical Reports Server (NTRS)

Polutchko, Robert J.

1989-01-01

A cooperative autopilot is developed for the control of the relative attitude, relative position and absolute attitude of two maneuvering spacecraft during on orbit proximity operations. The autopilot consists of an open-loop trajectory solver which computes a nine dimensional linearized nominal state trajectory at the beginning of each maneuver and a phase space regulator which maintains the two spacecraft on the nominal trajectory during coast phases of the maneuver. A linear programming algorithm is used to perform jet selection. Simulation tests using a system of two space shuttle vehicles are performed to verify the performance of the cooperative controller and comparisons are made to a traditional passive target/active pursuit vehicle approach to proximity operations. The cooperative autopilot is shown to be able to control the two vehicle system when both the would be pursuit vehicle and the target vehicle are not completely controllable in six degrees of freedom. The cooperative controller is also shown to use as much as 37 percent less fuel and 57 percent fewer jet firings than a single pursuit vehicle during a simple docking approach maneuver.

Near Earth Asteroid Rendezvous (NEAR) Revised Eros Orbit Phase Trajectory Design

NASA Technical Reports Server (NTRS)

Helfrich, J; Miller, J. K.; Antreasian, P. G.; Carranza, E.; Williams, B. G.; Dunham, D. W.; Farquhar, R. W.; McAdams, J. V.

1999-01-01

Trajectory design of the orbit phase of the NEAR mission involves a new process that departs significantly from those procedures used in previous missions. In most cases, a precise spacecraft ephemeris is designed well in advance of arrival at the target body. For NEAR, the uncertainty in the dynamic environment around Eros does not allow the luxury of a precise spacecraft trajectory to be defined in advance. The principal cause of this uncertainty is the limited knowledge oi' the gravity field a,-id rotational state of Eros. As a result, the concept for the NEAR trajectory design is to define a number of rules for satisfying spacecraft, mission, and science constraints, and then apply these rules to various assumptions for the model of Eros. Nominal, high, and low Eros mass models are used for testing the trajectory design strategy and to bracket the ranges of parameter variations that are expected upon arrival at the asteroid. The final design is completed after arrival at Eros and determination of the actual gravity field and rotational state. As a result of the unplanned termination of the deep space rendezvous maneuver on December 20, 1998, the NEAR spacecraft passed within 3830 km of Eros on December 23, 1998. This flyby provided a brief glimpse of Eros, and allowed for a more accurate model of the rotational parameters and gravity field uncertainty. Furthermore, after the termination of the deep space rendezvous burn, contact with the spacecraft was lost and the NEAR spacecraft lost attitude control. During the subsequent gyrations of the spacecraft, hydrazine thruster firings were used to regain attitude control. This unplanned thruster activity used Much of the fuel margin allocated for the orbit phase. Consequently, minimizing fuel consumption is now even more important.

Space tug geosynchronous mission simulation

NASA Technical Reports Server (NTRS)

Lang, T. J.

1973-01-01

Near-optimal three dimensional trajectories from a low earth park orbit inclined at 28.5 deg to a synchronous-equatorial mission orbit were developed for both the storable (thrust = 28,912 N (6,500 lbs), I sub sp = 339 sec) and cryogenic (thrust = 44,480 N (10,000 lbs), I sub sp = 470 sec) space tug using the iterative cost function minimization technique contained within the modularized vehicle simulation (MVS) program. The finite burn times, due to low thrust-to-weight ratios, and the associated gravity losses are accounted for in the trajectory simulation and optimization. The use of an ascent phasing orbit to achieve burnout in synchronous orbit at any longitude is investigated. The ascent phasing orbit is found to offer the additional advantage of significantly reducing the overall delta velocity by splitting the low altitude burn into two parts and thereby reducing gravity losses.

Lagrangian descriptors in dissipative systems.

PubMed

Junginger, Andrej; Hernandez, Rigoberto

2016-11-09

The reaction dynamics of time-dependent systems can be resolved through a recrossing-free dividing surface associated with the transition state trajectory-that is, the unique trajectory which is bound to the barrier region for all time in response to a given time-dependent potential. A general procedure based on the minimization of Lagrangian descriptors has recently been developed by Craven and Hernandez [Phys. Rev. Lett., 2015, 115, 148301] to construct this particular trajectory without requiring perturbative expansions relative to the naive transition state point at the top of the barrier. The extension of the method to account for dissipation in the equations of motion requires additional considerations established in this paper because the calculation of the Lagrangian descriptor involves the integration of trajectories in forward and backward time. The two contributions are in general very different because the friction term can act as a source (in backward time) or sink (in forward time) of energy, leading to the possibility that information about the phase space structure may be lost due to the dominance of only one of the terms. To compensate for this effect, we introduce a weighting scheme within the Lagrangian descriptor and demonstrate that for thermal Langevin dynamics it preserves the essential phase space structures, while they are lost in the nonweighted case.

Classical versus quantum dynamical chaos: Sensitivity to external perturbations, stability and reversibility

NASA Astrophysics Data System (ADS)

Sokolov, Valentin V.; Zhirov, Oleg V.; Kharkov, Yaroslav A.

The extraordinary complexity of classical trajectories of typical nonlinear systems that manifest stochastic behavior is intimately connected with exponential sensitivity to small variations of initial conditions and/or weak external perturbations. In rigorous terms, such classical systems are characterized by positive algorithmic complexity described by the Lyapunov exponent or, alternatively, by the Kolmogorov-Sinai entropy. The said implies that, in spite of the fact that, formally, any however complex trajectory of a perfectly isolated (closed) system is unique and differentiable for any certain initial conditions and the motion is perfectly reversible, it is impractical to treat that sort of classical systems as closed ones. Inevitably, arbitrary weak influence of an environment crucially impacts the dynamics. This influence, that can be considered as a noise, rapidly effaces the memory of initial conditions and turns the motion into an irreversible random process. In striking contrast, the quantum mechanics of the classically chaotic systems exhibit much weaker sensitivity and strong memory of the initial state. Qualitatively, this crucial difference could be expected in view of a much simpler structure of quantum states as compared to the extraordinary complexity of random and unpredictable classical trajectories. However the very notion of trajectories is absent in quantum mechanics so that the concept of exponential instability seems to be irrelevant in this case. The problem of a quantitative measure of complexity of a quantum state of motion, that is a very important and nontrivial issue of the theory of quantum dynamical chaos, is the one of our concern. With such a measure in hand, we quantitatively analyze the stability and reversibility of quantum dynamics in the presence of external noise. To solve this problem we point out that individual classical trajectories are of minor interest if the motion is chaotic. Properties of all of them are alike in this case and rather the behavior of their manifolds carries really valuable information. Therefore the phase-space methods and, correspondingly, the Liouville form of the classical mechanics become the most adequate. It is very important that, opposite to the classical trajectories, the classical phase space distribution and the Liouville equation have direct quantum analogs. Hence, the analogy and difference of classical and quantum dynamics can be traced by comparing the classical (W(c)(I,θ;t)) and quantum (Wigner function W(I,θ;t)) phase space distributions both expressed in identical phase-space variables but ruled by different(!) linear equations. The paramount property of the classical dynamical chaos is the exponentially fast structuring of the system's phase space on finer and finer scales. On the contrary, degree of structuring of the corresponding Wigner function is restricted by the quantization of the phase space. This makes Wigner function more coarse and relatively "simple" as compared to its classical counterpart. Fourier analysis affords quite suitable ground for analyzing complexity of a phase space distribution, that is equally valid in classical and quantum cases. We demonstrate that the typical number of Fourier harmonics is indeed a relevant measure of complexity of states of motion in both classical as well as quantum cases. This allowed us to investigate in detail and introduce a quantitative measure of sensitivity to an external noisy environment and formulate the conditions under which the quantum motion remains reversible. It turns out that while the mean number of harmonics of the classical phase-space distribution of a non-integrable system grows with time exponentially during the whole time of the motion, the time of exponential upgrowth of this number in the case of the corresponding quantum Wigner function is restricted only to the Ehrenfest interval 0 < t < tE - just the interval within which the Wigner function still satisfies the classical Liouville equation. We showed that the number of harmonics increases beyond this interval algebraically. This fact gains a crucial importance when the Ehrenfest time is so short that the exponential regime has no time to show up. Under this condition the quantum motion turns out to be quite stable and reversible.

Space-time thermodynamics of the glass transition

NASA Astrophysics Data System (ADS)

Merolle, Mauro; Garrahan, Juan P.; Chandler, David

2005-08-01

We consider the probability distribution for fluctuations in dynamical action and similar quantities related to dynamic heterogeneity. We argue that the so-called “glass transition” is a manifestation of low action tails in these distributions where the entropy of trajectory space is subextensive in time. These low action tails are a consequence of dynamic heterogeneity and an indication of phase coexistence in trajectory space. The glass transition, where the system falls out of equilibrium, is then an order-disorder phenomenon in space-time occurring at a temperature Tg, which is a weak function of measurement time. We illustrate our perspective ideas with facilitated lattice models and note how these ideas apply more generally. Author contributions: M.M., J.P.G., and D.C. performed research and wrote the paper.

Crossing the dividing surface of transition state theory. IV. Dynamical regularity and dimensionality reduction as key features of reactive trajectories

NASA Astrophysics Data System (ADS)

Lorquet, J. C.

2017-04-01

The atom-diatom interaction is studied by classical mechanics using Jacobi coordinates (R, r, θ). Reactivity criteria that go beyond the simple requirement of transition state theory (i.e., PR* > 0) are derived in terms of specific initial conditions. Trajectories that exactly fulfill these conditions cross the conventional dividing surface used in transition state theory (i.e., the plane in configuration space passing through a saddle point of the potential energy surface and perpendicular to the reaction coordinate) only once. Furthermore, they are observed to be strikingly similar and to form a tightly packed bundle of perfectly collimated trajectories in the two-dimensional (R, r) configuration space, although their angular motion is highly specific for each one. Particular attention is paid to symmetrical transition states (i.e., either collinear or T-shaped with C2v symmetry) for which decoupling between angular and radial coordinates is observed, as a result of selection rules that reduce to zero Coriolis couplings between modes that belong to different irreducible representations. Liapunov exponents are equal to zero and Hamilton's characteristic function is planar in that part of configuration space that is visited by reactive trajectories. Detailed consideration is given to the concept of average reactive trajectory, which starts right from the saddle point and which is shown to be free of curvature-induced Coriolis coupling. The reaction path Hamiltonian model, together with a symmetry-based separation of the angular degree of freedom, provides an appropriate framework that leads to the formulation of an effective two-dimensional Hamiltonian. The success of the adiabatic approximation in this model is due to the symmetry of the transition state, not to a separation of time scales. Adjacent trajectories, i.e., those that do not exactly fulfill the reactivity conditions have similar characteristics, but the quality of the approximation is lower. At higher energies, these characteristics persist, but to a lesser degree. Recrossings of the dividing surface then become much more frequent and the phase space volumes of initial conditions that generate recrossing-free trajectories decrease. Altogether, one ends up with an additional illustration of the concept of reactive cylinder (or conduit) in phase space that reactive trajectories must follow. Reactivity is associated with dynamical regularity and dimensionality reduction, whatever the shape of the potential energy surface, no matter how strong its anharmonicity, and whatever the curvature of its reaction path. Both simplifying features persist during the entire reactive process, up to complete separation of fragments. The ergodicity assumption commonly assumed in statistical theories is inappropriate for reactive trajectories.

Positional control of space robot manipulator

NASA Astrophysics Data System (ADS)

Kurochkin, Vladislav; Shymanchuk, Dzmitry

2018-05-01

In this article the mathematical model of a planar space robot manipulator is under study. The space robot manipulator represents a solid body with attached manipulators. The system of equations of motion is determined using the Lagrange's equations. The control problem concerning moving the robot to a given point and return it to a given trajectory in the phase space is solved. Changes of generalized coordinates and necessary control actions are plotted for a specific model.

Measurement of the Shear Lift Force on a Bubble in a Channel Flow

NASA Technical Reports Server (NTRS)

Nahra, Henry K.; Motil, Brian; Skor, Mark

2005-01-01

Two-phase flow systems play vital roles in the design of some current and anticipated space applications of two-phase systems which include: thermal management systems, transfer line flow in cryogenic storage, space nuclear power facilities, design and operation of thermal bus, life support systems, propulsion systems, In Situ Resource Utilization (ISRU), and space processes for pharmaceutical applications. The design of two-phase flow systems for space applications requires a clear knowledge of the behaviors of the dispersed phase (bubble), its interaction with the continuous phase (liquid) and its effect on heat and mass transfer processes, The need to understand the bubble generation process arises from the fact that for all space applications, the size and distribution of bubbles are extremely crucial for heat and mass transfer control. One important force in two-phase flow systems is the lift force on a bubble or particle in a liquid shear flow. The shear lift is usually overwhelmed by buoyancy in normal gravity, but it becomes an important force in reduced gravity. Since the liquid flow is usually sheared because of the confining wall, the trajectories of bubbles and particles injected into the liquid flow are affected by the shear lift in reduced gravity. A series of experiments are performed to investigate the lift force on a bubble in a liquid shear flow and its effect on the detachment of a bubble from a wall under low gravity conditions. Experiments are executed in a Poiseuille flow in a channel. An air-water system is used in these experiments that are performed in the 2.2 second drop tower. A bubble is injected into the shear flow from a small injector and the shear lift is measured while the bubble is held stationary relative to the fluid. The trajectory of the bubble prior, during and after its detachment from the injector is investigated. The measured shear lift force is calculated from the trajectory of the bubble at the detachment point. These values for the shear lift are then compared with the theoretical predictions from various published works on shear lift in the open literature, which include asymptotic solutions at low bubble Reynolds number, potential flow predictions and numerical studies that deal with intermediate bubble Reynolds numbers.

An investigation into possible quantum chaos in the H2 molecule under intense laser fields via Ehrenfest phase space (EPS) trajectories.

PubMed

Sadhukhan, Mainak; Deb, B M

2018-06-21

By employing the Ehrenfest "phase space" trajectory method for studying quantum chaos, developed in our laboratory, the present study reveals that the H 2 molecule under intense laser fields of three different intensities, I = 1 × 10 14  W/cm 2 , 5 × 10 14  W/cm 2 , and 1 × 10 15  W/cm 2 , does not show quantum chaos. A similar conclusion is also reached through the Loschmidt echo (also called quantum fidelity) calculations reported here for the first time for a real molecule under intense laser fields. Thus, a long-standing conjecture about the possible existence of quantum chaos in atoms and molecules under intense laser fields has finally been tested and not found to be valid in the present case.

Stochastic algorithm for simulating gas transport coefficients

NASA Astrophysics Data System (ADS)

Rudyak, V. Ya.; Lezhnev, E. V.

2018-02-01

The aim of this paper is to create a molecular algorithm for modeling the transport processes in gases that will be more efficient than molecular dynamics method. To this end, the dynamics of molecules are modeled stochastically. In a rarefied gas, it is sufficient to consider the evolution of molecules only in the velocity space, whereas for a dense gas it is necessary to model the dynamics of molecules also in the physical space. Adequate integral characteristics of the studied system are obtained by averaging over a sufficiently large number of independent phase trajectories. The efficiency of the proposed algorithm was demonstrated by modeling the coefficients of self-diffusion and the viscosity of several gases. It was shown that the accuracy comparable to the experimental one can be obtained on a relatively small number of molecules. The modeling accuracy increases with the growth of used number of molecules and phase trajectories.

Astronaut Carl Meade mans pilots station during trajectory control exercise

NASA Image and Video Library

1994-09-12

STS064-22-024 (9-20 Sept. 1994) --- With a manual and lap top computer in front of him, astronaut Carl J. Meade, STS-64 mission specialist, supports operations with the Trajectory Control Sensor (TCS) aboard the Earth-orbiting space shuttle Discovery. For this exercise, Meade temporarily mans the pilot's station on the forward flight deck. The TCS is the work of a team of workers at NASA's Johnson Space Center. Data gathered during this flight was expected to prove valuable in designing and developing a sensor for use during the rendezvous and mating phases of orbiter missions to the space station. For this demonstration, the Shuttle Pointed Autonomous Research Tool for Astronomy 201 (SPARTAN 201) was used as the target vehicle during release and retrieval operations. Photo credit: NASA or National Aeronautics and Space Administration

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.

Quantum dynamics in phase space: Moyal trajectories 2

NASA Astrophysics Data System (ADS)

Braunss, G.

2013-01-01

Continuing a previous paper [G. Braunss, J. Phys. A: Math. Theor. 43, 025302 (2010), 10.1088/1751-8113/43/2/025302] where we had calculated ℏ2-approximations of quantum phase space viz. Moyal trajectories of examples with one and two degrees of freedom, we present in this paper the calculation of ℏ2-approximations for four examples: a two-dimensional Toda chain, the radially symmetric Schwarzschild field, and two examples with three degrees of freedom, the latter being the nonrelativistic spherically Coulomb potential and the relativistic cylinder symmetrical Coulomb potential with a magnetic field H. We show in particular that an ℏ2-approximation of the nonrelativistic Coulomb field has no singularity at the origin (r = 0) whereas the classical trajectories are singular at r = 0. In the third example, we show in particular that for an arbitrary function γ(H, z) the expression β ≡ pz + γ(H, z) is classically (ℏ = 0) a constant of motion, whereas for ℏ ≠ 0 this holds only if γ(H, z) is an arbitrary polynomial of second order in z. This statement is shown to extend correspondingly to a cylinder symmetrical Schwarzschild field with a magnetic field. We exhibit in detail a number of properties of the radially symmetric Schwarzschild field. We exhibit finally the problems of the nonintegrable Hénon-Heiles Hamiltonian and give a short review of the regular Hilbert space representation of Moyal operators.

Phase-space analysis of the Schwinger effect in inhomogeneous electromagnetic fields

NASA Astrophysics Data System (ADS)

Kohlfürst, Christian

2018-05-01

Schwinger pair production in spatially and temporally inhomogeneous electric and magnetic fields is studied. The focus is on the particle phase-space distribution within a high-intensity few-cycle pulse. Accurate numerical solutions of a quantum kinetic theory (DHW formalism) are presented in momentum space and, with the aid of coarse-graining techniques, in a mixed spatial-momentum representation. Additionally, signatures of the carrier-envelope phase as well as spin-field interactions are discussed on the basis of a trajectory-based model taking into account instantaneous pair production and relativistic single-particle dynamics. Although our simple semi-classical single-particle model cannot describe every aspect of the particle production process (quantum interferences), essential features such as spin-field interactions are captured.

Gradient waveform pre-emphasis based on the gradient system transfer function.

PubMed

Stich, Manuel; Wech, Tobias; Slawig, Anne; Ringler, Ralf; Dewdney, Andrew; Greiser, Andreas; Ruyters, Gudrun; Bley, Thorsten A; Köstler, Herbert

2018-02-25

The gradient system transfer function (GSTF) has been used to describe the distorted k-space trajectory for image reconstruction. The purpose of this work was to use the GSTF to determine the pre-emphasis for an undistorted gradient output and intended k-space trajectory. The GSTF of the MR system was determined using only standard MR hardware without special equipment such as field probes or a field camera. The GSTF was used for trajectory prediction in image reconstruction and for a gradient waveform pre-emphasis. As test sequences, a gradient-echo sequence with phase-encoding gradient modulation and a gradient-echo sequence with a spiral read-out trajectory were implemented and subsequently applied on a structural phantom and in vivo head measurements. Image artifacts were successfully suppressed by applying the GSTF-based pre-emphasis. Equivalent results are achieved with images acquired using GSTF-based post-correction of the trajectory as a part of image reconstruction. In contrast, the pre-emphasis approach allows reconstruction using the initially intended trajectory. The artifact suppression shown for two sequences demonstrates that the GSTF can serve for a novel pre-emphasis. A pre-emphasis based on the GSTF information can be applied to any arbitrary sequence type. © 2018 International Society for Magnetic Resonance in Medicine.

Use of automated rendezvous trajectory planning to improve spacecraft operations efficiency

NASA Technical Reports Server (NTRS)

Mulder, Tom A.

1991-01-01

The current planning process for space shuttle rendezvous with a second Earth-orbiting vehicle is time consuming and costly. It is a labor-intensive, manual process performed pre-mission with the aid of specialized maneuver processing tools. Real-time execution of a rendezvous plan must closely follow a predicted trajectory, and targeted solutions leading up to the terminal phase are computed on the ground. Despite over 25 years of Gemini, Apollo, Skylab, and shuttle vehicle-to-vehicle rendezvous missions flown to date, rendezvous in Earth orbit still requires careful monitoring and cannot be taken for granted. For example, a significant trajectory offset was experienced during terminal phase rendezvous of the STS-32 Long Duration Exposure Facility retrieval mission. Several improvements can be introduced to the present rendezvous planning process to reduce costs, produce more fuel-efficient profiles, and increase the probability of mission success.

On the importance of an accurate representation of the initial state of the system in classical dynamics simulations

NASA Astrophysics Data System (ADS)

García-Vela, A.

2000-05-01

A definition of a quantum-type phase-space distribution is proposed in order to represent the initial state of the system in a classical dynamics simulation. The central idea is to define an initial quantum phase-space state of the system as the direct product of the coordinate and momentum representations of the quantum initial state. The phase-space distribution is then obtained as the square modulus of this phase-space state. The resulting phase-space distribution closely resembles the quantum nature of the system initial state. The initial conditions are sampled with the distribution, using a grid technique in phase space. With this type of sampling the distribution of initial conditions reproduces more faithfully the shape of the original phase-space distribution. The method is applied to generate initial conditions describing the three-dimensional state of the Ar-HCl cluster prepared by ultraviolet excitation. The photodissociation dynamics is simulated by classical trajectories, and the results are compared with those of a wave packet calculation. The classical and quantum descriptions are found in good agreement for those dynamical events less subject to quantum effects. The classical result fails to reproduce the quantum mechanical one for the more strongly quantum features of the dynamics. The properties and applicability of the phase-space distribution and the sampling technique proposed are discussed.

Illustration of microphysical processes in Amazonian deep convective clouds in the gamma phase space: introduction and potential applications

NASA Astrophysics Data System (ADS)

Cecchini, Micael A.; Machado, Luiz A. T.; Wendisch, Manfred; Costa, Anja; Krämer, Martina; Andreae, Meinrat O.; Afchine, Armin; Albrecht, Rachel I.; Artaxo, Paulo; Borrmann, Stephan; Fütterer, Daniel; Klimach, Thomas; Mahnke, Christoph; Martin, Scot T.; Minikin, Andreas; Molleker, Sergej; Pardo, Lianet H.; Pöhlker, Christopher; Pöhlker, Mira L.; Pöschl, Ulrich; Rosenfeld, Daniel; Weinzierl, Bernadett

2017-12-01

The behavior of tropical clouds remains a major open scientific question, resulting in poor representation by models. One challenge is to realistically reproduce cloud droplet size distributions (DSDs) and their evolution over time and space. Many applications, not limited to models, use the gamma function to represent DSDs. However, even though the statistical characteristics of the gamma parameters have been widely studied, there is almost no study dedicated to understanding the phase space of this function and the associated physics. This phase space can be defined by the three parameters that define the DSD intercept, shape, and curvature. Gamma phase space may provide a common framework for parameterizations and intercomparisons. Here, we introduce the phase space approach and its characteristics, focusing on warm-phase microphysical cloud properties and the transition to the mixed-phase layer. We show that trajectories in this phase space can represent DSD evolution and can be related to growth processes. Condensational and collisional growth may be interpreted as pseudo-forces that induce displacements in opposite directions within the phase space. The actually observed movements in the phase space are a result of the combination of such pseudo-forces. Additionally, aerosol effects can be evaluated given their significant impact on DSDs. The DSDs associated with liquid droplets that favor cloud glaciation can be delimited in the phase space, which can help models to adequately predict the transition to the mixed phase. We also consider possible ways to constrain the DSD in two-moment bulk microphysics schemes, in which the relative dispersion parameter of the DSD can play a significant role. Overall, the gamma phase space approach can be an invaluable tool for studying cloud microphysical evolution and can be readily applied in many scenarios that rely on gamma DSDs.

Influence of control parameters on the joint tracking performance of a coaxial weld vision system

NASA Technical Reports Server (NTRS)

Gangl, K. J.; Weeks, J. L.

1985-01-01

The first phase of a series of evaluations of a vision-based welding control sensor for the Space Shuttle Main Engine Robotic Welding System is described. The robotic welding system is presently under development at the Marshall Space Flight Center. This evaluation determines the standard control response parameters necessary for proper trajectory of the welding torch along the joint.

Interplanetary Program to Optimize Simulated Trajectories (IPOST). Volume 2: Analytic manual

NASA Technical Reports Server (NTRS)

Hong, P. E.; Kent, P. D.; Olson, D. W.; Vallado, C. A.

1992-01-01

The Interplanetary Program to Optimize Space Trajectories (IPOST) is intended to support many analysis phases, from early interplanetary feasibility studies through spacecraft development and operations. The IPOST output provides information for sizing and understanding mission impacts related to propulsion, guidance, communications, sensor/actuators, payload, and other dynamic and geometric environments. IPOST models three degree of freedom trajectory events, such as launch/ascent, orbital coast, propulsive maneuvering (impulsive and finite burn), gravity assist, and atmospheric entry. Trajectory propagation is performed using a choice of Cowell, Encke, Multiconic, Onestep, or Conic methods. The user identifies a desired sequence of trajectory events, and selects which parameters are independent (controls) and dependent (targets), as well as other constraints and the cost function. Targeting and optimization is performed using the Stanford NPSOL algorithm. IPOST structure allows subproblems within a master optimization problem to aid in the general constrained parameter optimization solution. An alternate optimization method uses implicit simulation and collocation techniques.

Understanding transient uncoupling induced synchronization through modified dynamic coupling

NASA Astrophysics Data System (ADS)

Ghosh, Anupam; Godara, Prakhar; Chakraborty, Sagar

2018-05-01

An important aspect of the recently introduced transient uncoupling scheme is that it induces synchronization for large values of coupling strength at which the coupled chaotic systems resist synchronization when continuously coupled. However, why this is so is an open problem? To answer this question, we recall the conventional wisdom that the eigenvalues of the Jacobian of the transverse dynamics measure whether a trajectory at a phase point is locally contracting or diverging with respect to another nearby trajectory. Subsequently, we go on to highlight a lesser appreciated fact that even when, under the corresponding linearised flow, the nearby trajectory asymptotically diverges away, its distance from the reference trajectory may still be contracting for some intermediate period. We term this phenomenon transient decay in line with the phenomenon of the transient growth. Using these facts, we show that an optimal coupling region, i.e., a region of the phase space where coupling is on, should ideally be such that at any of the constituent phase point either the maximum of the real parts of the eigenvalues is negative or the magnitude of the positive maximum is lesser than that of the negative minimum. We also invent and employ a modified dynamics coupling scheme—a significant improvement over the well-known dynamic coupling scheme—as a decisive tool to justify our results.

Navigation and Guidance for Low-Thrust Trajectories, LOTNAV

NASA Astrophysics Data System (ADS)

Cano, J. L.; Bello, M.; Rodriguez-Canabal, J.

A number of interplanetary low-thrust missions have already been flown by many space agencies. Examples of already flown missions based on the use of electric propulsion are Deep Space 1, Hayabusa and SMART-1. Many others are already in the assessment phase or in the development phase itself. In such perspective, it is required by the space agencies the procurement and utilisation of assessment tools for fast prototyping in the areas of mission design and navigation. The Low-Thrust Interplanetary Navigation Tool, which is the subject of this paper, allows the mission analyst performing such type of quick assessment studies for the early phases in the development of low-thrust missions. A number of test cases on low-thrust missions are also presented along with the utilities composing the LOTNAV tool.

Low-thrust roundtrip trajectories to Mars with one-synodic-period repeat time

NASA Astrophysics Data System (ADS)

Okutsu, Masataka; Landau, Damon F.; Rogers, Blake A.; Longuski, James M.

2015-05-01

Cycler trajectories-both ballistic and powered-are reported in the literature in which there are two-vehicle, three-vehicle, and four-vehicle cases. Such trajectories permit the installation of cycler vehicles which provide safe and comfortable living conditions for human space travel between Earth and Mars during every synodic opportunity. The question the present paper answers is a logical, obvious one: Does a single-vehicle, one-synodic-period cycler exist? The answer is yes: such a trajectory can be flown-but only with a high-power electric propulsion system. In our example, it is found that "stopover" trajectories that spend 30 days in orbit about Earth and 30 days about Mars, and return astronauts to Earth in one synodic period require a 90-t power generator with a power level of 11 MWe. Fortuitously, and in lieu of using chemical propulsion, the high power level of the electric propulsion system would also be effective in hauling the cargo payload via a spiral trajectory about the Earth. But because one synodic period is not enough for the cycler vehicle to fly both the interplanetary trajectories and the Earth-spiral trajectories, we suggest developing two nuclear power generators, which could alternate flying the interplanetary trajectories and the Earth-spiral trajectories. Once these power generators are launched and begin operating in space, the mass requirement in seven subsequent missions (over a period of 15 years beginning in 2022) would be modest at 250-300 metric tons to low-Earth orbit per mission. Thus two cargo launches of NASA's Space Launch System and one crew launch of the Falcon Heavy, for example, would be adequate to maintain support for each consecutive mission. Although we propose developing two sets of electric propulsion systems to account for the Earth-spiral phases, only one vehicle is flown on a heliocentric trajectory at any given time. Thus, our low-thrust stopover cycler with zero encounter velocities falls into a category of a "one-vehicle cycler," which completes the gap in the literature, where we have already seen multiple-vehicle cycler concepts.

Trajectory-probed instability and statistics of desynchronization events in coupled chaotic systems

NASA Astrophysics Data System (ADS)

de Oliveira, Gilson F.; Chevrollier, Martine; Passerat de Silans, Thierry; Oriá, Marcos; de Souza Cavalcante, Hugo L. D.

2015-11-01

Complex systems, such as financial markets, earthquakes, and neurological networks, exhibit extreme events whose mechanisms of formation are not still completely understood. These mechanisms may be identified and better studied in simpler systems with dynamical features similar to the ones encountered in the complex system of interest. For instance, sudden and brief departures from the synchronized state observed in coupled chaotic systems were shown to display non-normal statistical distributions similar to events observed in the complex systems cited above. The current hypothesis accepted is that these desynchronization events are influenced by the presence of unstable object(s) in the phase space of the system. Here, we present further evidence that the occurrence of large events is triggered by the visitation of the system's phase-space trajectory to the vicinity of these unstable objects. In the system studied here, this visitation is controlled by a single parameter, and we exploit this feature to observe the effect of the visitation rate in the overall instability of the synchronized state. We find that the probability of escapes from the synchronized state and the size of those desynchronization events are enhanced in attractors whose shapes permit the chaotic trajectories to approach the region of strong instability. This result shows that the occurrence of large events requires not only a large local instability to amplify noise, or to amplify the effect of parameter mismatch between the coupled subsystems, but also that the trajectories of the system wander close to this local instability.

Quantum to classical transition in the Hořava-Lifshitz quantum cosmology

NASA Astrophysics Data System (ADS)

Bernardini, A. E.; Leal, P.; Bertolami, O.

2018-02-01

A quasi-Gaussian quantum superposition of Hořava-Lifshitz (HL) stationary states is built in order to describe the transition of the quantum cosmological problem to the related classical dynamics. The obtained HL phase-space superposed Wigner function and its associated Wigner currents describe the conditions for the matching between classical and quantum phase-space trajectories. The matching quantum superposition parameter is associated to the total energy of the classical trajectory which, at the same time, drives the engendered Wigner function to the classical stationary regime. Through the analysis of the Wigner flows, the quantum fluctuations that distort the classical regime can be quantified as a measure of (non)classicality. Finally, the modifications to the Wigner currents due to the inclusion of perturbative potentials are computed in the HL quantum cosmological context. In particular, the inclusion of a cosmological constant provides complementary information that allows for connecting the age of the Universe with the overall stiff matter density profile.

Launch vehicle design and GNC sizing with ASTOS

NASA Astrophysics Data System (ADS)

Cremaschi, Francesco; Winter, Sebastian; Rossi, Valerio; Wiegand, Andreas

2018-03-01

The European Space Agency (ESA) is currently involved in several activities related to launch vehicle designs (Future Launcher Preparatory Program, Ariane 6, VEGA evolutions, etc.). Within these activities, ESA has identified the importance of developing a simulation infrastructure capable of supporting the multi-disciplinary design and preliminary guidance navigation and control (GNC) design of different launch vehicle configurations. Astos Solutions has developed the multi-disciplinary optimization and launcher GNC simulation and sizing tool (LGSST) under ESA contract. The functionality is integrated in the Analysis, Simulation and Trajectory Optimization Software for space applications (ASTOS) and is intended to be used from the early design phases up to phase B1 activities. ASTOS shall enable the user to perform detailed vehicle design tasks and assessment of GNC systems, covering all aspects of rapid configuration and scenario management, sizing of stages, trajectory-dependent estimation of structural masses, rigid and flexible body dynamics, navigation, guidance and control, worst case analysis, launch safety analysis, performance analysis, and reporting.

North Atlantic weather regimes: A synoptic study of phase space. M.S. Thesis

NASA Technical Reports Server (NTRS)

Orrhede, Anna Karin

1990-01-01

In the phase space of weather, low frequency variability (LFV) of the atmosphere can be captured in a large scale subspace, where a trajectory connects consecutive large scale weather maps, thus revealing flow changes and recurrences. Using this approach, Vautard applied the trajectory speed minimization method (Vautard and Legras) to atmospheric data. From 37 winters of 700 mb geopotential height anomalies over the North Atlantic and the adjacent land masses, four persistent and recurrent weather patterns, interpreted as weather regimes, were discernable: a blocking regime, a zonal regime, a Greenland anticyclone regime, and an Atlantic regime. These regimes are studied further in terms of maintenance and transitions. A regime survey unveils preferences regarding event durations and precursors for the onset or break of an event. The transition frequencies between regimes vary, and together with the transition times, suggest the existence of easier transition routes. These matters are more systematically studied using complete synoptic map sequences from a number of events.

Methodology Development for the Reconstruction of the ESA Huygens Probe Entry and Descent Trajectory

NASA Astrophysics Data System (ADS)

Kazeminejad, B.

2005-01-01

The European Space Agency's (ESA) Huygens probe performed a successful entry and descent into Titan's atmosphere on January 14, 2005, and landed safely on the satellite's surface. A methodology was developed, implemented, and tested to reconstruct the Huygens probe trajectory from its various science and engineering measurements, which were performed during the probe's entry and descent to the surface of Titan, Saturn's largest moon. The probe trajectory reconstruction is an essential effort that has to be done as early as possible in the post-flight data analysis phase as it guarantees a correct and consistent interpretation of all the experiment data and furthermore provides a reference set of data for "ground-truthing" orbiter remote sensing measurements. The entry trajectory is reconstructed from the measured probe aerodynamic drag force, which also provides a means to derive the upper atmospheric properties like density, pressure, and temperature. The descent phase reconstruction is based upon a combination of various atmospheric measurements such as pressure, temperature, composition, speed of sound, and wind speed. A significant amount of effort was spent to outline and implement a least-squares trajectory estimation algorithm that provides a means to match the entry and descent trajectory portions in case of discontinuity. An extensive test campaign of the algorithm is presented which used the Huygens Synthetic Dataset (HSDS) developed by the Huygens Project Scientist Team at ESA/ESTEC as a test bed. This dataset comprises the simulated sensor output (and the corresponding measurement noise and uncertainty) of all the relevant probe instruments. The test campaign clearly showed that the proposed methodology is capable of utilizing all the relevant probe data, and will provide the best estimate of the probe trajectory once real instrument measurements from the actual probe mission are available. As a further test case using actual flight data the NASA Mars Pathfinder entry and descent trajectory and the space craft attitude was reconstructed from the 3-axis accelerometer measurements which are archived on the Planetary Data System. The results are consistent with previously published reconstruction efforts.

Trajectory design for a lunar mapping and near-Earth-asteroid flyby mission

NASA Technical Reports Server (NTRS)

Dunham, David W.; Farquhar, Robert W.

1993-01-01

In August, 1994, the unusual asteroid (1620) Geographos will pass very close to the Earth. This provides one of the best opportunities for a low-cost asteroid flyby mission that can be achieved with the help of a gravity assist from the Moon during the years 1994 and 1995. A Geographos flyby mission, including a lunar orbiting phase, was recommended to the Startegic Defense Initiative (SDI) Office when they were searching for ideas for a deep-space mission to test small imaging systems and other lightweight technologies. The goals for this mission, called Clementine, were defined to consist of a comprehensive lunar mapping phase before leaving the Earth-Moon system to encounter Geographos. This paper describes how the authors calculated a trajectory that met the mission goals within a reasonable total Delta-V budget. The paper also describes some refinements of the initially computed trajectory and alternative trajectories were investigated. The paper concludes with a list of trajectories to fly by other near-Earth asteroids during the two years following the Geographos opportunity. Some of these could be used if the Geographos schedule can not be met. If the 140 deg phase angle of the Geographos encounter turns out to be too risky, a flyby of (2120) Tantalus in January, 1995, has a much more favorable approach illumination. Tantalus apparently can be reached from the same lunar orbit needed to get to Geographos. However, both the flyby speed and distance from the Earth are much larger for Tantalus than for Geographos.

Wigner's quantum phase-space current in weakly-anharmonic weakly-excited two-state systems

NASA Astrophysics Data System (ADS)

Kakofengitis, Dimitris; Steuernagel, Ole

2017-09-01

There are no phase-space trajectories for anharmonic quantum systems, but Wigner's phase-space representation of quantum mechanics features Wigner current J . This current reveals fine details of quantum dynamics —finer than is ordinarily thought accessible according to quantum folklore invoking Heisenberg's uncertainty principle. Here, we focus on the simplest, most intuitive, and analytically accessible aspects of J. We investigate features of J for bound states of time-reversible, weakly-anharmonic one-dimensional quantum-mechanical systems which are weakly-excited. We establish that weakly-anharmonic potentials can be grouped into three distinct classes: hard, soft, and odd potentials. We stress connections between each other and the harmonic case. We show that their Wigner current fieldline patterns can be characterised by J's discrete stagnation points, how these arise and how a quantum system's dynamics is constrained by the stagnation points' topological charge conservation. We additionally show that quantum dynamics in phase space, in the case of vanishing Planck constant ℏ or vanishing anharmonicity, does not pointwise converge to classical dynamics.

Aerodynamic Tests of the Space Launch System for Database Development

NASA Technical Reports Server (NTRS)

Pritchett, Victor E.; Mayle, Melody N.; Blevins, John A.; Crosby, William A.; Purinton, David C.

2014-01-01

The Aerosciences Branch (EV33) at the George C. Marshall Space Flight Center (MSFC) has been responsible for a series of wind tunnel tests on the National Aeronautics and Space Administration's (NASA) Space Launch System (SLS) vehicles. The primary purpose of these tests was to obtain aerodynamic data during the ascent phase and establish databases that can be used by the Guidance, Navigation, and Mission Analysis Branch (EV42) for trajectory simulations. The paper describes the test particulars regarding models and measurements and the facilities used, as well as database preparations.

Optimal lunar soft landing trajectories using taboo evolutionary programming

NASA Astrophysics Data System (ADS)

Mutyalarao, M.; Raj, M. Xavier James

A safe lunar landing is a key factor to undertake an effective lunar exploration. Lunar lander consists of four phases such as launch phase, the earth-moon transfer phase, circumlunar phase and landing phase. The landing phase can be either hard landing or soft landing. Hard landing means the vehicle lands under the influence of gravity without any deceleration measures. However, soft landing reduces the vertical velocity of the vehicle before landing. Therefore, for the safety of the astronauts as well as the vehicle lunar soft landing with an acceptable velocity is very much essential. So it is important to design the optimal lunar soft landing trajectory with minimum fuel consumption. Optimization of Lunar Soft landing is a complex optimal control problem. In this paper, an analysis related to lunar soft landing from a parking orbit around Moon has been carried out. A two-dimensional trajectory optimization problem is attempted. The problem is complex due to the presence of system constraints. To solve the time-history of control parameters, the problem is converted into two point boundary value problem by using the maximum principle of Pontrygen. Taboo Evolutionary Programming (TEP) technique is a stochastic method developed in recent years and successfully implemented in several fields of research. It combines the features of taboo search and single-point mutation evolutionary programming. Identifying the best unknown parameters of the problem under consideration is the central idea for many space trajectory optimization problems. The TEP technique is used in the present methodology for the best estimation of initial unknown parameters by minimizing objective function interms of fuel requirements. The optimal estimation subsequently results into an optimal trajectory design of a module for soft landing on the Moon from a lunar parking orbit. Numerical simulations demonstrate that the proposed approach is highly efficient and it reduces the minimum fuel consumption. The results are compared with the available results in literature shows that the solution of present algorithm is better than some of the existing algorithms. Keywords: soft landing, trajectory optimization, evolutionary programming, control parameters, Pontrygen principle.

A Time-Regularized, Multiple Gravity-Assist Low-Thrust, Bounded-Impulse Model for Trajectory Optimization

NASA Technical Reports Server (NTRS)

Ellison, Donald H.; Englander, Jacob A.; Conway, Bruce A.

2017-01-01

The multiple gravity assist low-thrust (MGALT) trajectory model combines the medium-fidelity Sims-Flanagan bounded-impulse transcription with a patched-conics flyby model and is an important tool for preliminary trajectory design. While this model features fast state propagation via Keplers equation and provides a pleasingly accurate estimation of the total mass budget for the eventual flight suitable integrated trajectory it does suffer from one major drawback, namely its temporal spacing of the control nodes. We introduce a variant of the MGALT transcription that utilizes the generalized anomaly from the universal formulation of Keplers equation as a decision variable in addition to the trajectory phase propagation time. This results in two improvements over the traditional model. The first is that the maneuver locations are equally spaced in generalized anomaly about the orbit rather than time. The second is that the Kepler propagator now has the generalized anomaly as its independent variable instead of time and thus becomes an iteration-free propagation method. The new algorithm is outlined, including the impact that this has on the computation of Jacobian entries for numerical optimization, and a motivating application problem is presented that illustrates the improvements that this model has over the traditional MGALT transcription.

A Time-Regularized Multiple Gravity-Assist Low-Thrust Bounded-Impulse Model for Trajectory Optimization

NASA Technical Reports Server (NTRS)

Ellison, Donald H.; Englander, Jacob A.; Conway, Bruce A.

2017-01-01

The multiple gravity assist low-thrust (MGALT) trajectory model combines the medium-fidelity Sims-Flanagan bounded-impulse transcription with a patched-conics flyby model and is an important tool for preliminary trajectory design. While this model features fast state propagation via Kepler's equation and provides a pleasingly accurate estimation of the total mass budget for the eventual flight-suitable integrated trajectory it does suffer from one major drawback, namely its temporal spacing of the control nodes. We introduce a variant of the MGALT transcription that utilizes the generalized anomaly from the universal formulation of Kepler's equation as a decision variable in addition to the trajectory phase propagation time. This results in two improvements over the traditional model. The first is that the maneuver locations are equally spaced in generalized anomaly about the orbit rather than time. The second is that the Kepler propagator now has the generalized anomaly as its independent variable instead of time and thus becomes an iteration-free propagation method. The new algorithm is outlined, including the impact that this has on the computation of Jacobian entries for numerical optimization, and a motivating application problem is presented that illustrates the improvements that this model has over the traditional MGALT transcription.

Characterization of cumulus cloud fields using trajectories in the center of gravity versus water mass phase space: 2. Aerosol effects on warm convective clouds: Center of Gravity Versus Water Mass 2

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

Heiblum, Reuven H.; Altaratz, Orit; Koren, Ilan

2016-06-07

In Part I of this work a 3D cloud tracking algorithm and phase-space of center of gravity altitude versus cloud liquid water mass (CvM space) were introduced and described in detail. We showed how new physical insight can be gained by following cloud trajectories in the CvM space. Here, this approach is used to investigate aerosol effects on cloud fields of warm cumuli. We show a clear effect of the aerosol loading on the shape and size of CvM clusters. We also find fundamental differences in the CvM space between simulations using bin versus bulk microphysical schemes, with the binmore » scheme precipitation expressing much higher sensitivity to changes in aerosol concentrations. Using the bin microphysical scheme, we find that the increase in cloud center of gravity altitude with increase in aerosol concentrations occurs for a wide range of cloud sizes. This is attributed to reduced sedimentation, increased buoyancy and vertical velocities, and increased environmental instability, all of which are tightly coupled to inhibition of precipitation processes and subsequent feedbacks of clouds on their environment. Many of the physical processes shown here are consistent with processes typically associated with cloud invigoration.« less

Ensemble Data Assimilation Without Ensembles: Methodology and Application to Ocean Data Assimilation

NASA Technical Reports Server (NTRS)

Keppenne, Christian L.; Rienecker, Michele M.; Kovach, Robin M.; Vernieres, Guillaume

2013-01-01

Two methods to estimate background error covariances for data assimilation are introduced. While both share properties with the ensemble Kalman filter (EnKF), they differ from it in that they do not require the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The first method is referred-to as SAFE (Space Adaptive Forecast error Estimation) because it estimates error covariances from the spatial distribution of model variables within a single state vector. It can thus be thought of as sampling an ensemble in space. The second method, named FAST (Flow Adaptive error Statistics from a Time series), constructs an ensemble sampled from a moving window along a model trajectory. The underlying assumption in these methods is that forecast errors in data assimilation are primarily phase errors in space and/or time.

Application of Metaheuristic and Deterministic Algorithms for Aircraft Reference Trajectory Optimization =

NASA Astrophysics Data System (ADS)

Murrieta Mendoza, Alejandro

Aircraft reference trajectory is an alternative method to reduce fuel consumption, thus the pollution released to the atmosphere. Fuel consumption reduction is of special importance for two reasons: first, because the aeronautical industry is responsible of 2% of the CO2 released to the atmosphere, and second, because it will reduce the flight cost. The aircraft fuel model was obtained from a numerical performance database which was created and validated by our industrial partner from flight experimental test data. A new methodology using the numerical database was proposed in this thesis to compute the fuel burn for a given trajectory. Weather parameters such as wind and temperature were taken into account as they have an important effect in fuel burn. The open source model used to obtain the weather forecast was provided by Weather Canada. A combination of linear and bi-linear interpolations allowed finding the required weather data. The search space was modelled using different graphs: one graph was used for mapping the different flight phases such as climb, cruise and descent, and another graph was used for mapping the physical space in which the aircraft would perform its flight. The trajectory was optimized in its vertical reference trajectory using the Beam Search algorithm, and a combination of the Beam Search algorithm with a search space reduction technique. The trajectory was optimized simultaneously for the vertical and lateral reference navigation plans while fulfilling a Required Time of Arrival constraint using three different metaheuristic algorithms: the artificial bee's colony, and the ant colony optimization. Results were validated using the software FlightSIMRTM, a commercial Flight Management System, an exhaustive search algorithm, and as flown flights obtained from flightawareRTM. All algorithms were able to reduce the fuel burn, and the flight costs. None None None None None None None

LORAKS Makes Better SENSE: Phase-Constrained Partial Fourier SENSE Reconstruction without Phase Calibration

PubMed Central

Kim, Tae Hyung; Setsompop, Kawin; Haldar, Justin P.

2016-01-01

Purpose Parallel imaging and partial Fourier acquisition are two classical approaches for accelerated MRI. Methods that combine these approaches often rely on prior knowledge of the image phase, but the need to obtain this prior information can place practical restrictions on the data acquisition strategy. In this work, we propose and evaluate SENSE-LORAKS, which enables combined parallel imaging and partial Fourier reconstruction without requiring prior phase information. Theory and Methods The proposed formulation is based on combining the classical SENSE model for parallel imaging data with the more recent LORAKS framework for MR image reconstruction using low-rank matrix modeling. Previous LORAKS-based methods have successfully enabled calibrationless partial Fourier parallel MRI reconstruction, but have been most successful with nonuniform sampling strategies that may be hard to implement for certain applications. By combining LORAKS with SENSE, we enable highly-accelerated partial Fourier MRI reconstruction for a broader range of sampling trajectories, including widely-used calibrationless uniformly-undersampled trajectories. Results Our empirical results with retrospectively undersampled datasets indicate that when SENSE-LORAKS reconstruction is combined with an appropriate k-space sampling trajectory, it can provide substantially better image quality at high-acceleration rates relative to existing state-of-the-art reconstruction approaches. Conclusion The SENSE-LORAKS framework provides promising new opportunities for highly-accelerated MRI. PMID:27037836

Motion-induced phase error estimation and correction in 3D diffusion tensor imaging.

PubMed

Van, Anh T; Hernando, Diego; Sutton, Bradley P

2011-11-01

A multishot data acquisition strategy is one way to mitigate B0 distortion and T2∗ blurring for high-resolution diffusion-weighted magnetic resonance imaging experiments. However, different object motions that take place during different shots cause phase inconsistencies in the data, leading to significant image artifacts. This work proposes a maximum likelihood estimation and k-space correction of motion-induced phase errors in 3D multishot diffusion tensor imaging. The proposed error estimation is robust, unbiased, and approaches the Cramer-Rao lower bound. For rigid body motion, the proposed correction effectively removes motion-induced phase errors regardless of the k-space trajectory used and gives comparable performance to the more computationally expensive 3D iterative nonlinear phase error correction method. The method has been extended to handle multichannel data collected using phased-array coils. Simulation and in vivo data are shown to demonstrate the performance of the method.

Trajectory Design for the Transiting Exoplanet Survey Satellite

NASA Technical Reports Server (NTRS)

Dichmann, Donald J.; Parker, Joel J. K.; Williams, Trevor W.; Mendelsohn, Chad R.

2014-01-01

The Transiting Exoplanet Survey Satellite (TESS) is a National Aeronautics and Space Administration (NASA) mission, scheduled to be launched in 2017. TESS will travel in a highly eccentric orbit around Earth, with initial perigee radius near 17 Earth radii (Re) and apogee radius near 59 Re. The orbit period is near 2:1 resonance with the Moon, with apogee nearly 90 degrees out-of-phase with the Moon, in a configuration that has been shown to be operationally stable. TESS will execute phasing loops followed by a lunar flyby, with a final maneuver to achieve 2:1 resonance with the Moon. The goals of a resonant orbit with long-term stability, short eclipses and limited oscillations of perigee present significant challenges to the trajectory design. To rapidly assess launch opportunities, we adapted the Schematics Window Methodology (SWM76) launch window analysis tool to assess the TESS mission constraints. To understand the long-term dynamics of such a resonant orbit in the Earth-Moon system we employed Dynamical Systems Theory in the Circular Restricted 3-Body Problem (CR3BP). For precise trajectory analysis we use a high-fidelity model and multiple shooting in the General Mission Analysis Tool (GMAT) to optimize the maneuver delta-V and meet mission constraints. Finally we describe how the techniques we have developed can be applied to missions with similar requirements. Keywords: resonant orbit, stability, lunar flyby, phasing loops, trajectory optimization

A new method in accelerating PROPELLER MRI.

PubMed

Li, Bing Keong; D'Arcy, Michael; Weber, Ewald; Crozier, Stuart

2008-01-01

In this work, a new method has been proposed to accelerate the PROPELLER MRI operation. The proposed method uses a rotary phased array coil and a new method in acquiring the k-space strips and preparing the complete k-space trajectories data set. It is numerically shown that for a 12 strips PROPELLER MR brain imaging sequence, the operation time can be reduced by four folds, with no apparent loss in the image quality.

The trajectories of EAEC countries development: Numerical analysis of competitive strategies in investments

NASA Astrophysics Data System (ADS)

Shelomentsev, A. G.; Medvedev, M. A.; Isaichik, K. F.; Dyomina, M. I.; Berg, I. A.; Kit, M.

2017-12-01

This paper discusses comparative analysis of trajectories in the development of participating countries of the Eurasian Economic Union (EAEC) in a two-dimensional phase space. The coordinates in the space is represented by the value of a dynamic variable that is a key indicator of the country's development, and the rate of its relative growth. This allows for construction of a ternary classification diagram describing competitive behavior strategies of countries in question. The comparative analysis was run for two primary factors: the size of investment in the main capital and R&D spendings. The authors carried out analysis and identification of competitive strategies for the behavior of the EAEC countries, as well as he proposed conclusions and recommendations on improving the policy of economic development.

Communication: transition state theory for dissipative systems without a dividing surface.

PubMed

Revuelta, F; Bartsch, Thomas; Benito, R M; Borondo, F

2012-03-07

Transition state theory is a central cornerstone in reaction dynamics. Its key step is the identification of a dividing surface that is crossed only once by all reactive trajectories. This assumption is often badly violated, especially when the reactive system is coupled to an environment. The calculations made in this way then overestimate the reaction rate and the results depend critically on the choice of the dividing surface. In this Communication, we study the phase space of a stochastically driven system close to an energetic barrier in order to identify the geometric structure unambiguously determining the reactive trajectories, which is then incorporated in a simple rate formula for reactions in condensed phase that is both independent of the dividing surface and exact. © 2012 American Institute of Physics

Accurate approximation of in-ecliptic trajectories for E-sail with constant pitch angle

NASA Astrophysics Data System (ADS)

Huo, Mingying; Mengali, Giovanni; Quarta, Alessandro A.

2018-05-01

Propellantless continuous-thrust propulsion systems, such as electric solar wind sails, may be successfully used for new space missions, especially those requiring high-energy orbit transfers. When the mass-to-thrust ratio is sufficiently large, the spacecraft trajectory is characterized by long flight times with a number of revolutions around the Sun. The corresponding mission analysis, especially when addressed within an optimal context, requires a significant amount of simulation effort. Analytical trajectories are therefore useful aids in a preliminary phase of mission design, even though exact solution are very difficult to obtain. The aim of this paper is to present an accurate, analytical, approximation of the spacecraft trajectory generated by an electric solar wind sail with a constant pitch angle, using the latest mathematical model of the thrust vector. Assuming a heliocentric circular parking orbit and a two-dimensional scenario, the simulation results show that the proposed equations are able to accurately describe the actual spacecraft trajectory for a long time interval when the propulsive acceleration magnitude is sufficiently small.

The ESA's Space Trajectory Analysis software suite

NASA Astrophysics Data System (ADS)

Ortega, Guillermo

The European Space Agency (ESA) initiated in 2005 an internal activity to develop an open source software suite involving university science departments and research institutions all over the world. This project is called the "Space Trajectory Analysis" or STA. This article describes the birth of STA and its present configuration. One of the STA aims is to promote the exchange of technical ideas, and raise knowledge and competence in the areas of applied mathematics, space engineering, and informatics at University level. Conceived as a research and education tool to support the analysis phase of a space mission, STA is able to visualize a wide range of space trajectories. These include among others ascent, re-entry, descent and landing trajectories, orbits around planets and moons, interplanetary trajectories, rendezvous trajectories, etc. The article explains that STA project is an original idea of the Technical Directorate of ESA. It was born in August 2005 to provide a framework in astrodynamics research at University level. As research and education software applicable to Academia, a number of Universities support this development by joining ESA in leading the development. ESA and Universities partnership are expressed in the STA Steering Board. Together with ESA, each University has a chair in the board whose tasks are develop, control, promote, maintain, and expand the software suite. The article describes that STA provides calculations in the fields of spacecraft tracking, attitude analysis, coverage and visibility analysis, orbit determination, position and velocity of solar system bodies, etc. STA implements the concept of "space scenario" composed of Solar system bodies, spacecraft, ground stations, pads, etc. It is able to propagate the orbit of a spacecraft where orbital propagators are included. STA is able to compute communication links between objects of a scenario (coverage, line of sight), and to represent the trajectory computations and relationship between objects in 2D and 3D formats, etc. Further, the article explains that the STA development is open source and it is based on the state of the art astrodynamics routines that are grouped into modules. The modules are programmed using the C++ language. The different STA modules are designed, developed, tested and verified by the different Universities. Software integration and overall validation is performed by ESA. Students are chosen to work in STA modules as part of their Master or PhD thesis programs. As part of their growing experience, the students learn how to write documentation for a space project using European Coorperation on Space Standardization (ECSS) standards, how to test and verify the software modules they write and, how to interact with ESA and each other in this process. Finally, the article concludes about the benefits of the STA initiative. The STA project allows a strong link among applied mathematics, space engineering, and informatics disciplines by reinforcing the academic community with requirements and needs coming from space agencies and industry real needs and missions.

Quantum dynamics in phase space: Moyal trajectories 2

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

Braunss, G.

Continuing a previous paper [G. Braunss, J. Phys. A: Math. Theor. 43, 025302 (2010)] where we had calculated Planck-Constant-Over-Two-Pi {sup 2}-approximations of quantum phase space viz. Moyal trajectories of examples with one and two degrees of freedom, we present in this paper the calculation of Planck-Constant-Over-Two-Pi {sup 2}-approximations for four examples: a two-dimensional Toda chain, the radially symmetric Schwarzschild field, and two examples with three degrees of freedom, the latter being the nonrelativistic spherically Coulomb potential and the relativistic cylinder symmetrical Coulomb potential with a magnetic field H. We show in particular that an Planck-Constant-Over-Two-Pi {sup 2}-approximation of the nonrelativisticmore » Coulomb field has no singularity at the origin (r= 0) whereas the classical trajectories are singular at r= 0. In the third example, we show in particular that for an arbitrary function {gamma}(H, z) the expression {beta}{identical_to}p{sub z}+{gamma}(H, z) is classically ( Planck-Constant-Over-Two-Pi = 0) a constant of motion, whereas for Planck-Constant-Over-Two-Pi {ne} 0 this holds only if {gamma}(H, z) is an arbitrary polynomial of second order in z. This statement is shown to extend correspondingly to a cylinder symmetrical Schwarzschild field with a magnetic field. We exhibit in detail a number of properties of the radially symmetric Schwarzschild field. We exhibit finally the problems of the nonintegrable Henon-Heiles Hamiltonian and give a short review of the regular Hilbert space representation of Moyal operators.« less

Simulation of wave packet tunneling of interacting identical particles

NASA Astrophysics Data System (ADS)

Lozovik, Yu. E.; Filinov, A. V.; Arkhipov, A. S.

2003-02-01

We demonstrate a different method of simulation of nonstationary quantum processes, considering the tunneling of two interacting identical particles, represented by wave packets. The used method of quantum molecular dynamics (WMD) is based on the Wigner representation of quantum mechanics. In the context of this method ensembles of classical trajectories are used to solve quantum Wigner-Liouville equation. These classical trajectories obey Hamiltonian-like equations, where the effective potential consists of the usual classical term and the quantum term, which depends on the Wigner function and its derivatives. The quantum term is calculated using local distribution of trajectories in phase space, therefore, classical trajectories are not independent, contrary to classical molecular dynamics. The developed WMD method takes into account the influence of exchange and interaction between particles. The role of direct and exchange interactions in tunneling is analyzed. The tunneling times for interacting particles are calculated.

Correlation dimension and phase space contraction via extreme value theory

NASA Astrophysics Data System (ADS)

Faranda, Davide; Vaienti, Sandro

2018-04-01

We show how to obtain theoretical and numerical estimates of correlation dimension and phase space contraction by using the extreme value theory. The maxima of suitable observables sampled along the trajectory of a chaotic dynamical system converge asymptotically to classical extreme value laws where: (i) the inverse of the scale parameter gives the correlation dimension and (ii) the extremal index is associated with the rate of phase space contraction for backward iteration, which in dimension 1 and 2, is closely related to the positive Lyapunov exponent and in higher dimensions is related to the metric entropy. We call it the Dynamical Extremal Index. Numerical estimates are straightforward to obtain as they imply just a simple fit to a univariate distribution. Numerical tests range from low dimensional maps, to generalized Henon maps and climate data. The estimates of the indicators are particularly robust even with relatively short time series.

Using the small alignment index chaos indicator to characterize the vibrational dynamics of a molecular system: LiNC-LiCN.

PubMed

Benitez, P; Losada, J C; Benito, R M; Borondo, F

2015-10-01

A study of the dynamical characteristics of the phase space corresponding to the vibrations of the LiNC-LiCN molecule using an analysis based on the small alignment index (SALI) is presented. SALI is a good indicator of chaos that can easily determine whether a given trajectory is regular or chaotic regardless of the dimensionality of the system, and can also provide a wealth of dynamical information when conveniently implemented. In two-dimensional (2D) systems SALI maps are computed as 2D phase space representations, where the SALI asymptotic values are represented in color scale. We show here how these maps provide full information on the dynamical phase space structure of the LiNC-LiCN system, even quantifying numerically the volume of the different zones of chaos and regularity as a function of the molecule excitation energy.

Convergent chaos

NASA Astrophysics Data System (ADS)

Pradas, Marc; Pumir, Alain; Huber, Greg; Wilkinson, Michael

2017-07-01

Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion should be refined. Despite their overall intrinsic instability, trajectories may be very strongly convergent in phase space over extremely long periods, as revealed by our investigation of a simple chaotic system (a realistic model for small bodies in a turbulent flow). We establish that this strong convergence is a multi-facetted phenomenon, in which the clustering is intense, widespread and balanced by lacunarity of other regions. Power laws, indicative of scale-free features, characterize the distribution of particles in the system. We use large-deviation and extreme-value statistics to explain the effect. Our results show that the interpretation of the ‘butterfly effect’ needs to be carefully qualified. We argue that the combination of mixing and clustering processes makes our specific model relevant to understanding the evolution of simple organisms. Lastly, this notion of convergent chaos, which implies the existence of conditions for which uncertainties are unexpectedly small, may also be relevant to the valuation of insurance and futures contracts.

Hierarchical structure in sharply divided phase space for the piecewise linear map

NASA Astrophysics Data System (ADS)

Akaishi, Akira; Aoki, Kazuki; Shudo, Akira

2017-05-01

We have studied a two-dimensional piecewise linear map to examine how the hierarchical structure of stable regions affects the slow dynamics in Hamiltonian systems. In the phase space there are infinitely many stable regions, each of which is polygonal-shaped, and the rest is occupied by chaotic orbits. By using symbolic representation of stable regions, a procedure to compute the edges of the polygons is presented. The stable regions are hierarchically distributed in phase space and the edges of the stable regions show the marginal instability. The cumulative distribution of the recurrence time obeys a power law as ˜t-2 , the same as the one for the system with phase space, which is composed of a single stable region and chaotic components. By studying the symbol sequence of recurrence trajectories, we show that the hierarchical structure of stable regions has no significant effect on the power-law exponent and that only the marginal instability on the boundary of stable regions is responsible for determining the exponent. We also discuss the relevance of the hierarchical structure to those in more generic chaotic systems.

Mapa MEGNO para satélites irregulares de Satuno

NASA Astrophysics Data System (ADS)

Moyano, M. M.; Leiva, A. M.

By implementing the elliptic restricted three-body model we obtain high resolution dynamical maps in the phase space region corresponding to that where Saturn's irregular satellites are currently found. The nature of the trajectories is characterized by the MEGNO chaos indicator (Cincotta P. and Simó C., 2000), which allows to identify regions of chaotic and quasi- periodic trajectories much faster than with other indicators (e.g. Lyapunov exponents). The results obtained allow to identify with great detail the boundaries of the regions of regular motion, chaotic motion, and substruc- tures associated to mean motion resonances. FULL TEXT IN SPANISH

Main methods of trajectory synthesis for scenarios of space missions with gravity assist maneuvers in the system of Jupiter and with landing on one of its satellites

NASA Astrophysics Data System (ADS)

Golubev, Yu. F.; Tuchin, A. G.; Grushevskii, A. V.; Koryanov, V. V.; Tuchin, D. A.; Morskoy, I. M.; Simonov, A. V.; Dobrovolskii, V. S.

2016-12-01

The development of a methodology for designing trajectories of spacecraft intended for the contact and remote studies of Jupiter and its natural satellites is considered. This methodology should take into account a number of specific features. Firstly, in order to maintain the propellant consumption at an acceptable level, the flight profile, ensuring the injection of the spacecraft into orbit around the Jovian moon, should include a large number of gravity assist maneuvers both in the interplanetary phase of the Earth-to-Jupiter flight and during the flight in the system of the giant planet. Secondly, the presence of Jupiter's powerful radiation belts also imposes fairly strict limitations on the trajectory parameters.

Decomposed direct matrix inversion for fast non-cartesian SENSE reconstructions.

PubMed

Qian, Yongxian; Zhang, Zhenghui; Wang, Yi; Boada, Fernando E

2006-08-01

A new k-space direct matrix inversion (DMI) method is proposed here to accelerate non-Cartesian SENSE reconstructions. In this method a global k-space matrix equation is established on basic MRI principles, and the inverse of the global encoding matrix is found from a set of local matrix equations by taking advantage of the small extension of k-space coil maps. The DMI algorithm's efficiency is achieved by reloading the precalculated global inverse when the coil maps and trajectories remain unchanged, such as in dynamic studies. Phantom and human subject experiments were performed on a 1.5T scanner with a standard four-channel phased-array cardiac coil. Interleaved spiral trajectories were used to collect fully sampled and undersampled 3D raw data. The equivalence of the global k-space matrix equation to its image-space version, was verified via conjugate gradient (CG) iterative algorithms on a 2x undersampled phantom and numerical-model data sets. When applied to the 2x undersampled phantom and human-subject raw data, the decomposed DMI method produced images with small errors (< or = 3.9%) relative to the reference images obtained from the fully-sampled data, at a rate of 2 s per slice (excluding 4 min for precalculating the global inverse at an image size of 256 x 256). The DMI method may be useful for noise evaluations in parallel coil designs, dynamic MRI, and 3D sodium MRI with fixed coils and trajectories. Copyright 2006 Wiley-Liss, Inc.

Study of geometric phase using classical coupled oscillators

NASA Astrophysics Data System (ADS)

Bhattacharjee, Sharba; Dey, Biprateep; Mohapatra, Ashok K.

2018-05-01

We illustrate the geometric phase associated with the cyclic dynamics of a classical system of coupled oscillators. We use an analogy between a classical coupled oscillator and a two-state quantum mechanical system to represent the evolution of the oscillator on an equivalent Hilbert space, which may be represented as a trajectory on the surface of a sphere. The cyclic evolution of the system leads to a change in phase, which consists of a dynamic phase along with an additional phase shift dependent on the geometry of the evolution. A simple experiment suitable for advanced undergraduate students is designed to study the geometric phase incurred during cyclic evolution of a coupled oscillator.

Spiral trajectory design: a flexible numerical algorithm and base analytical equations.

PubMed

Pipe, James G; Zwart, Nicholas R

2014-01-01

Spiral-based trajectories for magnetic resonance imaging can be advantageous, but are often cumbersome to design or create. This work presents a flexible numerical algorithm for designing trajectories based on explicit definition of radial undersampling, and also gives several analytical expressions for charactering the base (critically sampled) class of these trajectories. Expressions for the gradient waveform, based on slew and amplitude limits, are developed such that a desired pitch in the spiral k-space trajectory is followed. The source code for this algorithm, written in C, is publicly available. Analytical expressions approximating the spiral trajectory (ignoring the radial component) are given to characterize measurement time, gradient heating, maximum gradient amplitude, and off-resonance phase for slew-limited and gradient amplitude-limited cases. Several numerically calculated trajectories are illustrated, and base Archimedean spirals are compared with analytically obtained results. Several different waveforms illustrate that the desired slew and amplitude limits are reached, as are the desired undersampling patterns, using the numerical method. For base Archimedean spirals, the results of the numerical and analytical approaches are in good agreement. A versatile numerical algorithm was developed, and was written in publicly available code. Approximate analytical formulas are given that help characterize spiral trajectories. Copyright © 2013 Wiley Periodicals, Inc.

An adaptive reentry guidance method considering the influence of blackout zone

NASA Astrophysics Data System (ADS)

Wu, Yu; Yao, Jianyao; Qu, Xiangju

2018-01-01

Reentry guidance has been researched as a popular topic because it is critical for a successful flight. In view that the existing guidance methods do not take into account the accumulated navigation error of Inertial Navigation System (INS) in the blackout zone, in this paper, an adaptive reentry guidance method is proposed to obtain the optimal reentry trajectory quickly with the target of minimum aerodynamic heating rate. The terminal error in position and attitude can be also reduced with the proposed method. In this method, the whole reentry guidance task is divided into two phases, i.e., the trajectory updating phase and the trajectory planning phase. In the first phase, the idea of model predictive control (MPC) is used, and the receding optimization procedure ensures the optimal trajectory in the next few seconds. In the trajectory planning phase, after the vehicle has flown out of the blackout zone, the optimal reentry trajectory is obtained by online planning to adapt to the navigation information. An effective swarm intelligence algorithm, i.e. pigeon inspired optimization (PIO) algorithm, is applied to obtain the optimal reentry trajectory in both of the two phases. Compared to the trajectory updating method, the proposed method can reduce the terminal error by about 30% considering both the position and attitude, especially, the terminal error of height has almost been eliminated. Besides, the PIO algorithm performs better than the particle swarm optimization (PSO) algorithm both in the trajectory updating phase and the trajectory planning phases.

Fast isotropic banding-free bSSFP imaging using 3D dynamically phase-cycled radial bSSFP (3D DYPR-SSFP).

PubMed

Benkert, Thomas; Ehses, Philipp; Blaimer, Martin; Jakob, Peter M; Breuer, Felix A

2016-03-01

Dynamically phase-cycled radial balanced steady-state free precession (DYPR-SSFP) is a method for efficient banding artifact removal in bSSFP imaging. Based on a varying radiofrequency (RF) phase-increment in combination with a radial trajectory, DYPR-SSFP allows obtaining a banding-free image out of a single acquired k-space. The purpose of this work is to present an extension of this technique, enabling fast three-dimensional isotropic banding-free bSSFP imaging. While banding artifact removal with DYPR-SSFP relies on the applied dynamic phase-cycle, this aspect can lead to artifacts, at least when the number of acquired projections lies below a certain limit. However, by using a 3D radial trajectory with quasi-random view ordering for image acquisition, this problem is intrinsically solved, enabling 3D DYPR-SSFP imaging at or even below the Nyquist criterion. The approach is validated for brain and knee imaging at 3 Tesla. Volumetric, banding-free images were obtained in clinically acceptable scan times with an isotropic resolution up to 0.56mm. The combination of DYPR-SSFP with a 3D radial trajectory allows banding-free isotropic volumetric bSSFP imaging with no expense of scan time. Therefore, this is a promising candidate for clinical applications such as imaging of cranial nerves or articular cartilage. Copyright © 2015. Published by Elsevier GmbH.

LORAKS makes better SENSE: Phase-constrained partial fourier SENSE reconstruction without phase calibration.

PubMed

Kim, Tae Hyung; Setsompop, Kawin; Haldar, Justin P

2017-03-01

Parallel imaging and partial Fourier acquisition are two classical approaches for accelerated MRI. Methods that combine these approaches often rely on prior knowledge of the image phase, but the need to obtain this prior information can place practical restrictions on the data acquisition strategy. In this work, we propose and evaluate SENSE-LORAKS, which enables combined parallel imaging and partial Fourier reconstruction without requiring prior phase information. The proposed formulation is based on combining the classical SENSE model for parallel imaging data with the more recent LORAKS framework for MR image reconstruction using low-rank matrix modeling. Previous LORAKS-based methods have successfully enabled calibrationless partial Fourier parallel MRI reconstruction, but have been most successful with nonuniform sampling strategies that may be hard to implement for certain applications. By combining LORAKS with SENSE, we enable highly accelerated partial Fourier MRI reconstruction for a broader range of sampling trajectories, including widely used calibrationless uniformly undersampled trajectories. Our empirical results with retrospectively undersampled datasets indicate that when SENSE-LORAKS reconstruction is combined with an appropriate k-space sampling trajectory, it can provide substantially better image quality at high-acceleration rates relative to existing state-of-the-art reconstruction approaches. The SENSE-LORAKS framework provides promising new opportunities for highly accelerated MRI. Magn Reson Med 77:1021-1035, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Mission Analysis for the Don Quijote Phase-A Study

NASA Technical Reports Server (NTRS)

Cano, Juan L.; Sanchez, Mariano; Cornara, Stefania; Carnelli, Ian

2007-01-01

The Don Quijote Phase-A study is a definition study funded by ESA and devoted to the analysis of the possibilities to deflect a Near Earth Object (NEO) in the range of 300-800 m diameter. DEIMOS Space S.L. and EADS Astrium have teamed up within this study to form one of the three consortia that have analyzed these aspects for ESA. Target asteroids for the mission are 1989 ML, 2002 AT4 and Apophis. This paper presents the mission analysis activities within the consortium providing: low-thrust interplanetary rendezvous Orbiter trajectories to the target asteroids, ballistic interplanetary trajectories for the Impactor, Orbiter arrival description at the asteroids, Orbiter stable orbits characterization at the asteroid, deflection determination by means of a Radio Science Experiment (RSE) as well as the mission timelines and overall mission scenarios.

Fuel-Optimal Trajectories in a Planet-Moon Environment Using Multiple Gravity Assists

NASA Technical Reports Server (NTRS)

Ross, Shane D.; Grover, Piyush

2007-01-01

For low energy spacecraft trajectories such as multi-moon orbiters for the Jupiter system, multiple gravity assists by moons could be used in conjunction with ballistic capture to drastically decrease fuel usage. In this paper, we outline a procedure to obtain a family of zero-fuel multi-moon orbiter trajectories, using a family of Keplerian maps derived by the first author previously. The maps capture well the dynamics of the full equations of motion; the phase space contains a connected chaotic zone where intersections between unstable resonant orbit manifolds provide the template for lanes of fast migration between orbits of different semimajor axes. Patched three body approach is used and the four body problem is broken down into two three-body problems, and the search space is considerably reduced by the use of properties of the Keplerian maps. We also introduce the notion of Switching Region where the perturbations due to the two perturbing moons are of comparable strength, and which separates the domains of applicability of the corresponding two Keplerian maps.

Non-Cartesian Parallel Imaging Reconstruction

PubMed Central

Wright, Katherine L.; Hamilton, Jesse I.; Griswold, Mark A.; Gulani, Vikas; Seiberlich, Nicole

2014-01-01

Non-Cartesian parallel imaging has played an important role in reducing data acquisition time in MRI. The use of non-Cartesian trajectories can enable more efficient coverage of k-space, which can be leveraged to reduce scan times. These trajectories can be undersampled to achieve even faster scan times, but the resulting images may contain aliasing artifacts. Just as Cartesian parallel imaging can be employed to reconstruct images from undersampled Cartesian data, non-Cartesian parallel imaging methods can mitigate aliasing artifacts by using additional spatial encoding information in the form of the non-homogeneous sensitivities of multi-coil phased arrays. This review will begin with an overview of non-Cartesian k-space trajectories and their sampling properties, followed by an in-depth discussion of several selected non-Cartesian parallel imaging algorithms. Three representative non-Cartesian parallel imaging methods will be described, including Conjugate Gradient SENSE (CG SENSE), non-Cartesian GRAPPA, and Iterative Self-Consistent Parallel Imaging Reconstruction (SPIRiT). After a discussion of these three techniques, several potential promising clinical applications of non-Cartesian parallel imaging will be covered. PMID:24408499

Shuttle derived atmospheric density model. Part 2: STS atmospheric implications for AOTV trajectory analysis, a proposed GRAM perturbation density model

NASA Technical Reports Server (NTRS)

Findlay, J. T.; Kelly, G. M.; Troutman, P. A.

1984-01-01

A perturbation model to the Marshall Space Flight Center (MSFC) Global Reference Atmosphere Model (GRAM) was developed for use in the Aeroassist Orbital Transfer Vehicle (AOTV) trajectory and analysis. The model reflects NASA Space Shuttle experience over the first twelve entry flights. The GRAM was selected over the Air Force 1978 Reference Model because of its more general formulation and wider use throughout NASA. The add-on model, a simple scaling with altitude to reflect density structure encountered by the Shuttle Orbiter was selected principally to simplify implementation. Perturbations, by season, can be utilized to minimize the number of required simulations, however, exact Shuttle flight history can be exercised using the same model if desired. Such a perturbation model, though not meteorologically motivated, enables inclusion of High Resolution Accelerometer Package (HiRAP) results in the thermosphere. Provision is made to incorporate differing perturbations during the AOTV entry and exit phases of the aero-asist maneuver to account for trajectory displacement (geographic) along the ground track.

Real time correlation function in a single phase space integral beyond the linearized semiclassical initial value representation.

PubMed

Liu, Jian; Miller, William H

2007-06-21

It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSC-IVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the Wigner functions corresponding to the two operators. The difference is that the trajectories involved in the LSC-IVR evolve classically, i.e., according to the classical equations of motion, while in the exact theory they evolve according to generalized equations of motion that are derived here. Approximations to the exact equations of motion are then introduced to achieve practical methods that are applicable to complex (i.e., large) molecular systems. Four such methods are proposed in the paper--the full Wigner dynamics (full WD) and the second order WD based on "Wigner trajectories" [H. W. Lee and M. D. Scully, J. Chem. Phys. 77, 4604 (1982)] and the full Donoso-Martens dynamics (full DMD) and the second order DMD based on "Donoso-Martens trajectories" [A. Donoso and C. C. Martens, Phys. Rev. Lett. 8722, 223202 (2001)]--all of which can be viewed as generalizations of the original LSC-IVR method. Numerical tests of the four versions of this new approach are made for two anharmonic model problems, and for each the momentum autocorrelation function (i.e., operators linear in coordinate or momentum operators) and the force autocorrelation function (nonlinear operators) have been calculated. These four new approximate treatments are indeed seen to be significant improvements to the original LSC-IVR approximation.

Milestoning with coarse memory

NASA Astrophysics Data System (ADS)

Hawk, Alexander T.

2013-04-01

Milestoning is a method used to calculate the kinetics of molecular processes occurring on timescales inaccessible to traditional molecular dynamics (MD) simulations. In the method, the phase space of the system is partitioned by milestones (hypersurfaces), trajectories are initialized on each milestone, and short MD simulations are performed to calculate transitions between neighboring milestones. Long trajectories of the system are then reconstructed with a semi-Markov process from the observed statistics of transition. The procedure is typically justified by the assumption that trajectories lose memory between crossing successive milestones. Here we present Milestoning with Coarse Memory (MCM), a generalization of Milestoning that relaxes the memory loss assumption of conventional Milestoning. In the method, milestones are defined and sample transitions are calculated in the standard Milestoning way. Then, after it is clear where trajectories sample milestones, the milestones are broken up into distinct neighborhoods (clusters), and each sample transition is associated with two clusters: the cluster containing the coordinates the trajectory was initialized in, and the cluster (on the terminal milestone) containing trajectory's final coordinates. Long trajectories of the system are then reconstructed with a semi-Markov process in an extended state space built from milestone and cluster indices. To test the method, we apply it to a process that is particularly ill suited for Milestoning: the dynamics of a polymer confined to a narrow cylinder. We show that Milestoning calculations of both the mean first passage time and the mean transit time of reversal—which occurs when the end-to-end vector reverses direction—are significantly improved when MCM is applied. Finally, we note the overhead of performing MCM on top of conventional Milestoning is negligible.

Rosetta Navigation at its Mars Swing-By

NASA Technical Reports Server (NTRS)

Budnik, Frank; Morley, Trevor

2007-01-01

This paper reports on the navigation activities during Rosetta s Mars swing-by. It covers the Mars approach phase starting after a deterministic deep-space maneuver in September 2006, the swing-by proper on 25 February 2007, and ends with another deterministic deep-space maneuver in April 2007 which was also foreseen to compensate any navigation error. Emphasis is put on the orbit determination and prediction set-up and the evolution of the targeting estimates in the B-plane and their adjustments by trajectory correction maneuvers.

NASA/DOD (National Aeronautics and Space Administration/Department of Defense) Control/Structures Interaction Technology Conference (2nd) Held in Colorado Springs, Colorado on 17-19 November 1987.

DTIC Science & Technology

1988-06-01

James McKelvy and Harold Tinsley *," . CONCEPTUAL DESIGN OF A SPACE STATION DYNAMIC SCALE MODEL ............. 87 Robert Letchworth, Paul E... CONCEPTUAL SYSTEM DESIGN FOR ANTENNA THERMAL AND DYNAMIC DISTORTION COMPENSATION USING A PHASED ARRAY FEED ................... 145 G. R. Sharp, R. J...to achieve somne desired state or trajectory. For conceptual purposes, however, an alternate view is useful in which the measurement reference against

TH-EF-BRA-06: A Novel Retrospective 3D K-Space Sorting 4D-MRI Technique Using a Radial K-Space Acquisition MRI Sequence

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

Liu, Y; Subashi, E; Yin, F

Purpose: Current retrospective 4D-MRI provides superior tumor-to-tissue contrast and accurate respiratory motion information for radiotherapy motion management. The developed 4D-MRI techniques based on 2D-MRI image sorting require a high frame-rate of the MR sequences. However, several MRI sequences provide excellent image quality but have low frame-rate. This study aims at developing a novel retrospective 3D k-space sorting 4D-MRI technique using radial k-space acquisition MRI sequences to improve 4D-MRI image quality and temporal-resolution for imaging irregular organ/tumor respiratory motion. Methods: The method is based on a RF-spoiled, steady-state, gradient-recalled sequence with minimal echo time. A 3D radial k-space data acquisition trajectorymore » was used for sampling the datasets. Each radial spoke readout data line starts from the 3D center of Field-of-View. Respiratory signal can be extracted from the k-space center data point of each spoke. The spoke data was sorted based on its self-synchronized respiratory signal using phase sorting. Subsequently, 3D reconstruction was conducted to generate the time-resolved 4D-MRI images. As a feasibility study, this technique was implemented on a digital human phantom XCAT. The respiratory motion was controlled by an irregular motion profile. To validate using k-space center data as a respiratory surrogate, we compared it with the XCAT input controlling breathing profile. Tumor motion trajectories measured on reconstructed 4D-MRI were compared to the average input trajectory. The mean absolute amplitude difference (D) was calculated. Results: The signal extracted from k-space center data matches well with the input controlling respiratory profile of XCAT. The relative amplitude error was 8.6% and the relative phase error was 3.5%. XCAT 4D-MRI demonstrated a clear motion pattern with little serrated artifacts. D of tumor trajectories was 0.21mm, 0.23mm and 0.23mm in SI, AP and ML directions, respectively. Conclusion: A novel retrospective 3D k-space sorting 4D-MRI technique has been developed and evaluated on human digital phantom. NIH (1R21CA165384-01A1)« less

SPIRAL-SPRITE: a rapid single point MRI technique for application to porous media.

PubMed

Szomolanyi, P; Goodyear, D; Balcom, B; Matheson, D

2001-01-01

This study presents the application of a new, rapid, single point MRI technique which samples k space with spiral trajectories. The general principles of the technique are outlined along with application to porous concrete samples, solid pharmaceutical tablets and gas phase imaging. Each sample was chosen to highlight specific features of the method.

POCS-based reconstruction of multiplexed sensitivity encoded MRI (POCSMUSE): a general algorithm for reducing motion-related artifacts

PubMed Central

Chu, Mei-Lan; Chang, Hing-Chiu; Chung, Hsiao-Wen; Truong, Trong-Kha; Bashir, Mustafa R.; Chen, Nan-kuei

2014-01-01

Purpose A projection onto convex sets reconstruction of multiplexed sensitivity encoded MRI (POCSMUSE) is developed to reduce motion-related artifacts, including respiration artifacts in abdominal imaging and aliasing artifacts in interleaved diffusion weighted imaging (DWI). Theory Images with reduced artifacts are reconstructed with an iterative POCS procedure that uses the coil sensitivity profile as a constraint. This method can be applied to data obtained with different pulse sequences and k-space trajectories. In addition, various constraints can be incorporated to stabilize the reconstruction of ill-conditioned matrices. Methods The POCSMUSE technique was applied to abdominal fast spin-echo imaging data, and its effectiveness in respiratory-triggered scans was evaluated. The POCSMUSE method was also applied to reduce aliasing artifacts due to shot-to-shot phase variations in interleaved DWI data corresponding to different k-space trajectories and matrix condition numbers. Results Experimental results show that the POCSMUSE technique can effectively reduce motion-related artifacts in data obtained with different pulse sequences, k-space trajectories and contrasts. Conclusion POCSMUSE is a general post-processing algorithm for reduction of motion-related artifacts. It is compatible with different pulse sequences, and can also be used to further reduce residual artifacts in data produced by existing motion artifact reduction methods. PMID:25394325

Cole-Cole broadening in dielectric relaxation and strange kinetics.

PubMed

Puzenko, Alexander; Ishai, Paul Ben; Feldman, Yuri

2010-07-16

We present a fresh appraisal of the Cole-Cole (CC) description of dielectric relaxation. While the approach is phenomenological, it demonstrates a fundamental connection between the parameters of the CC dispersion. Based on the fractal nature of the time set representing the interaction of the relaxing dipole with its encompassing matrix, and the Kirkwood-Froehlich correlation factor, a new 3D phase space linking together the kinetic and structural properties is proposed. The evolution of the relaxation process is represented in this phase space by a trajectory, which is determined by the variation of external macroscopic parameters. As an example, the validity of the approach is demonstrated on two porous silica glasses exhibiting a CC relaxation process.

Correlated histogram representation of Monte Carlo derived medical accelerator photon-output phase space

DOEpatents

Schach Von Wittenau, Alexis E.

2003-01-01

A method is provided to represent the calculated phase space of photons emanating from medical accelerators used in photon teletherapy. The method reproduces the energy distributions and trajectories of the photons originating in the bremsstrahlung target and of photons scattered by components within the accelerator head. The method reproduces the energy and directional information from sources up to several centimeters in radial extent, so it is expected to generalize well to accelerators made by different manufacturers. The method is computationally both fast and efficient overall sampling efficiency of 80% or higher for most field sizes. The computational cost is independent of the number of beams used in the treatment plan.

Dark energy in six nearby galaxy flows: Synthetic phase diagrams and self-similarity

NASA Astrophysics Data System (ADS)

Chernin, A. D.; Teerikorpi, P.; Dolgachev, V. P.; Kanter, A. A.; Domozhilova, L. M.; Valtonen, M. J.; Byrd, G. G.

2012-09-01

Outward flows of galaxies are observed around groups of galaxies on spatial scales of about 1 Mpc, and around galaxy clusters on scales of 10 Mpc. Using recent data from the Hubble Space Telescope (HST), we have constructed two synthetic velocity-distance phase diagrams: one for four flows on galaxy-group scales and the other for two flows on cluster scales. It has been shown that, in both cases, the antigravity produced by the cosmic dark-energy background is stronger than the gravity produced by the matter in the outflow volume. The antigravity accelerates the flows and introduces a phase attractor that is common to all scales, corresponding to a linear velocity-distance relation (the local Hubble law). As a result, the bundle of outflow trajectories mostly follow the trajectory of the attractor. A comparison of the two diagrams reveals the universal self-similar nature of the outflows: their gross phase structure in dimensionless variables is essentially independent of their physical spatial scales, which differ by approximately a factor of 10 in the two diagrams.

Trajectory Design of the Lunar Impactor Mission Concept

NASA Technical Reports Server (NTRS)

Chung, Min-Kun J.; McElrath, Timothy P.; Roncoli, Ralph B.

2006-01-01

The National Aeronautics and Space Administration (NASA) solicited proposals in 2006 for an opportunity to include a small secondary payload with the launch of the Lunar Reconnaissance Orbiter (LRO) scheduled for October 2008. The cost cap of the proposal was between $50 and $80M, and the mass cap was 1,000 kilograms. JPL proposed a Lunar Impactor (LI) concept for this solicitation. The mission objective of LI was to impact the permanently shadowed region of a South polar crater ultimately to detect the presence of water. The detection of water ice would prove to be an important factor on future lunar exploration. NASA Ames Research Center also proposed a similar concept, the Lunar Crater observation and Sensing Satellite (LCROSS), which was selected by NASA for the mission. However, in this paper, the trajectory design of the LI proposed by JPL is considered. Since the LI spacecraft was to be launched on the LRO launch vehicle as a secondary payload, its initial trajectory must be diverted at some later time from the LRO trans-lunar trajectory for the subsequent impact. Several such trajectories have been considered, where each trajectory option fields some specific values for the mission parameters. The mission parameters include the availability of LRO instruments at the time of impact for the observation by LRO, the mission duration, the impact velocity, the impact angle, etc. It is possible for the LI to be deflected with a relatively low delta-V to impact a South polar crater at a reasonable impact velocity and impact angle directly with no delay. However, the instruments on-board LRO may not be ready for observation. Thus, several delayed trajectory options have been considered further. The lunar phase at the time of impact may also play an important factor for observation, especially from Earth. Several lunar flyby trajectory maneuvers have been identified to arrive at the Moon for impact at the desired lunar phase. By using a combination of these successive lunar flyby maneuvers, the impact lunar phase may be adjusted to the desired location. A few such trajectories have been suggested. Also, some attempts have been made to maximize the impact velocity by converting the impact trajectory into a retrograde orbit with respect to Earth. Since these types of trajectories take advantage of the Sun-Earth three-body region to minimize the delta-V, the mission duration is relatively long. A few such trajectories are suggested. Also, an attempt has been made to adjust the lunar impact within a desired time period for the optimum Earth observation for the above trajectories. The mission parameters resulting from each trajectory option above are considered and weighed against the cost and robustness of the mission in a brief summary.

Augmenting Parametric Optimal Ascent Trajectory Modeling with Graph Theory

NASA Technical Reports Server (NTRS)

Dees, Patrick D.; Zwack, Matthew R.; Edwards, Stephen; Steffens, Michael

2016-01-01

It has been well documented that decisions made in the early stages of Conceptual and Pre-Conceptual design commit up to 80% of total Life-Cycle Cost (LCC) while engineers know the least about the product they are designing [1]. Once within Preliminary and Detailed design however, making changes to the design becomes far more difficult to enact in both cost and schedule. Primarily this has been due to a lack of detailed data usually uncovered later during the Preliminary and Detailed design phases. In our current budget-constrained environment, making decisions within Conceptual and Pre-Conceptual design which minimize LCC while meeting requirements is paramount to a program's success. Within the arena of launch vehicle design, optimizing the ascent trajectory is critical for minimizing the costs present within such concerns as propellant, aerodynamic, aeroheating, and acceleration loads while meeting requirements such as payload delivered to a desired orbit. In order to optimize the vehicle design its constraints and requirements must be known, however as the design cycle proceeds it is all but inevitable that the conditions will change. Upon that change, the previously optimized trajectory may no longer be optimal, or meet design requirements. The current paradigm for adjusting to these updates is generating point solutions for every change in the design's requirements [2]. This can be a tedious, time-consuming task as changes in virtually any piece of a launch vehicle's design can have a disproportionately large effect on the ascent trajectory, as the solution space of the trajectory optimization problem is both non-linear and multimodal [3]. In addition, an industry standard tool, Program to Optimize Simulated Trajectories (POST), requires an expert analyst to produce simulated trajectories that are feasible and optimal [4]. In a previous publication the authors presented a method for combatting these challenges [5]. In order to bring more detailed information into Conceptual and Pre-Conceptual design, knowledge of the effects originating from changes to the vehicle must be calculated. In order to do this, a model capable of quantitatively describing any vehicle within the entire design space under consideration must be constructed. This model must be based upon analysis of acceptable fidelity, which in this work comes from POST. Design space interrogation can be achieved with surrogate modeling, a parametric, polynomial equation representing a tool. A surrogate model must be informed by data from the tool with enough points to represent the solution space for the chosen number of variables with an acceptable level of error. Therefore, Design Of Experiments (DOE) is used to select points within the design space to maximize information gained on the design space while minimizing number of data points required. To represent a design space with a non-trivial number of variable parameters the number of points required still represent an amount of work which would take an inordinate amount of time via the current paradigm of manual analysis, and so an automated method was developed. The best practices of expert trajectory analysts working within NASA Marshall's Advanced Concepts Office (ACO) were implemented within a tool called multiPOST. These practices include how to use the output data from a previous run of POST to inform the next, determining whether a trajectory solution is feasible from a real-world perspective, and how to handle program execution errors. The tool was then augmented with multiprocessing capability to enable analysis on multiple trajectories simultaneously, allowing throughput to scale with available computational resources. In this update to the previous work the authors discuss issues with the method and solutions.

Biological Implications of Dynamical Phases in Non-equilibrium Networks

NASA Astrophysics Data System (ADS)

Murugan, Arvind; Vaikuntanathan, Suriyanarayanan

2016-03-01

Biology achieves novel functions like error correction, ultra-sensitivity and accurate concentration measurement at the expense of free energy through Maxwell Demon-like mechanisms. The design principles and free energy trade-offs have been studied for a variety of such mechanisms. In this review, we emphasize a perspective based on dynamical phases that can explain commonalities shared by these mechanisms. Dynamical phases are defined by typical trajectories executed by non-equilibrium systems in the space of internal states. We find that coexistence of dynamical phases can have dramatic consequences for function vs free energy cost trade-offs. Dynamical phases can also provide an intuitive picture of the design principles behind such biological Maxwell Demons.

HyPlane for Space Tourism and Business Transportation

NASA Astrophysics Data System (ADS)

Savino, R.

In the present work a preliminary study on a small hypersonic airplane for a long duration space tourism mission is presented. It is also consistent with a point-to-point medium range (5000-6000 km) hypersonic trip, in the frame of the "urgent business travel" market segment. The main ideas is to transfer technological solutions developed for aeronautical and space atmospheric re-entry systems to the design of such a hypersonic airplane. A winged vehicle characterized by high aerodynamic efficiency and able to manoeuvre along the flight path, in all aerodynamic regimes encountered, is taken into consideration. Rocket-Based Combined Cycle and Turbine-Based Combined Cycle engines are investigated to ensure higher performances in terms of flight duration and range. Different flight-paths are also considered, including sub-orbital parabolic trajectories and steady state hypersonic cruise. The former, in particular, takes advantage of the high aerodynamic efficiency during the unpowered phase, in combination with a periodic engine actuation, to guarantee a long duration oscillating flight path. These trajectories offer Space tourists the opportunity of extended missions, characterized by repeated periods of low-gravity at altitudes high enough to ensure a wide view of the Earth from Space.

Co-state initialization for the minimum-time low-thrust trajectory optimization

NASA Astrophysics Data System (ADS)

Taheri, Ehsan; Li, Nan I.; Kolmanovsky, Ilya

2017-05-01

This paper presents an approach for co-state initialization which is a critical step in solving minimum-time low-thrust trajectory optimization problems using indirect optimal control numerical methods. Indirect methods used in determining the optimal space trajectories typically result in two-point boundary-value problems and are solved by single- or multiple-shooting numerical methods. Accurate initialization of the co-state variables facilitates the numerical convergence of iterative boundary value problem solvers. In this paper, we propose a method which exploits the trajectory generated by the so-called pseudo-equinoctial and three-dimensional finite Fourier series shape-based methods to estimate the initial values of the co-states. The performance of the approach for two interplanetary rendezvous missions from Earth to Mars and from Earth to asteroid Dionysus is compared against three other approaches which, respectively, exploit random initialization of co-states, adjoint-control transformation and a standard genetic algorithm. The results indicate that by using our proposed approach the percent of the converged cases is higher for trajectories with higher number of revolutions while the computation time is lower. These features are advantageous for broad trajectory search in the preliminary phase of mission designs.

Tracking and data system support for the Pioneer project. Pioneers 6-9, extended missions: 1 July 1972 - 1 July 1973, volume 12

NASA Technical Reports Server (NTRS)

Miller, R. B.

1974-01-01

The Tracking and Data System supported the deep space phases of the Pioneer 6, 7, 8, and 9 missions, with two spacecraft in an inward trajectory and two spacecraft in an outward trajectory from the earth in heliocentric orbits. During the period of this report, scientific instruments aboard each of the spacecraft continued to register information relative to interplanetary particles and fields, and radiometric data generated by the network continued to contribute to knowledge of the celestial mechanics of the solar system. In addition, to network support activity detail, network performance and special support activities are covered.

Global Optimization of Interplanetary Trajectories in the Presence of Realistic Mission Contraints

NASA Technical Reports Server (NTRS)

Hinckley, David, Jr.; Englander, Jacob; Hitt, Darren

2015-01-01

Interplanetary missions are often subject to difficult constraints, like solar phase angle upon arrival at the destination, velocity at arrival, and altitudes for flybys. Preliminary design of such missions is often conducted by solving the unconstrained problem and then filtering away solutions which do not naturally satisfy the constraints. However this can bias the search into non-advantageous regions of the solution space, so it can be better to conduct preliminary design with the full set of constraints imposed. In this work two stochastic global search methods are developed which are well suited to the constrained global interplanetary trajectory optimization problem.

Tracking and data system support for the pioneer project. Volume 11 Pioneers 6-9. Extended missions: 1 July 1971 - 1 July 1973

NASA Technical Reports Server (NTRS)

Renzetti, N. A.; Siegmeth, A. J.

1973-01-01

The Tracking and Data System supported the deep space phases of the Pioneer 6, 7, 8, and 9 missions, with two spacecraft in an inward trajectory and two spacecraft in an outward trajectory from the earth in heliocentric orbits. Scientific instruments aboard each of the spacecraft continued to register information relative to interplanetary particles and fields, and radio metric data generated by the network continued to improve our knowledge of the celestial mechanics of the solar system. In addition to network support activity detail, network performance and special support activities are covered.

Spectral-clustering approach to Lagrangian vortex detection.

PubMed

Hadjighasem, Alireza; Karrasch, Daniel; Teramoto, Hiroshi; Haller, George

2016-06-01

One of the ubiquitous features of real-life turbulent flows is the existence and persistence of coherent vortices. Here we show that such coherent vortices can be extracted as clusters of Lagrangian trajectories. We carry out the clustering on a weighted graph, with the weights measuring pairwise distances of fluid trajectories in the extended phase space of positions and time. We then extract coherent vortices from the graph using tools from spectral graph theory. Our method locates all coherent vortices in the flow simultaneously, thereby showing high potential for automated vortex tracking. We illustrate the performance of this technique by identifying coherent Lagrangian vortices in several two- and three-dimensional flows.

Optimizing interplanetary trajectories with deep space maneuvers. M.S. Thesis

NASA Technical Reports Server (NTRS)

Navagh, John

1993-01-01

Analysis of interplanetary trajectories is a crucial area for both manned and unmanned missions of the Space Exploration Initiative. A deep space maneuver (DSM) can improve a trajectory in much the same way as a planetary swingby. However, instead of using a gravitational field to alter the trajectory, the on-board propulsion system of the spacecraft is used when the vehicle is not near a planet. The purpose is to develop an algorithm to determine where and when to use deep space maneuvers to reduce the cost of a trajectory. The approach taken to solve this problem uses primer vector theory in combination with a non-linear optimizing program to minimize Delta(V). A set of necessary conditions on the primer vector is shown to indicate whether a deep space maneuver will be beneficial. Deep space maneuvers are applied to a round trip mission to Mars to determine their effect on the launch opportunities. Other studies which were performed include cycler trajectories and Mars mission abort scenarios. It was found that the software developed was able to locate quickly DSM's which lower the total Delta(V) on these trajectories.

Optimizing interplanetary trajectories with deep space maneuvers

NASA Astrophysics Data System (ADS)

Navagh, John

1993-09-01

Analysis of interplanetary trajectories is a crucial area for both manned and unmanned missions of the Space Exploration Initiative. A deep space maneuver (DSM) can improve a trajectory in much the same way as a planetary swingby. However, instead of using a gravitational field to alter the trajectory, the on-board propulsion system of the spacecraft is used when the vehicle is not near a planet. The purpose is to develop an algorithm to determine where and when to use deep space maneuvers to reduce the cost of a trajectory. The approach taken to solve this problem uses primer vector theory in combination with a non-linear optimizing program to minimize Delta(V). A set of necessary conditions on the primer vector is shown to indicate whether a deep space maneuver will be beneficial. Deep space maneuvers are applied to a round trip mission to Mars to determine their effect on the launch opportunities. Other studies which were performed include cycler trajectories and Mars mission abort scenarios. It was found that the software developed was able to locate quickly DSM's which lower the total Delta(V) on these trajectories.

Reduced aliasing artifacts using shaking projection k-space sampling trajectory

NASA Astrophysics Data System (ADS)

Zhu, Yan-Chun; Du, Jiang; Yang, Wen-Chao; Duan, Chai-Jie; Wang, Hao-Yu; Gao, Song; Bao, Shang-Lian

2014-03-01

Radial imaging techniques, such as projection-reconstruction (PR), are used in magnetic resonance imaging (MRI) for dynamic imaging, angiography, and short-T2 imaging. They are less sensitive to flow and motion artifacts, and support fast imaging with short echo times. However, aliasing and streaking artifacts are two main sources which degrade radial imaging quality. For a given fixed number of k-space projections, data distributions along radial and angular directions will influence the level of aliasing and streaking artifacts. Conventional radial k-space sampling trajectory introduces an aliasing artifact at the first principal ring of point spread function (PSF). In this paper, a shaking projection (SP) k-space sampling trajectory was proposed to reduce aliasing artifacts in MR images. SP sampling trajectory shifts the projection alternately along the k-space center, which separates k-space data in the azimuthal direction. Simulations based on conventional and SP sampling trajectories were compared with the same number projections. A significant reduction of aliasing artifacts was observed using the SP sampling trajectory. These two trajectories were also compared with different sampling frequencies. A SP trajectory has the same aliasing character when using half sampling frequency (or half data) for reconstruction. SNR comparisons with different white noise levels show that these two trajectories have the same SNR character. In conclusion, the SP trajectory can reduce the aliasing artifact without decreasing SNR and also provide a way for undersampling reconstruction. Furthermore, this method can be applied to three-dimensional (3D) hybrid or spherical radial k-space sampling for a more efficient reduction of aliasing artifacts.

Phase-space dynamics of opposition control in wall-bounded turbulent flows

NASA Astrophysics Data System (ADS)

Hwang, Yongyun; Ibrahim, Joseph; Yang, Qiang; Doohan, Patrick

2017-11-01

The phase-space dynamics of wall-bounded shear flow in the presence of opposition control is explored by examining the behaviours of a pair of nonlinear equilibrium solutions (exact coherent structures), edge state and life time of turbulence at low Reynolds numbers. While the control modifies statistics and phase-space location of the edge state and the lower-branch equilibrium solution very little, it is also found to regularise the periodic orbit on the edge state by reverting a period-doubling bifurcation. Only the upper-branch equilibrium solution and mean turbulent state are significantly modified by the control, and, in phase space, they gradually approach the edge state on increasing the control gain. It is found that this behaviour results in a significant reduction of the life time of turbulence, indicating that the opposition control significantly increases the probability that the turbulent solution trajectory passes through the edge state. Finally, it is shown that the opposition control increases the critical Reynolds number of the onset of the equilibrium solutions, indicating its capability of transition delay. This work is sponsored by the Engineering and Physical Sciences Research Council (EPSRC) in the UK (EP/N019342/1).

Imaginary geometric phases of quantum trajectories in high-order terahertz sideband generation

NASA Astrophysics Data System (ADS)

Yang, Fan; Liu, Ren-Bao

2014-03-01

Quantum evolution of particles under strong fields can be described by a small number of quantum trajectories that satisfy the stationary phase condition in the Dirac-Feynmann path integral. The quantum trajectories are the key concept to understand the high-order terahertz siedeband generation (HSG) in semiconductors. Due to the nontrivial ``vacuum'' states of band materials, the quantum trajectories of optically excited electron-hole pairs in semiconductors can accumulate geometric phases under the driving of an elliptically polarized THz field. We find that the geometric phase of the stationary trajectory is generally complex with both real and imaginary parts. In monolayer MoS2, the imaginary parts of the geometric phase leads to a changing of the polarization ellipticity of the sideband. We further show that the imaginary part originates from the quantum interference of many trajectories with different phases. Thus the observation of the polarization ellipticity of the sideband shall be a good indication of the quantum nature of the stationary trajectory. This work is supported by Hong Kong RGC/GRF 401512 and the CUHK Focused Investments Scheme.

Trapping of high-energy electrons into regime of surfatron acceleration by electromagnetic waves in space plasma

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

Erokhin, A. N.; Erokhin, N. S.; Milant'ev, V. P.

2012-05-15

The phenomenon of trapping of weakly relativistic charged particles (with kinetic energies on the order of mc{sup 2}) into a regime of surfatron acceleration by an electromagnetic wave that propagates in plasma across a weak external magnetic field has been studied using nonlinear numerical calculations based on a solution of the relativistic equations of motion. Analysis showed that, for the wave amplitude above a certain threshold value and the initial wave phase outside the interval favorable for the surfing regime, the trajectory of a charged particle initially corresponds to its cyclotron rotation in the external magnetic field. For the initialmore » particle energies studied, the period of this rotation is relatively short. After a certain number (from several dozen to several thousand and above) of periods of rotation, the wave phase takes a value that is favorable for trapping of the charged particle on its trajectory by the electromagnetic wave, provided the Cherenkov resonance conditions are satisfied. As a result, the wave traps the charged particle and imparts it an ultrarelativistic acceleration. In momentum space, the region of trapping into the regime of surfing on an electromagnetic wave turns out to be rather large.« less

Dissipative quantum trajectories in complex space: Damped harmonic oscillator

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

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation formore » the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.« less

Stickiness in Hamiltonian systems: From sharply divided to hierarchical phase space

NASA Astrophysics Data System (ADS)

Altmann, Eduardo G.; Motter, Adilson E.; Kantz, Holger

2006-02-01

We investigate the dynamics of chaotic trajectories in simple yet physically important Hamiltonian systems with nonhierarchical borders between regular and chaotic regions with positive measures. We show that the stickiness to the border of the regular regions in systems with such a sharply divided phase space occurs through one-parameter families of marginally unstable periodic orbits and is characterized by an exponent γ=2 for the asymptotic power-law decay of the distribution of recurrence times. Generic perturbations lead to systems with hierarchical phase space, where the stickiness is apparently enhanced due to the presence of infinitely many regular islands and Cantori. In this case, we show that the distribution of recurrence times can be composed of a sum of exponentials or a sum of power laws, depending on the relative contribution of the primary and secondary structures of the hierarchy. Numerical verification of our main results are provided for area-preserving maps, mushroom billiards, and the newly defined magnetic mushroom billiards.

Semiclassical propagation of Wigner functions.

PubMed

Dittrich, T; Gómez, E A; Pachón, L A

2010-06-07

We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are discussed. The propagator of the Wigner function based on van Vleck's approximation replaces the Liouville propagator by a quantum spot with an oscillatory pattern reflecting the interference between pairs of classical trajectories. Employing phase-space path integration instead, caustics in the quantum spot are resolved in terms of Airy functions. We apply both to two benchmark models of nonlinear molecular potentials, the Morse oscillator and the quartic double well, to test them in standard tasks such as computing autocorrelation functions and propagating coherent states. The performance of semiclassical Wigner propagation is very good even in the presence of marked quantum effects, e.g., in coherent tunneling and in propagating Schrodinger cat states, and of classical chaos in four-dimensional phase space. We suggest options for an effective numerical implementation of our method and for integrating it in Monte-Carlo-Metropolis algorithms suitable for high-dimensional systems.

Space Shuttle Ascent Flight Design Process: Evolution and Lessons Learned

NASA Technical Reports Server (NTRS)

Picka, Bret A.; Glenn, Christopher B.

2011-01-01

The Space Shuttle Ascent Flight Design team is responsible for defining a launch to orbit trajectory profile that satisfies all programmatic mission objectives and defines the ground and onboard reconfiguration requirements for this high-speed and demanding flight phase. This design, verification and reconfiguration process ensures that all applicable mission scenarios are enveloped within integrated vehicle and spacecraft certification constraints and criteria, and includes the design of the nominal ascent profile and trajectory profiles for both uphill and ground-to-ground aborts. The team also develops a wide array of associated training, avionics flight software verification, onboard crew and operations facility products. These key ground and onboard products provide the ultimate users and operators the necessary insight and situational awareness for trajectory dynamics, performance and event sequences, abort mode boundaries and moding, flight performance and impact predictions for launch vehicle stages for use in range safety, and flight software performance. These products also provide the necessary insight to or reconfiguration of communications and tracking systems, launch collision avoidance requirements, and day of launch crew targeting and onboard guidance, navigation and flight control updates that incorporate the final vehicle configuration and environment conditions for the mission. Over the course of the Space Shuttle Program, ascent trajectory design and mission planning has evolved in order to improve program flexibility and reduce cost, while maintaining outstanding data quality. Along the way, the team has implemented innovative solutions and technologies in order to overcome significant challenges. A number of these solutions may have applicability to future human spaceflight programs.

Phase-space perspective on the wavelength-dependent electron correlation of strong-field double ionization of Xe

NASA Astrophysics Data System (ADS)

Shao, Yun; Yuan, Zongqiang; Ye, Difa; Fu, Libin; Liu, Ming-Ming; Sun, Xufei; Wu, Chengyin; Liu, Jie; Gong, Qihuang; Liu, Yunquan

2017-12-01

We measure the wavelength-dependent correlated-electron momentum (CEM) spectra of strong-field double ionization of Xe atoms, and observe a significant change from a roughly nonstructured (uncorrelated) pattern at 795 nm to an elongated distribution with V-shaped structure (correlated) at higher wavelengths of 1320 and 1810 nm, pointing to the transition of the ionization dynamics imprinted in the momentum distributions. These observations are well reproduced by a semiclassical model using Green-Sellin-Zachor potential to take into account the screening effect. We show that the momentum distribution of Xe2+ undergoes a bifurcation structure emerging from single-hump to double-hump structure as the laser wavelength increases, which is dramatically different from that of He2+, indicating the complex multi-electron effect. By back analyzing the double ionization trajectories in the phase space (the initial transverse momentum and the laser phase at the tunneling exit) of the first tunneled electrons, we provide deep insight into the physical origin for electron correlation dynamics. We find that a random distribution in phase-space is responsible for a less distinct structured CEM spectrum at shorter wavelength. While increasing the laser wavelength, a topology-invariant pattern in phase-space appears, leading to the clearly visible V-shaped structures.

Affordable Flight Demonstration of the GTX Air-Breathing SSTO Vehicle Concept

NASA Technical Reports Server (NTRS)

Krivanek, Thomas M.; Roche, Joseph M.; Riehl, John P.; Kosareo, Daniel N.

2002-01-01

The rocket based combined cycle (RBCC) powered single-stage-to-orbit (SSTO) reusable launch vehicle has the potential to significantly reduce the total cost per pound for orbital payload missions. To validate overall system performance, a flight demonstration must be performed. This paper presents an overview of the first phase of a flight demonstration program for the GTX SSTO vehicle concept. Phase 1 will validate the propulsion performance of the vehicle configuration over the supersonic and hypersonic airbreathing portions of the trajectory. The focus and goal of Phase 1 is to demonstrate the integration and performance of the propulsion system flowpath with the vehicle aerodynamics over the air-breathing trajectory. This demonstrator vehicle will have dual mode ramjet/scramjets, which include the inlet, combustor, and nozzle with geometrically scaled aerodynamic surface outer mold lines (OML) defining the forebody, boundary layer diverter, wings, and tail. The primary objective of this study is to demonstrate propulsion system performance and operability including the ram to scram transition, as well as to validate vehicle aerodynamics and propulsion airframe integration. To minimize overall risk and development cost the effort will incorporate proven materials, use existing turbomachinery in the propellant delivery systems, launch from an existing unmanned remote launch facility, and use basic vehicle recovery techniques to minimize control and landing requirements. A second phase would demonstrate propulsion performance across all critical portions of a space launch trajectory (lift off through transition to all-rocket) integrated with flight-like vehicle systems.

Affordable Flight Demonstration of the GTX Air-Breathing SSTO Vehicle Concept

NASA Technical Reports Server (NTRS)

Krivanek, Thomas M.; Roche, Joseph M.; Riehl, John P.; Kosareo, Daniel N.

2003-01-01

The rocket based combined cycle (RBCC) powered single-stage-to-orbit (SSTO) reusable launch vehicle has the potential to significantly reduce the total cost per pound for orbital payload missions. To validate overall system performance, a flight demonstration must be performed. This paper presents an overview of the first phase of a flight demonstration program for the GTX SSTO vehicle concept. Phase 1 will validate the propulsion performance of the vehicle configuration over the supersonic and hypersonic air- breathing portions of the trajectory. The focus and goal of Phase 1 is to demonstrate the integration and performance of the propulsion system flowpath with the vehicle aerodynamics over the air-breathing trajectory. This demonstrator vehicle will have dual mode ramjetkcramjets, which include the inlet, combustor, and nozzle with geometrically scaled aerodynamic surface outer mold lines (OML) defining the forebody, boundary layer diverter, wings, and tail. The primary objective of this study is to demon- strate propulsion system performance and operability including the ram to scram transition, as well as to validate vehicle aerodynamics and propulsion airframe integration. To minimize overall risk and develop ment cost the effort will incorporate proven materials, use existing turbomachinery in the propellant delivery systems, launch from an existing unmanned remote launch facility, and use basic vehicle recovery techniques to minimize control and landing requirements. A second phase would demonstrate propulsion performance across all critical portions of a space launch trajectory (lift off through transition to all-rocket) integrated with flight-like vehicle systems.

Fuzzy Logic Trajectory Design and Guidance for Terminal Area Energy Management

NASA Technical Reports Server (NTRS)

Burchett, Bradley

2003-01-01

The second generation reusable launch vehicle will leverage many new technologies to make flight to low earth orbit safer and more cost effective. One important capability will be completely autonomous flight during reentry and landing, thus making it unnecessary to man the vehicle for cargo missions with stringent weight constraints. Implementation of sophisticated new guidance and control methods will enable the vehicle to return to earth under less than favorable conditions. The return to earth consists of three phases--Entry, Terminal Area Energy Management (TAEM), and Approach and Landing. The Space Shuttle is programmed to fly all three phases of flight automatically, and under normal circumstances the astronaut-pilot takes manual control only during the Approach and Landing phase. The automatic control algorithms used in the Shuttle for TAEM and Approach and Landing have been developed over the past 30 years. They are computationally efficient, and based on careful study of the spacecraft's flight dynamics, and heuristic reasoning. The gliding return trajectory is planned prior to the mission, and only minor adjustments are made during flight for perturbations in the vehicle energy state. With the advent of the X-33 and X-34 technology demonstration vehicles, several authors investigated implementing advanced control methods to provide autonomous real-time design of gliding return trajectories thus enhancing the ability of the vehicle to adjust to unusual energy states. The bulk of work published to date deals primarily with the approach and landing phase of flight where changes in heading angle are small, and range to the runway is monotonically decreasing. These benign flight conditions allow for model simplification and fairly straightforward optimization. This project focuses on the TAEM phase of flight where mathematically precise methods have produced limited results. Fuzzy Logic methods are used to make onboard autonomous gliding return trajectory design robust to a wider energy envelope, and the possibility of control surface failures, thus increasing the flexibility of unmanned gliding recovery and landing.

Time-dependent importance sampling in semiclassical initial value representation calculations for time correlation functions.

PubMed

Tao, Guohua; Miller, William H

2011-07-14

An efficient time-dependent importance sampling method is developed for the Monte Carlo calculation of time correlation functions via the initial value representation (IVR) of semiclassical (SC) theory. A prefactor-free time-dependent sampling function weights the importance of a trajectory based on the magnitude of its contribution to the time correlation function, and global trial moves are used to facilitate the efficient sampling the phase space of initial conditions. The method can be generally applied to sampling rare events efficiently while avoiding being trapped in a local region of the phase space. Results presented in the paper for two system-bath models demonstrate the efficiency of this new importance sampling method for full SC-IVR calculations.

Determining the Capability Requirements for a Space-Based Optical Sensor to Determine the Trajectory of an Incoming Antisatellite Weapon

DTIC Science & Technology

2008-03-01

Figure a, b, shows Thor and Nike-Zeus missiles respectively . [3], [19] a series of high altitude nuclear tests in 1962 and later. The Thor system was...satellites simultaneously and scan large areas of space in a very short time. 16 For instance, the AN/FPS-85 phased-array radar at Eglin AFB in Florida is...sensors, located at different SSN sites such as Maui, Eglin , Thule, and Diego Garcia collect up to 80,000 satellite observations each day. 18 Each

Tracking and data system support for the Pioneer project. Volume 2: Pioneer 11 prelaunch planning through second trajectory correction, to 1 May 1973

NASA Technical Reports Server (NTRS)

Barton, W. R.; Miller, R. B.

1975-01-01

The tracking and data system support of the planning, testing, launch, near-earth, and deep space phases of the Pioneer 11 Jupiter Mission are described, including critical phases of spacecraft flight and guidance. Scientific instruments aboard the spacecraft registered information relative to interplanetary particles and fields. Knowledge of the celestial mechanics of the solar system was improved through radiometric data gathering. Network performance, details of network support activity, and special support activities are discussed.

Mission and vehicle sizing sensitivities

NASA Technical Reports Server (NTRS)

Young, Archie C.

1986-01-01

Representative interplanetary space vehicle systems are sized to compare and show sensitivity of the initial mass required in low Earth orbit to one mission mode and mission opportunity. Data are presented to show the requirements for Earth-Mars opposition and conjunction class roundtrip flyby and stopover mission opportunities available during the time period from year 1997 to year 2045. The interplanetary space vehicle consists of a spacecraft and a space vehicle acceleration system. Propellant boil-off for the various mission phases is given for the Lox/LH (Liquid Oxygen/Liquid Hydrogen) propulsion systems. Mission abort information is presented for the 1999 Venus outbound swingby trajectory, transfer profile.

Contingency Trajectory Design for a Lunar Orbit Insertion Maneuver Failure by the Lunar Atmosphere Dust Environment Explorer (LADEE) Spacecraft

NASA Technical Reports Server (NTRS)

Genova, Anthony L.; Loucks, Michael; Carrico, John

2014-01-01

The purpose of this extended abstract is to present results from a failed lunar-orbit insertion (LOI) maneuver contingency analysis for the Lunar Atmosphere Dust Environment Explorer (LADEE) mission, managed and operated by NASA Ames Research Center in Moffett Field, CA. The LADEE spacecrafts nominal trajectory implemented multiple sub-lunar phasing orbits centered at Earth before eventually reaching the Moon (Fig. 1) where a critical LOI maneuver was to be performed [1,2,3]. If this LOI was missed, the LADEE spacecraft would be on an Earth-escape trajectory, bound for heliocentric space. Although a partial mission recovery is possible from a heliocentric orbit (to be discussed in the full paper), it was found that an escape-prevention maneuver could be performed several days after a hypothetical LOI-miss, allowing a return to the desired science orbit around the Moon without leaving the Earths sphere-of-influence (SOI).

Communication: HK propagator uniformized along a one-dimensional manifold in weakly anharmonic systems

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

Kocia, Lucas, E-mail: lkocia@fas.harvard.edu; Heller, Eric J.

2014-11-14

A simplification of the Heller-Herman-Kluk-Kay (HK) propagator is presented that does not suffer from the need for an increasing number of trajectories with dimensions of the system under study. This is accomplished by replacing HK’s uniformizing integral over all of phase space by a one-dimensional curve that is appropriately selected to lie along the fastest growing manifold of a defining trajectory. It is shown that this modification leads to eigenspectra of quantum states in weakly anharmonic systems that can outperform the comparatively computationally cheap thawed Gaussian approximation method and frequently approach the accuracy of spectra obtained with the full HKmore » propagator.« less

A combined Eulerian-Lagrangian two-phase flow analysis of SSME HPOTP nozzle plug trajectories. II - Results

NASA Technical Reports Server (NTRS)

Mcconnaughey, P. K.; Garcia, R.; Dejong, F. J.; Sabnis, J. S.; Pribik, D. A.

1989-01-01

An analysis of Space Shuttle Main Engine high-pressure oxygen turbopump nozzle plug trajectories has been performed, using a Lagrangian method to track nozzle plug particles expelled from a turbine through a high Reynolds number flow in a turnaround duct with turning vanes. Axisymmetric and parametric analyses reveal that if nozzle plugs exited the turbine they would probably impact the LOX heat exchanger with impact velocities which are significantly less than the penetration velocity. The finding that only slight to moderate damage will result from nozzle plug failure in flight is supported by the results of a hot-fire engine test with induced nozzle plug failures.

Reactive Collisions and Final State Analysis in Hypersonic Flight Regime

DTIC Science & Technology

2016-09-13

Kelvin.[7] The gas-phase, surface reactions and energy transfer at these tempera- tures are essentially uncharacterized and the experimental methodologies...high temperatures (1000 to 20000 K) and compared with results from experimentally derived thermodynamics quantities from the NASA CEA (NASA Chemical...with a reproducing kernel Hilbert space (RKHS) method[13] combined with Legendre polynomials; (2) quasi classical trajectory (QCT) calculations to study

A space-time look at two-phase estimation for improved annual inventory estimates

Treesearch

Jay Breidt; Jean Opsomer; Xiyue Liao; Gretchen Moisen

2015-01-01

Over the past several years, three sets of new temporal remote sensing data have become available improving FIA’s ability to detect, characterize and forecast land cover changes. First, historic Landsat data has been processed for the conterminous US to provide disturbance history, agents of change, and fitted spectral trajectories annually over the last 30+ years at...

Equilibration of experimentally determined protein structures for molecular dynamics simulation

NASA Astrophysics Data System (ADS)

Walton, Emily B.; Vanvliet, Krystyn J.

2006-12-01

Preceding molecular dynamics simulations of biomolecular interactions, the molecule of interest is often equilibrated with respect to an initial configuration. This so-called equilibration stage is required because the input structure is typically not within the equilibrium phase space of the simulation conditions, particularly in systems as complex as proteins, which can lead to artifactual trajectories of protein dynamics. The time at which nonequilibrium effects from the initial configuration are minimized—what we will call the equilibration time—marks the beginning of equilibrium phase-space exploration. Note that the identification of this time does not imply exploration of the entire equilibrium phase space. We have found that current equilibration methodologies contain ambiguities that lead to uncertainty in determining the end of the equilibration stage of the trajectory. This results in equilibration times that are either too long, resulting in wasted computational resources, or too short, resulting in the simulation of molecular trajectories that do not accurately represent the physical system. We outline and demonstrate a protocol for identifying the equilibration time that is based on the physical model of Normal Mode Analysis. We attain the computational efficiency required of large-protein simulations via a stretched exponential approximation that enables an analytically tractable and physically meaningful form of the root-mean-square deviation of atoms comprising the protein. We find that the fitting parameters (which correspond to physical properties of the protein) fluctuate initially but then stabilize for increased simulation time, independently of the simulation duration or sampling frequency. We define the end of the equilibration stage—and thus the equilibration time—as the point in the simulation when these parameters attain constant values. Compared to existing methods, our approach provides the objective identification of the time at which the simulated biomolecule has entered an energetic basin. For the representative protein considered, bovine pancreatic trypsin inhibitor, existing methods indicate a range of 0.2-10ns of simulation until a local minimum is attained. Our approach identifies a substantially narrower range of 4.5-5.5ns , which will lead to a much more objective choice of equilibration time.

A position-dependent mass harmonic oscillator and deformed space

NASA Astrophysics Data System (ADS)

da Costa, Bruno G.; Borges, Ernesto P.

2018-04-01

We consider canonically conjugated generalized space and linear momentum operators x^ q and p^ q in quantum mechanics, associated with a generalized translation operator which produces infinitesimal deformed displacements controlled by a deformation parameter q. A canonical transformation (x ^ ,p ^ ) →(x^ q,p^ q ) leads the Hamiltonian of a position-dependent mass particle in usual space to another Hamiltonian of a particle with constant mass in a conservative force field of the deformed space. The equation of motion for the classical phase space (x, p) may be expressed in terms of the deformed (dual) q-derivative. We revisit the problem of a q-deformed oscillator in both classical and quantum formalisms. Particularly, this canonical transformation leads a particle with position-dependent mass in a harmonic potential to a particle with constant mass in a Morse potential. The trajectories in phase spaces (x, p) and (xq, pq) are analyzed for different values of the deformation parameter. Finally, we compare the results of the problem in classical and quantum formalisms through the principle of correspondence and the WKB approximation.

Characterization of Metering, Merging and Spacing Requirements for Future Trajectory-Based Operations

NASA Technical Reports Server (NTRS)

Johnson, Sally

2017-01-01

Trajectory-Based Operations (TBO) is one of the essential paradigm shifts in the NextGen transformation of the National Airspace System. Under TBO, aircraft are managed by 4-dimensional trajectories, and airborne and ground-based metering, merging, and spacing operations are key to managing those trajectories. This paper presents the results of a study of potential metering, merging, and spacing operations within a future TBO environment. A number of operational scenarios for tactical and strategic uses of metering, merging, and spacing are described, and interdependencies between concurrent tactical and strategic operations are identified.

Optimal trajectory planning of free-floating space manipulator using differential evolution algorithm

NASA Astrophysics Data System (ADS)

Wang, Mingming; Luo, Jianjun; Fang, Jing; Yuan, Jianping

2018-03-01

The existence of the path dependent dynamic singularities limits the volume of available workspace of free-floating space robot and induces enormous joint velocities when such singularities are met. In order to overcome this demerit, this paper presents an optimal joint trajectory planning method using forward kinematics equations of free-floating space robot, while joint motion laws are delineated with application of the concept of reaction null-space. Bézier curve, in conjunction with the null-space column vectors, are applied to describe the joint trajectories. Considering the forward kinematics equations of the free-floating space robot, the trajectory planning issue is consequently transferred to an optimization issue while the control points to construct the Bézier curve are the design variables. A constrained differential evolution (DE) scheme with premature handling strategy is implemented to find the optimal solution of the design variables while specific objectives and imposed constraints are satisfied. Differ from traditional methods, we synthesize null-space and specialized curve to provide a novel viewpoint for trajectory planning of free-floating space robot. Simulation results are presented for trajectory planning of 7 degree-of-freedom (DOF) kinematically redundant manipulator mounted on a free-floating spacecraft and demonstrate the feasibility and effectiveness of the proposed method.

Interplanetary Mission Design Handbook: Earth-to-Mars Mission Opportunities 2026 to 2045

NASA Technical Reports Server (NTRS)

Burke, Laura M.; Falck, Robert D.; McGuire, Melissa L.

2010-01-01

The purpose of this Mission Design Handbook is to provide trajectory designers and mission planners with graphical information about Earth to Mars ballistic trajectory opportunities for the years of 2026 through 2045. The plots, displayed on a departure date/arrival date mission space, show departure energy, right ascension and declination of the launch asymptote, and target planet hyperbolic arrival excess speed, V(sub infinity), for each launch opportunity. Provided in this study are two sets of contour plots for each launch opportunity. The first set of plots shows Earth to Mars ballistic trajectories without the addition of any deep space maneuvers. The second set of plots shows Earth to Mars transfer trajectories with the addition of deep space maneuvers, which further optimize the determined trajectories. The accompanying texts explains the trajectory characteristics, transfers using deep space maneuvers, mission assumptions and a summary of the minimum departure energy for each opportunity.

Equilibrium sampling by reweighting nonequilibrium simulation trajectories

NASA Astrophysics Data System (ADS)

Yang, Cheng; Wan, Biao; Xu, Shun; Wang, Yanting; Zhou, Xin

2016-03-01

Based on equilibrium molecular simulations, it is usually difficult to efficiently visit the whole conformational space of complex systems, which are separated into some metastable regions by high free energy barriers. Nonequilibrium simulations could enhance transitions among these metastable regions and then be applied to sample equilibrium distributions in complex systems, since the associated nonequilibrium effects can be removed by employing the Jarzynski equality (JE). Here we present such a systematical method, named reweighted nonequilibrium ensemble dynamics (RNED), to efficiently sample equilibrium conformations. The RNED is a combination of the JE and our previous reweighted ensemble dynamics (RED) method. The original JE reproduces equilibrium from lots of nonequilibrium trajectories but requires that the initial distribution of these trajectories is equilibrium. The RED reweights many equilibrium trajectories from an arbitrary initial distribution to get the equilibrium distribution, whereas the RNED has both advantages of the two methods, reproducing equilibrium from lots of nonequilibrium simulation trajectories with an arbitrary initial conformational distribution. We illustrated the application of the RNED in a toy model and in a Lennard-Jones fluid to detect its liquid-solid phase coexistence. The results indicate that the RNED sufficiently extends the application of both the original JE and the RED in equilibrium sampling of complex systems.

Equilibrium sampling by reweighting nonequilibrium simulation trajectories.

PubMed

Yang, Cheng; Wan, Biao; Xu, Shun; Wang, Yanting; Zhou, Xin

2016-03-01

Based on equilibrium molecular simulations, it is usually difficult to efficiently visit the whole conformational space of complex systems, which are separated into some metastable regions by high free energy barriers. Nonequilibrium simulations could enhance transitions among these metastable regions and then be applied to sample equilibrium distributions in complex systems, since the associated nonequilibrium effects can be removed by employing the Jarzynski equality (JE). Here we present such a systematical method, named reweighted nonequilibrium ensemble dynamics (RNED), to efficiently sample equilibrium conformations. The RNED is a combination of the JE and our previous reweighted ensemble dynamics (RED) method. The original JE reproduces equilibrium from lots of nonequilibrium trajectories but requires that the initial distribution of these trajectories is equilibrium. The RED reweights many equilibrium trajectories from an arbitrary initial distribution to get the equilibrium distribution, whereas the RNED has both advantages of the two methods, reproducing equilibrium from lots of nonequilibrium simulation trajectories with an arbitrary initial conformational distribution. We illustrated the application of the RNED in a toy model and in a Lennard-Jones fluid to detect its liquid-solid phase coexistence. The results indicate that the RNED sufficiently extends the application of both the original JE and the RED in equilibrium sampling of complex systems.

A SPACE TRAJECTORY RADIATION EXPOSURE PROCEDURE FOR CISLUNAR MISSIONS

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

Cranford, W.; Falkenbury, R.F.; Miller, R.A.

1962-07-31

The Space Trajectory Radiation Exposure Procedure (STREP) is designed for use in computing the timeintegrated spectra for any specified trajectory in cislunar space for any combination of the several components of space radiations. These components include Van Allen protons and electrons; solar-flare protons, electrons, heavy particles, and gamma radiation; cosmic protons and heavy particles; albedo neutrons, and aurora borealis gamma radiation. The program can also be used to calculate the accumulated dose behind a thin vehicle skin at any time after the start of the mission. The technique of interpolation for intermediate points along the prescribed space trajectory is describedmore » in detail. The method of representation of the space radiation data as input for the calculation of the dose and time-integrated spectra is discussed. (auth)« less

Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space

PubMed Central

An, Shuoming; Lv, Dingshun; del Campo, Adolfo; Kim, Kihwan

2016-01-01

The application of adiabatic protocols in quantum technologies is severely limited by environmental sources of noise and decoherence. Shortcuts to adiabaticity by counterdiabatic driving constitute a powerful alternative that speed up time-evolution while mimicking adiabatic dynamics. Here we report the experimental implementation of counterdiabatic driving in a continuous variable system, a shortcut to the adiabatic transport of a trapped ion in phase space. The resulting dynamics is equivalent to a ‘fast-motion video' of the adiabatic trajectory. The robustness of this protocol is shown to surpass that of competing schemes based on classical local controls and Fourier optimization methods. Our results demonstrate that shortcuts to adiabaticity provide a robust speedup of quantum protocols of wide applicability in quantum technologies. PMID:27669897

Determination of Stable-Unstable Regions of the Slosh Motion in Spinning Space Vehicle by Perturbation Technique

NASA Astrophysics Data System (ADS)

Kang, Jai Young

2005-12-01

The objectives of this study are to perform extensive analysis on internal mass motion for a wider parameter space and to provide suitable design criteria for a broader applicability for the class of spinning space vehicles. In order to examine the stability criterion determined by a perturbation method, some numerical simulations will be performed and compared at various parameter points. In this paper, Ince-Strutt diagram for determination of stable-unstable regions of the internal mass motion of the spinning thrusting space vehicle in terms of design parameters will be obtained by an analytical method. Also, phase trajectories of the motion will be obtained for various parameter values and their characteristics are compared.

Non-statistical effects in bond fission reactions of 1,2-difluoroethane

NASA Astrophysics Data System (ADS)

Schranz, Harold W.; Raff, Lionel M.; Thompson, Donald L.

1991-08-01

A microcanonical, classical variational transition-state theory based on the use of the efficient microcanonical sampling (EMS) procedure is applied to simple bond fission in 1,2-difluoroethane. Comparison is made with results of trajectory calculations performed on the same global potential-energy surface. Agreement between the statistical theory and trajectory results for CC CF and CH bond fissions is poor with differences as large as a factor of 125. Most importantly, at the lower energy studied, 6.0 eV, the statistical calculations predict considerably slower rates than those computed from trajectories. We conclude from these results that the statistical assumptions inherent in the transition-state theory method are not valid for 1,2-difluoroethane in spite of the fact that the total intramolecular energy transfer rate out of CH and CC normal and local modes is large relative to the bond fission rates. The IVR rate is not globally rapid and the trajectories do not access all of the energetically available phase space uniformly on the timescale of the reactions.

Rule-based programming paradigm: a formal basis for biological, chemical and physical computation.

PubMed

Krishnamurthy, V; Krishnamurthy, E V

1999-03-01

A rule-based programming paradigm is described as a formal basis for biological, chemical and physical computations. In this paradigm, the computations are interpreted as the outcome arising out of interaction of elements in an object space. The interactions can create new elements (or same elements with modified attributes) or annihilate old elements according to specific rules. Since the interaction rules are inherently parallel, any number of actions can be performed cooperatively or competitively among the subsets of elements, so that the elements evolve toward an equilibrium or unstable or chaotic state. Such an evolution may retain certain invariant properties of the attributes of the elements. The object space resembles Gibbsian ensemble that corresponds to a distribution of points in the space of positions and momenta (called phase space). It permits the introduction of probabilities in rule applications. As each element of the ensemble changes over time, its phase point is carried into a new phase point. The evolution of this probability cloud in phase space corresponds to a distributed probabilistic computation. Thus, this paradigm can handle tor deterministic exact computation when the initial conditions are exactly specified and the trajectory of evolution is deterministic. Also, it can handle probabilistic mode of computation if we want to derive macroscopic or bulk properties of matter. We also explain how to support this rule-based paradigm using relational-database like query processing and transactions.

An Overview of a Trajectory-Based Solution for En Route and Terminal Area Self-Spacing to Include Parallel Runway Operations

NASA Technical Reports Server (NTRS)

Abbott, Terence S.

2011-01-01

This paper presents an overview of an algorithm specifically designed to support NASA's Airborne Precision Spacing concept. This airborne self-spacing concept is trajectory-based, allowing for spacing operations prior to the aircraft being on a common path. This implementation provides the ability to manage spacing against two traffic aircraft, with one of these aircraft operating to a parallel dependent runway. Because this algorithm is trajectory-based, it also has the inherent ability to support required-time-of-arrival (RTA) operations

Simulation of Range Safety for the NASA Space Shuttle

NASA Technical Reports Server (NTRS)

Rabelo, Luis; Sepulveda, Jose; Compton, Jeppie; Turner, Robert

2005-01-01

This paper describes a simulation environment that seamlessly combines a number of safety and environmental models for the launch phase of a NASA Space Shuttle mission. The components of this simulation environment represent the different systems that must interact in order to determine the Expectation of casualties (E(sub c)) resulting from the toxic effects of the gas dispersion that occurs after a disaster affecting a Space Shuttle within 120 seconds of lift-off. The utilization of the Space Shuttle reliability models, trajectory models, weather dissemination systems, population models, amount and type of toxicants, gas dispersion models, human response functions to toxicants, and a geographical information system are all integrated to create this environment. This simulation environment can help safety managers estimate the population at risk in order to plan evacuation, make sheltering decisions, determine the resources required to provide aid and comfort, and mitigate damages in case of a disaster. This simulation environment may also be modified and used for the landing phase of a space vehicle but will not be discussed in this paper.

Inertial effects in suspension dynamics

NASA Astrophysics Data System (ADS)

Subramanian, Ganesh

2002-04-01

This work analyses the role of small but finite particle inertia on the microstructure of suspensions of heavy particles subjected to an external flow. The magnitude of particle inertia is characterized by the Stokes number (St), defined as the ratio of the inertial relaxation time of a particle to the flow time scale. Fluid inertia is neglected so that the fluid motion satisfies the quasi-steady Stokes equations. The statistics of the particles is governed by a Fokker-Planck equation in position and velocity space. For small St, a multiple scales formalism is developed to solve for the phase-space probability density of a single spherical Brownian particle in a linear flow. Though valid for an arbitrary flow field, the method fails for a spatially varying mass and drag coefficient. In all cases, however, a Chapman-Enskog-like formulation provides a valid multi-scale description of the dynamics both for a single Brownian particle and a suspension of interacting particles. For long times, the leading order solution simplifies to the product of a local Maxwellian in velocity space and a spatial density satisfying the Smoluchowski equation. The higher order corrections capture both short-time momentum relaxations and long-time deviations from the Maxwellian. The inertially corrected Smoluchowski equation includes a non-Fickian term at O( St). The pair problem is solved to O(St) for non-Brownian spherical particles in simple shear flow. In contrast to the zero inertia case, the relative trajectories of two particles are asymmetric. Open trajectories in the plane of shear suffer a downward displacement in the velocity gradient direction. The surface of the reference sphere 'repels' nearby trajectories that spiral out onto a new stable limit cycle in the shearing plane. This limit cycle acts as a local attractor and all in-plane trajectories from an initial offset of O(St½ ) or less approach the limit cycle. The topology of the off-plane trajectories is more complicated because the gradient displacement changes sign away from the plane of shear. The 'neutral' off-plane trajectory with zero net gradient displacement acts to separate trajectories spiralling onto contact from those that go off to infinity. The aforementioned asymmetry leads to a non-Newtonian rheology and self-diffusivities in the gradient and vorticity directions that scale as St2ln St and St2, respectively.

Mechanisms to deploy the two-stage IUS from the shuttle cargo bay

NASA Technical Reports Server (NTRS)

Haynie, H. T.

1980-01-01

The Inertial Upper Stage (IUS) is a two-stage or three-stage booster used to transport spacecraft from the space shuttle orbit to synchronous orbit or on an interplanetary trajectory. The mechanisms which were designed specifically to perform the two-stage IUS required functions while contained within the cargo bay of the space shuttle during the boost phase and while in a low Earth orbit are discussed. The requirements, configuration, and operation of the mechanisms are described, with particular emphasis on the tilt actuator and the mechanism for decoupling the actuators during boost to eliminate redundant load paths.

KSC-2009-5208

NASA Image and Video Library

2009-09-23

CAPE CANAVERAL, Fla. – Approaching rain clouds at dawn hover over Central Florida's east coast, effectively causing the scrub of the Space Tracking and Surveillance System - Demonstrator spacecraft from Launch Pad 17-B at Cape Canaveral Air Force Station. STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detection, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 24. Photo credit: NASA/Jack Pfaller

KSC-2009-5068

NASA Image and Video Library

2009-08-27

CAPE CANAVERAL, Fla. – The enclosed Space Tracking and Surveillance System – Demonstrators, or STSS-Demo, spacecraft arrives on Cape Canaveral Air Force Station's Launch Pad 17-B. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jack Pfaller

Limitations on the applicability of FODO lattices for electron cooling

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

Bertsche, K.J.

1997-09-01

Assuming a KV beam distribution (a uniform distribution over an elliptical region of transverse phase space), the beam envelop equations are shown, where X and Y are the transverse beam sizes, {kappa} is the lens strength, K is the generalized beam perveance, and {epsilon} is the beam emittance. If we further assume operation in a space-charge dominated regime, the right most term can be ignored in each equation. In this case, particle flow will be laminar, and the above equations not only describe the envelope of the beam, but also the trajectory of the outermost particles.

Consequences of using nonlinear particle trajectories to compute spatial diffusion coefficients. [for cosmic ray propagation in interstellar and interplanetary space

NASA Technical Reports Server (NTRS)

Goldstein, M. L.

1977-01-01

In a study of cosmic ray propagation in interstellar and interplanetary space, a perturbed orbit resonant scattering theory for pitch angle diffusion in a slab model of magnetostatic turbulence is slightly generalized and used to compute the diffusion coefficient for spatial propagation parallel to the mean magnetic field. This diffusion coefficient has been useful for describing the solar modulation of the galactic cosmic rays, and for explaining the diffusive phase in solar flares in which the initial anisotropy of the particle distribution decays to isotropy.

Space Shuttle Avionics: a Redundant IMU On-Board Checkout and Redundancy Management System

NASA Technical Reports Server (NTRS)

Mckern, R. A.; Brown, D. G.; Dove, D. W.; Gilmore, J. P.; Landey, M. E.; Musoff, H.; Amand, J. S.; Vincent, K. T., Jr.

1972-01-01

A failure detection and isolation philosophy applicable to multiple off-the-shelf gimbaled IMUs are discussed. The equations developed are implemented and evaluated with actual shuttle trajectory simulations. The results of these simulations are presented for both powered and unpowered flight phases and at operational levels of four, three, and two IMUs. A multiple system checkout philosophy is developed and simulation results presented. The final task develops a laboratory test plan and defines the hardware and software requirements to implement an actual multiple system and evaluate the interim study results for space shuttle application.

Analysis of the dependence of surfatron acceleration of electrons by an electromagnetic wave in space plasma on the particle momentum along the wave front

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

Erokhin, A. N., E-mail: nerokhin@mx.iki.rssi.ru; Zol’nikova, N. N.; Erokhin, N. S.

Based on the numerical solution of the nonlinear nonstationary second-order equation for the wave phase on the particle trajectory, the dynamics of surfatron acceleration of electrons by an electromagnetic wave propagating across the external magnetic field in space plasma is analyzed as a function of the electron momentum along the wave front. Numerical calculations show that, for strongly relativistic initial values of the electron momentum component along the wave front g{sub y}(0) (the other parameters of the problem being the same), electrons are trapped into the regime of ultrarelativistic surfatron acceleration within a certain interval of the initial wave phasemore » Ψ(0) on the particle trajectory. It is assumed in the calculations that vertical bar Ψ(0) vertical bar ≤ π. For strongly relativistic values of g{sub y}(0), electrons are immediately trapped by the wave for 19% of the initial values of the phase Ψ(0) (favorable phases). For the rest of the values of Ψ(0), trapping does not occur even at long times. This circumstance substantially simplifies estimations of the wave damping due to particle acceleration in subsequent calculations. The dynamics of the relativistic factor and the components of the electron velocity and momentum under surfatron acceleration is also analyzed. The obtained results are of interest for the development of modern concepts of possible mechanisms of generation of ultrarelativistic particle fluxes in relatively calm space plasma, as well as for correct interpretation of observational data on the fluxes of such particles and explanation of possible reasons for the deviation of ultrarelativistic particle spectra detected in the heliosphere from the standard power-law scalings and the relation of these variations to space weather and large-scale atmospheric processes similar to tropical cyclones.« less

Autonomous space processor for orbital debris

NASA Technical Reports Server (NTRS)

Ramohalli, Kumar; Marine, Micky; Colvin, James; Crockett, Richard; Sword, Lee; Putz, Jennifer; Woelfle, Sheri

1991-01-01

The development of an Autonomous Space Processor for Orbital Debris (ASPOD) was the goal. The nature of this craft, which will process, in situ, orbital debris using resources available in low Earth orbit (LEO) is explained. The serious problem of orbital debris is briefly described and the nature of the large debris population is outlined. The focus was on the development of a versatile robotic manipulator to augment an existing robotic arm, the incorporation of remote operation of the robotic arms, and the formulation of optimal (time and energy) trajectory planning algorithms for coordinated robotic arms. The mechanical design of the new arm is described in detail. The work envelope is explained showing the flexibility of the new design. Several telemetry communication systems are described which will enable the remote operation of the robotic arms. The trajectory planning algorithms are fully developed for both the time optimal and energy optimal problems. The time optimal problem is solved using phase plane techniques while the energy optimal problem is solved using dynamic programming.

Coordinated trajectory planning of dual-arm space robot using constrained particle swarm optimization

NASA Astrophysics Data System (ADS)

Wang, Mingming; Luo, Jianjun; Yuan, Jianping; Walter, Ulrich

2018-05-01

Application of the multi-arm space robot will be more effective than single arm especially when the target is tumbling. This paper investigates the application of particle swarm optimization (PSO) strategy to coordinated trajectory planning of the dual-arm space robot in free-floating mode. In order to overcome the dynamics singularities issue, the direct kinematics equations in conjunction with constrained PSO are employed for coordinated trajectory planning of dual-arm space robot. The joint trajectories are parametrized with Bézier curve to simplify the calculation. Constrained PSO scheme with adaptive inertia weight is implemented to find the optimal solution of joint trajectories while specific objectives and imposed constraints are satisfied. The proposed method is not sensitive to the singularity issue due to the application of forward kinematic equations. Simulation results are presented for coordinated trajectory planning of two kinematically redundant manipulators mounted on a free-floating spacecraft and demonstrate the effectiveness of the proposed method.

Trajectory planning of free-floating space robot using Particle Swarm Optimization (PSO)

NASA Astrophysics Data System (ADS)

Wang, Mingming; Luo, Jianjun; Walter, Ulrich

2015-07-01

This paper investigates the application of Particle Swarm Optimization (PSO) strategy to trajectory planning of the kinematically redundant space robot in free-floating mode. Due to the path dependent dynamic singularities, the volume of available workspace of the space robot is limited and enormous joint velocities are required when such singularities are met. In order to overcome this effect, the direct kinematics equations in conjunction with PSO are employed for trajectory planning of free-floating space robot. The joint trajectories are parametrized with the Bézier curve to simplify the calculation. Constrained PSO scheme with adaptive inertia weight is implemented to find the optimal solution of joint trajectories while specific objectives and imposed constraints are satisfied. The proposed method is not sensitive to the singularity issue due to the application of forward kinematic equations. Simulation results are presented for trajectory planning of 7 degree-of-freedom (DOF) redundant manipulator mounted on a free-floating spacecraft and demonstrate the effectiveness of the proposed method.

Rotation number of integrable symplectic mappings of the plane

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

Zolkin, Timofey; Nagaitsev, Sergei; Danilov, Viatcheslav

2017-04-11

Symplectic mappings are discrete-time analogs of Hamiltonian systems. They appear in many areas of physics, including, for example, accelerators, plasma, and fluids. Integrable mappings, a subclass of symplectic mappings, are equivalent to a Twist map, with a rotation number, constant along the phase trajectory. In this letter, we propose a succinct expression to determine the rotation number and present two examples. Similar to the period of the bounded motion in Hamiltonian systems, the rotation number is the most fundamental property of integrable maps and it provides a way to analyze the phase-space dynamics.

New type of synchronization of oscillators with hard excitation

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

Kovaleva, M. A., E-mail: margo.kovaleva@gmail.com; Manevich, L. I., E-mail: manevichleonid3@gmail.com; Pilipchuk, V. N.

2013-08-15

It is shown that stable limiting cycles corresponding to nonlinear beats with complete energy exchange between oscillators can exist in a system of two weakly coupled active oscillators (generators). The oscillatory regime of this type, which implements a new type of synchronization in an active system, is an alternative to the well-studied synchronization in a regime close to a nonlinear normal mode. In this case, the ranges of dissipative parameters corresponding to different types of synchronization do not intersect. The analytic description of attractors revealed in analysis is based on the concept of limiting phase trajectories, which was developed earliermore » by one of the authors for conservative systems. A transition (in the parametric space) from the complete energy exchange between oscillators to predominant localization of energy in one of the oscillators can be naturally described using this concept. The localized normal mode is an attractor in the range of parameters in which neither the limiting phase trajectory nor any of the collective normal modes is an attractor.« less

Tracking and data system support for the Mariner Mars 1971 mission. Prelaunch phase through first trajectory correction maneuver, volume 1

NASA Technical Reports Server (NTRS)

Laeser, R. P.; Textor, G. P.; Kelly, L. B.; Kelly, M.

1972-01-01

The DSN command system provided the capability to enter commands in a computer at the deep space stations for transmission to the spacecraft. The high-rate telemetry system operated at 16,200 bits/sec. This system will permit return to DSS 14 of full-resolution television pictures from the spacecraft tape recorder, plus the other science experiment data, during the two playback periods of each Goldstone pass planned for each corresponding orbit. Other features included 4800 bits/sec modem high-speed data lines from all deep space stations to Space Flight Operations Facility (SFOF) and the Goddard Space Flight Center, as well as 50,000 bits/sec wideband data lines from DSS 14 to the SFOF, thus providing the capability for data flow of two 16,200 bits/sec high-rate telemetry data streams in real time. The TDS performed prelaunch training and testing and provided support for the Mariner Mars 1971/Mission Operations System training and testing. The facilities of the ETR, DSS 71, and stations of the MSFN provided flight support coverage at launch and during the near-earth phase. The DSSs 12, 14, 41, and 51 of the DSN provided the deep space phase support from 30 May 1971 through 4 June 1971.

EDIN design study alternate space shuttle booster replacement concepts. Volume 2: Design simulation results

NASA Technical Reports Server (NTRS)

Demakes, P. T.; Hirsch, G. N.; Stewart, W. A.; Glatt, C. R.

1976-01-01

Historical weight estimating relationships were developed for the liquid rocket booster (LRB) using Saturn technology, and modified as required to support the EDIN05 study. Mission performance was computed using February 1975 shuttle configuration groundrules to allow reasonable comparison of the existing shuttle with the EDIN05 designs. The launch trajectory was constrained to pass through both the RTLS/AOA and main engine cut-off points. Performance analysis was based on a point design trajectory model which optimized initial tilt rate and exo-atmospheric pitch profile. A gravity turn was employed during the boost phase in place of the shuttle angle-of-attack profile. Engine throttling add/or shutdown was used to constrain dynamic pressure and/or longitudinal acceleration where necessary.

Tracking and data system support for the Pioneer project. Volume 1: Pioneer 10-prelaunch planning through second trajectory correction, 4 December 1969 - 1 April 1972

NASA Technical Reports Server (NTRS)

Siegmeth, A. J.; Purdue, R. E.; Ryan, R. E.

1973-01-01

The tracking and data system support of the launch, near-earth, and deep space phases of the Pioneer 10 mission, which sent a Pioneer spacecraft into a flyby of Jupiter that would eventually allow the spacecraft to escape the solar system is discussed. The support through the spacecraft's second trajectory correction is reported. During this period, scientific instruments aboard the spacecraft registered information relative to interplanetary particles and fields, and radiometric data generated by the network continued to improve knowledge of the celestial mechanics of the solar system. In addition to network support activity detail, network performance and special support activities are covered.

Hierarchical relaxation dynamics in a tilted two-band Bose-Hubbard model

NASA Astrophysics Data System (ADS)

Cosme, Jayson G.

2018-04-01

We numerically examine slow and hierarchical relaxation dynamics of interacting bosons described by a tilted two-band Bose-Hubbard model. The system is found to exhibit signatures of quantum chaos within the spectrum and the validity of the eigenstate thermalization hypothesis for relevant physical observables is demonstrated for certain parameter regimes. Using the truncated Wigner representation in the semiclassical limit of the system, dynamics of relevant observables reveal hierarchical relaxation and the appearance of prethermalized states is studied from the perspective of statistics of the underlying mean-field trajectories. The observed prethermalization scenario can be attributed to different stages of glassy dynamics in the mode-time configuration space due to dynamical phase transition between ergodic and nonergodic trajectories.

Mars entry-to-landing trajectory optimization and closed loop guidance

NASA Technical Reports Server (NTRS)

Ilgen, Marc R.; Manning, Raymund A.; Cruz, Manuel I.

1991-01-01

The guidance strategy of the Mars Rover Sample Return mission is presented in detail. Aeromaneuver versus aerobrake trades are examined, and an aerobrake analysis is presented which takes into account targeting, guidance, flight control, trajectory profile, delivery accuracy. An aeromaneuver analysis is given which includes the entry corridor, maneuver footprint, guidance, preentry phase, constant drag phase, equilibrium guide phase, variable drag phase, influence of trajectory profile on the entry flight loads, parachute deployment conditions and strategies, and landing accuracy. The Mars terminal descent phase is analyzed.

Allowable Trajectory Variations for Space Shuttle Orbiter Entry-Aeroheating CFD

NASA Technical Reports Server (NTRS)

Wood, William A.; Alter, Stephen J.

2008-01-01

Reynolds-number criteria are developed for acceptable variations in Space Shuttle Orbiter entry trajectories for use in computational aeroheating analyses. The criteria determine if an existing computational fluid dynamics solution for a particular trajectory can be extrapolated to a different trajectory. The criteria development begins by estimating uncertainties for seventeen types of computational aeroheating data, such as boundary layer thickness, at exact trajectory conditions. For each type of datum, the allowable uncertainty contribution due to trajectory variation is set to be half of the value of the estimated exact-trajectory uncertainty. Then, for the twelve highest-priority datum types, Reynolds-number relations between trajectory variation and output uncertainty are determined. From these relations the criteria are established for the maximum allowable trajectory variations. The most restrictive criterion allows a 25% variation in Reynolds number at constant Mach number between trajectories.

Mixed semiclassical-classical propagators for the Wigner phase space representation

NASA Astrophysics Data System (ADS)

Koda, Shin-ichi

2016-04-01

We formulate mixed semiclassical-classical (SC-Cl) propagators by adding a further approximation to the phase-space SC propagators, which have been formulated in our previous paper [S. Koda, J. Chem. Phys. 143, 244110 (2015)]. We first show that the stationary phase approximation over the operation of the phase-space van Vleck propagator on initial distribution functions results in the classical mechanical time propagation. Then, after dividing the degrees of freedom (DOFs) of the total system into the semiclassical DOFs and the classical DOFs, the SC-Cl van Vleck propagator and the SC-Cl Herman-Kluk (HK) propagator are derived by performing the stationary phase approximation only with respect to the classical DOFs. These SC-Cl propagators are naturally decomposed to products of the phase-space SC propagators and the classical mechanical propagators when the system does not have any interaction between the semiclassical and the classical DOFs. In addition, we also numerically compare the original phase-space HK (full HK) propagator and the SC-Cl HK propagator in terms of accuracy and efficiency to find that the accuracy of the SC-Cl HK propagator can be comparable to that of the full HK propagator although the latter is more accurate than the former in general. On the other hand, we confirm that the convergence speed of the SC-Cl HK propagator is faster than that of the full HK propagator. The present numerical tests indicate that the SC-Cl HK propagator can be more accurate than the full HK propagator when they use a same and finite number of classical trajectories due to the balance of the accuracy and the efficiency.

Mixed semiclassical-classical propagators for the Wigner phase space representation.

PubMed

Koda, Shin-Ichi

2016-04-21

We formulate mixed semiclassical-classical (SC-Cl) propagators by adding a further approximation to the phase-space SC propagators, which have been formulated in our previous paper [S. Koda, J. Chem. Phys. 143, 244110 (2015)]. We first show that the stationary phase approximation over the operation of the phase-space van Vleck propagator on initial distribution functions results in the classical mechanical time propagation. Then, after dividing the degrees of freedom (DOFs) of the total system into the semiclassical DOFs and the classical DOFs, the SC-Cl van Vleck propagator and the SC-Cl Herman-Kluk (HK) propagator are derived by performing the stationary phase approximation only with respect to the classical DOFs. These SC-Cl propagators are naturally decomposed to products of the phase-space SC propagators and the classical mechanical propagators when the system does not have any interaction between the semiclassical and the classical DOFs. In addition, we also numerically compare the original phase-space HK (full HK) propagator and the SC-Cl HK propagator in terms of accuracy and efficiency to find that the accuracy of the SC-Cl HK propagator can be comparable to that of the full HK propagator although the latter is more accurate than the former in general. On the other hand, we confirm that the convergence speed of the SC-Cl HK propagator is faster than that of the full HK propagator. The present numerical tests indicate that the SC-Cl HK propagator can be more accurate than the full HK propagator when they use a same and finite number of classical trajectories due to the balance of the accuracy and the efficiency.

A six degree of freedom, plume-fuel optimal trajectory planner for spacecraft proximity operations using an A* node search. M.S. Thesis - MIT

NASA Technical Reports Server (NTRS)

Jackson, Mark Charles

1994-01-01

Spacecraft proximity operations are complicated by the fact that exhaust plume impingement from the reaction control jets of space vehicles can cause structural damage, contamination of sensitive arrays and instruments, or attitude misalignment during docking. The occurrence and effect of jet plume impingement can be reduced by planning approach trajectories with plume effects considered. An A* node search is used to find plume-fuel optimal trajectories through a discretized six dimensional attitude-translation space. A plume cost function which approximates jet plume isopressure envelopes is presented. The function is then applied to find relative costs for predictable 'trajectory altering' firings and unpredictable 'deadbanding' firings. Trajectory altering firings are calculated by running the spacecraft jet selection algorithm and summing the cost contribution from each jet fired. A 'deadbanding effects' function is defined and integrated to determine the potential for deadbanding impingement along candidate trajectories. Plume costs are weighed against fuel costs in finding the optimal solution. A* convergence speed is improved by solving approach trajectory problems in reverse time. Results are obtained on a high fidelity space shuttle/space station simulation. Trajectory following is accomplished by a six degree of freedom autopilot. Trajectories planned with, and without, plume costs are compared in terms of force applied to the target structure.

Trajectory Design for the Transiting Exoplanet Survey Satellite (TESS)

NASA Technical Reports Server (NTRS)

Dichmann, Donald J.; Parker, Joel; Williams, Trevor; Mendelsohn, Chad

2014-01-01

The Transiting Exoplanet Survey Satellite (TESS) is a National Aeronautics and Space Administration (NASA) mission launching in 2017. TESS will travel in a highly eccentric orbit around Earth, with initial perigee radius near 17 Earth radii (Re) and apogee radius near 59 Re. The orbit period is near 2:1 resonance with the Moon, with apogee nearly 90 degrees out-of-phase with the Moon, in a configuration that has been shown to be operationally stable. TESS will execute phasing loops followed by a lunar flyby, with a final maneuver to achieve 2:1 resonance with the Moon. The goals of a resonant orbit with long-term stability, short eclipses and limited oscillations of perigee present significant challenges to the trajectory design. To rapidly assess launch opportunities, we adapted the SWM76 launch window tool to assess the TESS mission constraints. To understand the long-term dynamics of such a resonant orbit in the Earth-Moon system we employed Dynamical Systems Theory in the Circular Restricted 3-Body Problem (CR3BP). For precise trajectory analysis we use a high-fidelity model and multiple shooting in the General Mission Analysis Tool (GMAT) to optimize the maneuver delta-V and meet mission constraints. Finally we describe how the techniques we have developed can be applied to missions with similar requirements.

An Overview of a Trajectory-Based Solution for En Route and Terminal Area Self-Spacing: Third Revision

NASA Technical Reports Server (NTRS)

Abbott, Terence S.

2012-01-01

This paper presents an overview of the third major revision to an algorithm specifically designed to support NASA's Airborne Precision Spacing concept. This algorithm is referred to as the Airborne Spacing for Terminal Arrival Routes version 11 (ASTAR11). This airborne self-spacing concept is trajectory-based, allowing for spacing operations prior to the aircraft being on a common path. Because this algorithm is trajectory-based, it also has the inherent ability to support required time-of-arrival (RTA) operations. This algorithm was also designed specifically to support a standalone, non-integrated implementation in the spacing aircraft.

Zero-Point Energy Constraint for Unimolecular Dissociation Reactions. Giving Trajectories Multiple Chances To Dissociate Correctly.

PubMed

Paul, Amit K; Hase, William L

2016-01-28

A zero-point energy (ZPE) constraint model is proposed for classical trajectory simulations of unimolecular decomposition and applied to CH4* → H + CH3 decomposition. With this model trajectories are not allowed to dissociate unless they have ZPE in the CH3 product. If not, they are returned to the CH4* region of phase space and, if necessary, given additional opportunities to dissociate with ZPE. The lifetime for dissociation of an individual trajectory is the time it takes to dissociate with ZPE in CH3, including multiple possible returns to CH4*. With this ZPE constraint the dissociation of CH4* is exponential in time as expected for intrinsic RRKM dynamics and the resulting rate constant is in good agreement with the harmonic quantum value of RRKM theory. In contrast, a model that discards trajectories without ZPE in the reaction products gives a CH4* → H + CH3 rate constant that agrees with the classical and not quantum RRKM value. The rate constant for the purely classical simulation indicates that anharmonicity may be important and the rate constant from the ZPE constrained classical trajectory simulation may not represent the complete anharmonicity of the RRKM quantum dynamics. The ZPE constraint model proposed here is compared with previous models for restricting ZPE flow in intramolecular dynamics, and connecting product and reactant/product quantum energy levels in chemical dynamics simulations.

Trajectories and traversal times in quantum tunneling

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

Huang, Zhi Hong.

1989-01-01

The classical concepts of trajectories and traversal times applied to quantum tunneling are discussed. By using the Wentzel-Kramers-Brillouin approximation, it is found that in a forbidden region of a multidimensional space the wave function can be described by two sets of trajectories, or equivalently by two sets of wave fronts. The trajectories belonging to different sets are mutually orthogonal. An extended Huygens construction is proposed to determine these wave fronts and trajectories. In contrast to the classical results in the allowed region, these trajectories couple to each other. However, if the incident wave is normal to the turning surface, themore » trajectories are found to be independent and can be determined by Newton's equations of motion with inverted potential and energy. The multidimensional tunneling theory is then applied to the scanning tunneling microscope to calculate the current density distribution and to derive the expressions for the lateral resolution and the surface corrugation amplitude. The traversal time in quantum tunneling, i.e. tunneling time, is found to depend on model calculations and simulations. Computer simulation of a wave packet tunneling through a square barrier is performed. Several approaches, including the phase method, Larmor clock, and time-dependent barrier model, are investigated. For a square barrier, two characteristic times are found: One is equal to the barrier width divided by the magnitude of the imaginary velocity; the other is equal to the decay length divided by the incident velocity. It is believed that the tunneling time can only be defined operationally.« less

Feature space trajectory for distorted-object classification and pose estimation in synthetic aperture radar

NASA Astrophysics Data System (ADS)

Casasent, David P.; Shenoy, Rajesh

1997-10-01

Classification and pose estimation of distorted input objects are considered. The feature space trajectory representation of distorted views of an object is used with a new eigenfeature space. For a distorted input object, the closest trajectory denotes the class of the input and the closest line segment on it denotes its pose. If an input point is too far from a trajectory, it is rejected as clutter. New methods for selecting Fukunaga-Koontz discriminant vectors, the number of dominant eigenvectors per class and for determining training, and test set compatibility are presented.

An Overview of a Trajectory-Based Solution for En Route and Terminal Area Self-Spacing: Fourth Revision

NASA Technical Reports Server (NTRS)

Abbott, Terence S.

2013-01-01

This paper presents an overview of the fourth major revision to an algorithm specifically designed to support NASA's Airborne Precision Spacing concept. This airborne self-spacing concept is trajectory-based, allowing for spacing operations prior to the aircraft being on a common path. Because this algorithm is trajectory-based, it also has the inherent ability to support required-time-of-arrival (RTA) operations. This algorithm was also designed specifically to support a standalone, non-integrated implementation in the spacing aircraft. Revisions to this algorithm were based on a change to the expected operational environment.

Trajectory data analyses for pedestrian space-time activity study.

PubMed

Qi, Feng; Du, Fei

2013-02-25

It is well recognized that human movement in the spatial and temporal dimensions has direct influence on disease transmission(1-3). An infectious disease typically spreads via contact between infected and susceptible individuals in their overlapped activity spaces. Therefore, daily mobility-activity information can be used as an indicator to measure exposures to risk factors of infection. However, a major difficulty and thus the reason for paucity of studies of infectious disease transmission at the micro scale arise from the lack of detailed individual mobility data. Previously in transportation and tourism research detailed space-time activity data often relied on the time-space diary technique, which requires subjects to actively record their activities in time and space. This is highly demanding for the participants and collaboration from the participants greatly affects the quality of data(4). Modern technologies such as GPS and mobile communications have made possible the automatic collection of trajectory data. The data collected, however, is not ideal for modeling human space-time activities, limited by the accuracies of existing devices. There is also no readily available tool for efficient processing of the data for human behavior study. We present here a suite of methods and an integrated ArcGIS desktop-based visual interface for the pre-processing and spatiotemporal analyses of trajectory data. We provide examples of how such processing may be used to model human space-time activities, especially with error-rich pedestrian trajectory data, that could be useful in public health studies such as infectious disease transmission modeling. The procedure presented includes pre-processing, trajectory segmentation, activity space characterization, density estimation and visualization, and a few other exploratory analysis methods. Pre-processing is the cleaning of noisy raw trajectory data. We introduce an interactive visual pre-processing interface as well as an automatic module. Trajectory segmentation(5) involves the identification of indoor and outdoor parts from pre-processed space-time tracks. Again, both interactive visual segmentation and automatic segmentation are supported. Segmented space-time tracks are then analyzed to derive characteristics of one's activity space such as activity radius etc. Density estimation and visualization are used to examine large amount of trajectory data to model hot spots and interactions. We demonstrate both density surface mapping(6) and density volume rendering(7). We also include a couple of other exploratory data analyses (EDA) and visualizations tools, such as Google Earth animation support and connection analysis. The suite of analytical as well as visual methods presented in this paper may be applied to any trajectory data for space-time activity studies.

Simulations of phase space distributions of storm time proton ring current

NASA Technical Reports Server (NTRS)

Chen, Margaret W.; Lyons, Larry R.; Schulz, Michael

1994-01-01

We use results of guiding-center simulations of ion transport to map phase space densities of the stormtime proton ring current. We model a storm as a sequence of substorm-associated enhancements in the convection electric field. Our pre-storm phase space distribution is an analytical solution to a steady-state transport model in which quiet-time radial diffusion balances charge exchange. This pre-storm phase space spectra at L approximately 2 to 4 reproduce many of the features found in observed quiet-time spectra. Using results from simulations of ion transport during model storms having main phases of 3, 6, and 12 hr, we map phase space distributions from the pre-storm distribution in accordance with Liouville's theorem. We find stormtime enhancements in the phase space densities at energies E approximately 30-160 keV for L approximately 2.5 to 4. These enhancements agree well with the observed stormtime ring current. For storms with shorter main phases (approximately 3 hr), the enhancements are caused mainly by the trapping of ions injected from open night side trajectories, and diffusive transport of higher-energy (greater than or approximately 160 keV) ions contributes little to the stormtime ring current. However, the stormtime ring current is augmented also by the diffusive transport of higher-energy ions (E greater than or approximately 160 keV) durinng stroms having longer main phases (greater than or approximately 6 hr). In order to account for the increase in Dst associated with the formation of the stormtime ring current, we estimate the enhancement in particle-energy content that results from stormtime ion transport in the equatorial magnetosphere. We find that transport alone cannot account for the entire increase in absolute value of Dst typical of a major storm. However, we can account for the entire increase in absolute value of Dst by realistically increasing the stormtime outer boundary value of the phase space density relative to the quiet-time value. We compute the magnetic field produced by the ring current itself and find that radial profiles of the magnetic field depression resemble those obtained from observational data.

Chaos in War: Is It Present and What Does It Mean?

DTIC Science & Technology

1994-06-01

the Poincare map. The results of this work indicated that chaos is, in fact, present in warfare. The implications of this result include IV...confirmed the validity of our software and provided us with the Poincare maps and the power spectrum. LTC Pentland of the School for Advanced...nearly identical initial conditions for the logistics equation 20 8 . Poincare map 22 9. Phase-space trajectories of chaotic systems 23 10

Ascent trajectory dispersion analysis for WTR heads-up space shuttle trajectory

NASA Technical Reports Server (NTRS)

1986-01-01

The results of a Space Transportation System ascent trajectory dispersion analysis are discussed. The purpose is to provide critical trajectory parameter values for assessing the Space Shuttle in a heads-up configuration launched from the Western Test Range (STR). This analysis was conducted using a trajectory profile based on a launch from the WTR in December. The analysis consisted of the following steps: (1) nominal trajectories were simulated under the conditions as specified by baseline reference mission guidelines; (2) dispersion trajectories were simulated using predetermined parametric variations; (3) requirements for a system-related composite trajectory were determined by a root-sum-square (RSS) analysis of the positive deviations between values of the aerodynamic heating indicator (AHI) generated by the dispersion and nominal trajectories; (4) using the RSS assessment as a guideline, the system related composite trajectory was simulated by combinations of dispersion parameters which represented major contributors; (5) an assessment of environmental perturbations via a RSS analysis was made by the combination of plus or minus 2 sigma atmospheric density variation and 95% directional design wind dispersions; (6) maximum aerodynamic heating trajectories were simulated by variation of dispersion parameters which would emulate the summation of the system-related RSS and environmental RSS values of AHI. The maximum aerodynamic heating trajectories were simulated consistent with the directional winds used in the environmental analysis.

Adaptive density trajectory cluster based on time and space distance

NASA Astrophysics Data System (ADS)

Liu, Fagui; Zhang, Zhijie

2017-10-01

There are some hotspot problems remaining in trajectory cluster for discovering mobile behavior regularity, such as the computation of distance between sub trajectories, the setting of parameter values in cluster algorithm and the uncertainty/boundary problem of data set. As a result, based on the time and space, this paper tries to define the calculation method of distance between sub trajectories. The significance of distance calculation for sub trajectories is to clearly reveal the differences in moving trajectories and to promote the accuracy of cluster algorithm. Besides, a novel adaptive density trajectory cluster algorithm is proposed, in which cluster radius is computed through using the density of data distribution. In addition, cluster centers and number are selected by a certain strategy automatically, and uncertainty/boundary problem of data set is solved by designed weighted rough c-means. Experimental results demonstrate that the proposed algorithm can perform the fuzzy trajectory cluster effectively on the basis of the time and space distance, and obtain the optimal cluster centers and rich cluster results information adaptably for excavating the features of mobile behavior in mobile and sociology network.

NASA Advanced Concepts Office, Earth-To-Orbit Team Design Process and Tools

NASA Technical Reports Server (NTRS)

Waters, Eric D.; Creech, Dennis M.; Garcia, Jessica; Threet, Grady E., Jr.; Phillips, Alan

2012-01-01

The Earth-to-Orbit Team (ETO) of the Advanced Concepts Office (ACO) at NASA Marshall Space Flight Center (MSFC) is considered the pre-eminent go-to group for pre-phase A and phase A concept definition. Over the past several years the ETO team has evaluated thousands of launch vehicle concept variations for a significant number of studies including agency-wide efforts such as the Exploration Systems Architecture Study (ESAS), Constellation, Heavy Lift Launch Vehicle (HLLV), Augustine Report, Heavy Lift Propulsion Technology (HLPT), Human Exploration Framework Team (HEFT), and Space Launch System (SLS). The ACO ETO Team is called upon to address many needs in NASA s design community; some of these are defining extremely large trade-spaces, evaluating advanced technology concepts which have not been addressed by a large majority of the aerospace community, and the rapid turn-around of highly time critical actions. It is the time critical actions, those often limited by schedule or little advanced warning, that have forced the five member ETO team to develop a design process robust enough to handle their current output level in order to meet their customer s needs. Based on the number of vehicle concepts evaluated over the past year this output level averages to four completed vehicle concepts per day. Each of these completed vehicle concepts includes a full mass breakdown of the vehicle to a tertiary level of subsystem components and a vehicle trajectory analysis to determine optimized payload delivery to specified orbital parameters, flight environments, and delta v capability. A structural analysis of the vehicle to determine flight loads based on the trajectory output, material properties, and geometry of the concept is also performed. Due to working in this fast-paced and sometimes rapidly changing environment, the ETO Team has developed a finely tuned process to maximize their delivery capabilities. The objective of this paper is to describe the interfaces between the three disciplines used in the design process: weights and sizing, trajectory, and structural analysis. The tools used to perform such analysis are INtegrated Rocket Sizing (INTROS), Program to Optimize Simulated Trajectories (POST), and Launch Vehicle Analysis (LVA) respectively. The methods each discipline uses to streamline their particular part of the design process will also be discussed.

NASA Advanced Concepts Office, Earth-To-Orbit Team Design Process and Tools

NASA Technical Reports Server (NTRS)

Waters, Eric D.; Garcia, Jessica; Threet, Grady E., Jr.; Phillips, Alan

2013-01-01

The Earth-to-Orbit Team (ETO) of the Advanced Concepts Office (ACO) at NASA Marshall Space Flight Center (MSFC) is considered the pre-eminent "go-to" group for pre-phase A and phase A concept definition. Over the past several years the ETO team has evaluated thousands of launch vehicle concept variations for a significant number of studies including agency-wide efforts such as the Exploration Systems Architecture Study (ESAS), Constellation, Heavy Lift Launch Vehicle (HLLV), Augustine Report, Heavy Lift Propulsion Technology (HLPT), Human Exploration Framework Team (HEFT), and Space Launch System (SLS). The ACO ETO Team is called upon to address many needs in NASA's design community; some of these are defining extremely large trade-spaces, evaluating advanced technology concepts which have not been addressed by a large majority of the aerospace community, and the rapid turn-around of highly time critical actions. It is the time critical actions, those often limited by schedule or little advanced warning, that have forced the five member ETO team to develop a design process robust enough to handle their current output level in order to meet their customer's needs. Based on the number of vehicle concepts evaluated over the past year this output level averages to four completed vehicle concepts per day. Each of these completed vehicle concepts includes a full mass breakdown of the vehicle to a tertiary level of subsystem components and a vehicle trajectory analysis to determine optimized payload delivery to specified orbital parameters, flight environments, and delta v capability. A structural analysis of the vehicle to determine flight loads based on the trajectory output, material properties, and geometry of the concept is also performed. Due to working in this fast-paced and sometimes rapidly changing environment, the ETO Team has developed a finely tuned process to maximize their delivery capabilities. The objective of this paper is to describe the interfaces between the three disciplines used in the design process: weights and sizing, trajectory, and structural analysis. The tools used to perform such analysis are INtegrated Rocket Sizing (INTROS), Program to Optimize Simulated Trajectories (POST), and Launch Vehicle Analysis (LVA) respectively. The methods each discipline uses to streamline their particular part of the design process will also be discussed.

Dynamics and control of robot for capturing objects in space

NASA Astrophysics Data System (ADS)

Huang, Panfeng

Space robots are expected to perform intricate tasks in future space services, such as satellite maintenance, refueling, and replacing the orbital replacement unit (ORU). To realize these missions, the capturing operation may not be avoided. Such operations will encounter some challenges because space robots have some unique characteristics unfound on ground-based robots, such as, dynamic singularities, dynamic coupling between manipulator and space base, limited energy supply and working without a fixed base, and so on. In addition, since contacts and impacts may not be avoided during capturing operation. Therefore, dynamics and control problems of space robot for capturing objects are significant research topics if the robots are to be deployed for the space services. A typical servicing operation mainly includes three phases: capturing the object, berthing and docking the object, then repairing the target. Therefore, this thesis will focus on resolving some challenging problems during capturing the object, berthing and docking, and so on. In this thesis, I study and analyze the dynamics and control problems of space robot for capturing objects. This work has potential impact in space robotic applications. I first study the contact and impact dynamics of space robot and objects. I specifically focus on analyzing the impact dynamics and mapping the relationship of influence and speed. Then, I develop the fundamental theory for planning the minimum-collision based trajectory of space robot and designing the configuration of space robot at the moment of capture. To compensate for the attitude of the space base during the capturing approach operation, a new balance control concept which can effectively balance the attitude of the space base using the dynamic couplings is developed. The developed balance control concept helps to understand of the nature of space dynamic coupling, and can be readily applied to compensate or minimize the disturbance to the space base. After capturing the object, the space robot must complete the following two tasks: one is to berth the object, and the other is to re-orientate the attitude of the whole robot system for communication and power supply. Therefore, I propose a method to accomplish these two tasks simultaneously using manipulator motion only. The ultimate goal of space services is to realize the capture and manipulation autonomously. Therefore, I propose an affective approach based on learning human skill to track and capture the objects automatically in space. With human-teaching demonstration, the space robot is able to learn and abstract human tracking and capturing skill using an efficient neural-network learning architecture that combines flexible Cascade Neural Networks with Node Decoupled Extended Kalman Filtering (CNN-NDEKF). The simulation results attest that this approach is useful and feasible in tracking trajectory planning and capturing of space robot. Finally I propose a novel approach based on Genetic Algorithms (GAs) to optimize the approach trajectory of space robots in order to realize effective and stable operations. I complete the minimum-torque path planning in order to save the limited energy in space, and design the minimum jerk trajectory for the stabilization of the space manipulator and its space base. These optimal algorithms are very important and useful for the application of space robot.

A study of numerical methods for computing reentry trajectories for shuttle-type space vehicles

NASA Technical Reports Server (NTRS)

1972-01-01

The reuseable exterior insulation system (REI) is studied to determine the optimal reentry trajectory for a space shuttle, which minimizes the heat input to the fuselage. The REI is composed of titanium, covered by a surface insulation material. The method of perturbation functions was used to generate the trajectories, and proved to be an effective technique for generating families of solutions, once an initial trajectory has been obtained.

Superintegrability of the Fock-Darwin system

NASA Astrophysics Data System (ADS)

Drigho-Filho, E.; Kuru, Ş.; Negro, J.; Nieto, L. M.

2017-08-01

The Fock-Darwin system is analyzed from the point of view of its symmetry properties in the quantum and classical frameworks. The quantum Fock-Darwin system is known to have two sets of ladder operators, a fact which guarantees its solvability. We show that for rational values of the quotient of two relevant frequencies, this system is superintegrable, the quantum symmetries being responsible for the degeneracy of the energy levels. These symmetries are of higher order and close a polynomial algebra. In the classical case, the ladder operators are replaced by ladder functions and the symmetries by constants of motion. We also prove that the rational classical system is superintegrable and its trajectories are closed. The constants of motion are also generators of symmetry transformations in the phase space that have been integrated for some special cases. These transformations connect different trajectories with the same energy. The coherent states of the quantum superintegrable system are found and they reproduce the closed trajectories of the classical one.

The design of transfer trajectory for Ivar asteroid exploration mission

NASA Astrophysics Data System (ADS)

Qiao, Dong; Cui, Hutao; Cui, Pingyuan

2009-12-01

An impending demand for exploring the small bodies, such as the comets and the asteroids, envisioned the Chinese Deep Space exploration mission to the Near Earth asteroid Ivar. A design and optimal method of transfer trajectory for asteroid Ivar is discussed in this paper. The transfer trajectory for rendezvous with asteroid Ivar is designed by means of Earth gravity assist with deep space maneuver (Delta-VEGA) technology. A Delta-VEGA transfer trajectory is realized by several trajectory segments, which connect the deep space maneuver and swingby point. Each trajectory segment is found by solving Lambert problem. Through adjusting deep maneuver and arrival time, the match condition of swingby is satisfied. To reduce the total mission velocity increments further, a procedure is developed which minimizes total velocity increments for this scheme of transfer trajectory for asteroid Ivar. The trajectory optimization problem is solved with a quasi-Newton algorithm utilizing analytic first derivatives, which are derived from the transversality conditions associated with the optimization formulation and primer vector theory. The simulation results show the scheme for transfer trajectory causes C3 and total velocity increments decrease of 48.80% and 13.20%, respectively.

Radio science ground data system for the Voyager-Neptune encounter, part 1

NASA Technical Reports Server (NTRS)

Kursinski, E. R.; Asmar, S. W.

1991-01-01

The Voyager radio science experiments at Neptune required the creation of a ground data system array that includes a Deep Space Network complex, the Parkes Radio Observatory, and the Usuda deep space tracking station. The performance requirements were based on experience with the previous Voyager encounters, as well as the scientific goals at Neptune. The requirements were stricter than those of the Uranus encounter because of the need to avoid the phase-stability problems experienced during that encounter and because the spacecraft flyby was faster and closer to the planet than previous encounters. The primary requirement on the instrument was to recover the phase and amplitude of the S- and X-band (2.3 and 8.4 GHz) signals under the dynamic conditions encountered during the occultations. The primary receiver type for the measurements was open loop with high phase-noise and frequency stability performance. The receiver filter bandwidth was predetermined based on the spacecraft's trajectory and frequency uncertainties.

Otolithic and extraocular muscle proprioceptive influences on the spatial organization of the vestibulo- and cervico-ocular quick phases.

PubMed

Pettorossi, V E; Manni, E; Errico, P; Ferraresi, A; Bortolami, R

1997-03-01

The cervico-ocular reflex (COR) was studied alone or in combination with the vestibulo-ocular reflex (VOR) in the rabbit. Step stimulations of the body with respect to the fixed head induced small slow compensatory responses followed by large compensatory quick phases (QP). These responses remained aligned with the horizon at different head pitch angles. The QP reorientation in space was due to the gravity influence on the otolithic receptors. The vestibular induced QPs exhibit a similar pattern. Because of this reorientation, the reduction of the amplitude of the vestibular induced QPs, due to the addition of the COR, was maintained even at different static head positions. The electrolytic lesion of the ophthalmic branch of the trigeminal nerve deeply affected the space orientation of the COR. In particular, the cervically induced compensatory QPs of the eye ipsilateral to the lesion showed a remarkable variability of their trajectories and they lost space reorientation. These findings suggest that the coordinate system controlling the QPs is influenced by signals originating from both head position in space and eye position in the orbit.

Phase transitions in trajectories of a superconducting single-electron transistor coupled to a resonator.

PubMed

Genway, Sam; Garrahan, Juan P; Lesanovsky, Igor; Armour, Andrew D

2012-05-01

Recent progress in the study of dynamical phase transitions has been made with a large-deviation approach to study trajectories of stochastic jumps using a thermodynamic formalism. We study this method applied to an open quantum system consisting of a superconducting single-electron transistor, near the Josephson quasiparticle resonance, coupled to a resonator. We find that the dynamical behavior shown in rare trajectories can be rich even when the mean dynamical activity is small, and thus the formalism gives insights into the form of fluctuations. The structure of the dynamical phase diagram found from the quantum-jump trajectories of the resonator is studied, and we see that sharp transitions in the dynamical activity may be related to the appearance and disappearance of bistabilities in the state of the resonator as system parameters are changed. We also demonstrate that for a fast resonator, the trajectories of quasiparticles are similar to the resonator trajectories.

An Overview of a Trajectory-Based Solution for En Route and Terminal Area Self-Spacing: Sixth Revision

NASA Technical Reports Server (NTRS)

Abbott, Terence S.

2015-01-01

This paper presents an overview of the sixth revision to an algorithm specifically designed to support NASA's Airborne Precision Spacing concept. This algorithm is referred to as the Airborne Spacing for Terminal Arrival Routes version 13 (ASTAR13). This airborne self-spacing concept contains both trajectory-based and state-based mechanisms for calculating the speeds required to achieve or maintain a precise spacing interval. The trajectory-based capability allows for spacing operations prior to the aircraft being on a common path. This algorithm was also designed specifically to support a standalone, non-integrated implementation in the spacing aircraft. This current revision to the algorithm adds the state-based capability in support of evolving industry standards relating to airborne self-spacing.

Four-Dimensional Magnetic Resonance Imaging With 3-Dimensional Radial Sampling and Self-Gating–Based K-Space Sorting: Early Clinical Experience on Pancreatic Cancer Patients

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

Yang, Wensha, E-mail: wensha.yang@cshs.org; Fan, Zhaoyang; Tuli, Richard

2015-12-01

Purpose: To apply a novel self-gating k-space sorted 4-dimensional MRI (SG-KS-4D-MRI) method to overcome limitations due to anisotropic resolution and rebinning artifacts and to monitor pancreatic tumor motion. Methods and Materials: Ten patients were imaged using 4D-CT, cine 2-dimensional MRI (2D-MRI), and the SG-KS-4D-MRI, which is a spoiled gradient recalled echo sequence with 3-dimensional radial-sampling k-space projections and 1-dimensional projection-based self-gating. Tumor volumes were defined on all phases in both 4D-MRI and 4D-CT and then compared. Results: An isotropic resolution of 1.56 mm was achieved in the SG-KS-4D-MRI images, which showed superior soft-tissue contrast to 4D-CT and appeared to be free of stitchingmore » artifacts. The tumor motion trajectory cross-correlations (mean ± SD) between SG-KS-4D-MRI and cine 2D-MRI in superior–inferior, anterior–posterior, and medial–lateral directions were 0.93 ± 0.03, 0.83 ± 0.10, and 0.74 ± 0.18, respectively. The tumor motion trajectories cross-correlations between SG-KS-4D-MRI and 4D-CT in superior–inferior, anterior–posterior, and medial–lateral directions were 0.91 ± 0.06, 0.72 ± 0.16, and 0.44 ± 0.24, respectively. The average standard deviation of gross tumor volume calculated from the 10 breathing phases was 0.81 cm{sup 3} and 1.02 cm{sup 3} for SG-KS-4D-MRI and 4D-CT, respectively (P=.012). Conclusions: A novel SG-KS-4D-MRI acquisition method capable of reconstructing rebinning artifact–free, high-resolution 4D-MRI images was used to quantify pancreas tumor motion. The resultant pancreatic tumor motion trajectories agreed well with 2D-cine-MRI and 4D-CT. The pancreatic tumor volumes shown in the different phases for the SG-KS-4D-MRI were statistically significantly more consistent than those in the 4D-CT.« less

Flow of Combustion Products Containing Condensed-Phase Particles over a Recessed Vectorable Jet Nozzle

NASA Astrophysics Data System (ADS)

Volkov, K. N.; Denisikhin, S. V.; Emel'yanov, V. N.; Teterina, I. V.

2017-09-01

The flow of combustion products containing condensed-phase particles over the recessed vectorable nozzle of a solid-propellant rocket motor was investigated with the use of the Reynolds-averaged Navier-Stokes equations, equations of the k-ɛ model of turbulence, and the Lagrange approach. The fields of flows of combustion products and the mechanical trajectories of condensed-phase particles in the charge channel, the prenozzle space, and the nozzle unit of this motor were calculated for different angles of swing of the nozzle. The formation of vortices in the gas flow in the neighborhood of the downstream cover of the nozzle and their influence on the movement of particles different in size were considered.

KSC-2009-5225

NASA Image and Video Library

2009-09-25

CAPE CANAVERAL, Fla. – The United Launch Alliance Delta II rocket carrying the Space Tracking and Surveillance System - Demonstrator, or STSS-Demo, spacecraft leaps into the sky from Launch Pad 17-B at Cape Canaveral Air Force Station. STSS-Demo was launched at 8:20:22 a.m. EDT by NASA for the U.S. Missile Defense Agency. The STSS-Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. Photo credit: NASA/Sandra Joseph- Kevin O'Connell

KSC-2009-5221

NASA Image and Video Library

2009-09-25

CAPE CANAVERAL, Fla. – The United Launch Alliance Delta II rocket with Space Tracking and Surveillance System - Demonstrator, or STSS-Demo, spacecraft leaps from Launch Pad 17-B at Cape Canaveral Air Force Station amid clouds of smoke. STSS-Demo was launched at 8:20:22 a.m. EDT by NASA for the U.S. Missile Defense Agency. The STSS-Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. Photo credit: NASA/Sandra Joseph- Kevin O'Connell

KSC-2009-5220

NASA Image and Video Library

2009-09-25

CAPE CANAVERAL, Fla. – The United Launch Alliance Delta II rocket with Space Tracking and Surveillance System - Demonstrator, or STSS-Demo, spacecraft aboard races into the sky leaving a trail of fire and smoke after liftoff from Launch Pad 17-B at Cape Canaveral Air Force Station. It was launched by NASA for the U.S. Missile Defense Agency at 8:20:22 a.m. EDT. The STSS-Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. Photo credit: NASA/Alan Ault

KSC-2009-5191

NASA Image and Video Library

2009-09-23

CAPE CANAVERAL, Fla. – The mobile service tower on Launch Pad 17-B at Cape Canaveral Air Force Station rolls back to reveal the United Launch Alliance Delta II rocket that will launch the Space Tracking and Surveillance System - Demonstrator into orbit. It is being launched by NASA for the Missile Defense System. The hour-long launch window opens at 8 a.m. EDT today. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. Photo credit: NASA/Dimitri Gerondidakis

KSC-2009-5067

NASA Image and Video Library

2009-08-27

CAPE CANAVERAL, Fla. – The enclosed Space Tracking and Surveillance System – Demonstrators, or STSS-Demo, spacecraft leaves the Astrotech payload processing facility on its way to Cape Canaveral Air Force Station's Launch Pad 17-B. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jack Pfaller

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.

KSC-2009-5193

NASA Image and Video Library

2009-09-23

CAPE CANAVERAL, Fla. – The mobile service tower on Launch Pad 17-B at Cape Canaveral Air Force Station has been rolled back to reveal the United Launch Alliance Delta II rocket ready to launch the Space Tracking and Surveillance System - Demonstrator into orbit. It is being launched by NASA for the Missile Defense System. The hour-long launch window opens at 8 a.m. EDT today. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. Photo credit: NASA/Dimitri Gerondidakis

KSC-2009-5226

NASA Image and Video Library

2009-09-25

CAPE CANAVERAL, Fla. –The United Launch Alliance Delta II rocket with Space Tracking and Surveillance System - Demonstrator, or STSS-Demo, spacecraft leaps from Launch Pad 17-B at Cape Canaveral Air Force Station amid clouds of smoke. STSS-Demo was launched at 8:20:22 a.m. EDT by NASA for the U.S. Missile Defense Agency. The STSS-Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. Photo credit: NASA/Tony Gray-Tim Powers

KSC-2009-5223

NASA Image and Video Library

2009-09-25

CAPE CANAVERAL, Fla. – The United Launch Alliance Delta II rocket carrying the Space Tracking and Surveillance System - Demonstrator, or STSS-Demo, spacecraft rises from a mantle of smoke as it lifts off from Launch Pad 17-B at Cape Canaveral Air Force Station. STSS-Demo was launched at 8:20:22 a.m. EDT by NASA for the U.S. Missile Defense Agency. The STSS-Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. Photo credit: NASA/Sandra Joseph- Kevin O'Connell

KSC-2009-5192

NASA Image and Video Library

2009-09-23

CAPE CANAVERAL, Fla. – The mobile service tower on Launch Pad 17-B at Cape Canaveral Air Force Station has been rolled back to reveal the United Launch Alliance Delta II rocket that will launch the Space Tracking and Surveillance System - Demonstrator into orbit. It is being launched by NASA for the Missile Defense System. The hour-long launch window opens at 8 a.m. EDT today. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. Photo credit: NASA/Dimitri Gerondidakis

KSC-2009-5219

NASA Image and Video Library

2009-09-25

CAPE CANAVERAL, Fla. – The Space Tracking and Surveillance System - Demonstrator, or STSS-Demo, spacecraft lifts off through a cloud of smoke from Launch Pad 17-B at Cape Canaveral Air Force Station aboard a United Launch Alliance Delta II rocket. It was launched by NASA for the U.S. Missile Defense Agency. Launch was at 8:20:22 a.m. EDT. The STSS-Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. Photo credit: NASA/Alan Ault

KSC-2009-5215

NASA Image and Video Library

2009-09-25

CAPE CANAVERAL, Fla. – Under a cloud-streaked sky, the Space Tracking and Surveillance System – Demonstrator, or STSS-Demo, waits through the countdown to liftoff Launch Pad 17-B at Cape Canaveral Air Force Station aboard a United Launch Alliance Delta II rocket. STSS-Demo is being launched by NASA for the U.S. Missile Defense Agency. Liftoff is at 8:20 a.m. EDT. The STSS-Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. Photo credit: NASA/Jack Pfaller

KSC-2009-5216

NASA Image and Video Library

2009-09-25

CAPE CANAVERAL, Fla. – Under a cloud-streaked sky, the Space Tracking and Surveillance System – Demonstrator, or STSS-Demo, waits through the countdown to liftoff Launch Pad 17-B at Cape Canaveral Air Force Station aboard a United Launch Alliance Delta II rocket. STSS-Demo is being launched by NASA for the U.S. Missile Defense Agency. Liftoff was at 8:20:22 a.m. EDT. The STSS-Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. Photo credit: NASA/Jack Pfaller

KSC-2009-5209

NASA Image and Video Library

2009-09-23

CAPE CANAVERAL, Fla. – On Launch Pad 17-B at Cape Canaveral Air Force Station in Florida, the Space Tracking and Surveillance System - Demonstrator spacecraft is bathed in light under a dark, cloudy sky. Rain over Central Florida's east coast caused the scrub of the launch. STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detection, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 24. Photo credit: NASA/Jack Pfaller

KSC-2009-5070

NASA Image and Video Library

2009-08-27

CAPE CANAVERAL, Fla. – The enclosed Space Tracking and Surveillance System – Demonstrators, or STSS-Demo, spacecraft is being lifted into the mobile service tower on Cape Canaveral Air Force Station's Launch Pad 17-B. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jack Pfaller

KSC-2009-5217

NASA Image and Video Library

2009-09-25

CAPE CANAVERAL, Fla. – The Space Tracking and Surveillance System - Demonstrator, or STSS-Demo, spacecraft lifts off through a cloud of smoke from Launch Pad 17-B at Cape Canaveral Air Force Station aboard a United Launch Alliance Delta II rocket. It was launched by NASA for the U.S. Missile Defense Agency. Launch was at 8:20:22 a.m. EDT. The STSS-Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. Photo credit: NASA/Jack Pfaller

KSC-2009-5210

NASA Image and Video Library

2009-09-23

CAPE CANAVERAL, Fla. – On Launch Pad 17-B at Cape Canaveral Air Force Station in Florida, the Space Tracking and Surveillance System Demonstrator spacecraft waits for launch under dark, cloudy sky. Rain over Central Florida's east coast caused the scrub of the launch. STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detection, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 24. Photo credit: NASA/Jack Pfaller

Entry Abort Determination Using Non-Adaptive Neural Networks for Mars Precision Landers

NASA Technical Reports Server (NTRS)

Graybeal, Sarah R.; Kranzusch, Kara M.

2005-01-01

The 2009 Mars Science Laboratory (MSL) will attempt the first precision landing on Mars using a modified version of the Apollo Earth entry guidance program. The guidance routine, Entry Terminal Point Controller (ETPC), commands the deployment of a supersonic parachute after converging the range to the landing target. For very dispersed cases, ETPC may not converge the range to the target and safely command parachute deployment within Mach number and dynamic pressure constraints. A full-lift up abort can save 85% of these failed trajectories while abandoning the precision landing objective. Though current MSL requirements do not call for an abort capability, an autonomous abort capability may be desired, for this mission or future Mars precision landers, to make the vehicle more robust. The application of artificial neural networks (NNs) as an abort determination technique was evaluated by personnel at the National Aeronautics and Space Administration (NASA) Johnson Space Center (JSC). In order to implement an abort, a failed trajectory needs to be recognized in real time. Abort determination is dependent upon several trajectory parameters whose relationships to vehicle survival are not well understood, and yet the lander must be trained to recognize unsafe situations. Artificial neural networks (NNs) provide a way to model these parameters and can provide MSL with the artificial intelligence necessary to independently declare an abort. Using the 2009 Mars Science Laboratory (MSL) mission as a case study, a non-adaptive NN was designed, trained and tested using Monte Carlo simulations of MSL descent and incorporated into ETPC. Neural network theory, the development history of the MSL NN, and initial testing with severe dust storm entry trajectory cases are discussed in Reference 1 and will not be repeated here. That analysis demonstrated that NNs are capable of recognizing failed descent trajectories and can significantly increase the survivability of MSL for very dispersed cases. NN testing was then broadened to evaluate fully dispersed entry trajectories. The NN correctly classified 99.7% of descent trajectories as abort or nonabort and reduced the probability of an unsafe parachute deployment by 83%. This second, broader testing phase is discussed in this paper.

Virtual trajectories, joint stiffness, and changes in the limb natural frequency during single-joint oscillatory movements.

PubMed

Latash, M L

1992-07-01

In the framework of the equilibrium-point hypothesis, virtual trajectories and patterns of joint stiffness were reconstructed during voluntary single-joint oscillatory movements in the elbow joint at a variety of frequencies and against two inertial loads. At low frequencies, virtual trajectories were in-phase with the actual joint trajectories. Joint stiffness changed at a doubled frequency. An increase in movement frequency and/or inertial load led to an increase in the difference between the peaks of the actual and virtual trajectories and in both peak and averaged values of joint stiffness. At a certain, critical frequency, virtual trajectory was nearly flat. Further increase in movement frequency led to a 180 degree phase shift between the actual and virtual trajectories. The assessed values of the natural frequency of the system "limb + manipulandum" were close to the critical frequencies for both low and high inertial loads. Peak levels and integrals of the electromyograms of two flexor and two extensor muscles changed monotonically with movement frequency without any special behavior at the critical frequencies. Nearly flat virtual trajectories at the natural frequency make physical sense as hypothetical control signals, unlike the electromyographic recordings, since a system at its natural frequency requires minimal central interference. Modulation of joint stiffness is assumed to be an important adaptive mechanism attenuating difference between the system's natural frequency and desired movement frequency. Virtual trajectory is considered a behavioral observable. Phase transitions between the virtual and actual trajectories are illustrations of behavioral discontinuities introduced by slow changes in a higher level control parameter, movement frequency. Relative phase shift between these two trajectories may be considered an order parameter.

Research study on materials processing in space Skylab experiment M553 - sphere forming

NASA Technical Reports Server (NTRS)

Johnson, P. C.; Peters, E. T.; Wechsler, A. E.

1973-01-01

A research program was conducted to study the solidification of metals in the form of small spheres both in the one gravity environment of the earth laboratory and the low gravity environment of KC-135 trajectory flights and the Skylab 1/2 mission. The program had three phases. The details of the results of this program are contained in interim reports prepared at the conclusion of each of the three phases. This final report is intended to summarize the efforts and results described in detail in each of these interim reports, with particular emphasis on the differences observed between the ground-based and Skylab flight specimens.

Querying databases of trajectories of differential equations: Data structures for trajectories

NASA Technical Reports Server (NTRS)

Grossman, Robert

1989-01-01

One approach to qualitative reasoning about dynamical systems is to extract qualitative information by searching or making queries on databases containing very large numbers of trajectories. The efficiency of such queries depends crucially upon finding an appropriate data structure for trajectories of dynamical systems. Suppose that a large number of parameterized trajectories gamma of a dynamical system evolving in R sup N are stored in a database. Let Eta is contained in set R sup N denote a parameterized path in Euclidean Space, and let the Euclidean Norm denote a norm on the space of paths. A data structure is defined to represent trajectories of dynamical systems, and an algorithm is sketched which answers queries.

STEREO Mission Design

NASA Technical Reports Server (NTRS)

Dunham, David W.; Guzman, Jose J.; Sharer, Peter J.; Friessen, Henry D.

2007-01-01

STEREO (Solar-TErestrial RElations Observatory) is the third mission in the Solar Terrestrial Probes program (STP) of the National Aeronautics and Space Administration (NASA). STEREO is the first mission to utilize phasing loops and multiple lunar flybys to alter the trajectories of more than one satellite. This paper describes the launch computation methodology, the launch constraints, and the resulting nine launch windows that were prepared for STEREO. More details are provided for the window in late October 2006 that was actually used.

Solar power satellite system definition study, volume 4, phase 2

NASA Technical Reports Server (NTRS)

1979-01-01

Results of an overall evaluation of the solar power satellite concept are reported. Specific topics covered include: solid state sandwich configuration; parametric development of reliability design; power distribution system for solid state solar power satellites; multibeam transmission; GEO base system configuration; suppression of the heavy lift launch vehicle trajectory; conceptual design of an offshore space center facility; solar power satellite development and operations scenario; and microwave power transmission technology, advancement, development, and facility requirements.

Testing algorithms for critical slowing down

NASA Astrophysics Data System (ADS)

Cossu, Guido; Boyle, Peter; Christ, Norman; Jung, Chulwoo; Jüttner, Andreas; Sanfilippo, Francesco

2018-03-01

We present the preliminary tests on two modifications of the Hybrid Monte Carlo (HMC) algorithm. Both algorithms are designed to travel much farther in the Hamiltonian phase space for each trajectory and reduce the autocorrelations among physical observables thus tackling the critical slowing down towards the continuum limit. We present a comparison of costs of the new algorithms with the standard HMC evolution for pure gauge fields, studying the autocorrelation times for various quantities including the topological charge.

Optical Interface States Protected by Synthetic Weyl Points

NASA Astrophysics Data System (ADS)

Wang, Qiang; Xiao, Meng; Liu, Hui; Zhu, Shining; Chan, C. T.

2017-07-01

Weyl fermions have not been found in nature as elementary particles, but they emerge as nodal points in the band structure of electronic and classical wave crystals. Novel phenomena such as Fermi arcs and chiral anomaly have fueled the interest in these topological points which are frequently perceived as monopoles in momentum space. Here, we report the experimental observation of generalized optical Weyl points inside the parameter space of a photonic crystal with a specially designed four-layer unit cell. The reflection at the surface of a truncated photonic crystal exhibits phase vortexes due to the synthetic Weyl points, which in turn guarantees the existence of interface states between photonic crystals and any reflecting substrates. The reflection phase vortexes have been confirmed for the first time in our experiments, which serve as an experimental signature of the generalized Weyl points. The existence of these interface states is protected by the topological properties of the Weyl points, and the trajectories of these states in the parameter space resembles those of Weyl semimetal "Fermi arc surface states" in momentum space. Tracing the origin of interface states to the topological character of the parameter space paves the way for a rational design of strongly localized states with enhanced local field.

Study of multiple unfolding trajectories and unfolded states of the protein GB1 under the physical property space.

PubMed

Wang, Jihua; Zhao, Liling; Dou, Xianghua; Zhang, Zhiyong

2008-06-01

Forty nine molecular dynamics simulations of unfolding trajectories of the segment B1 of streptococcal protein G (GB1) provide a direct demonstration of the diversity of unfolding pathway and give a statistically utmost unfolding pathway under the physical property space. Twelve physical properties of the protein were chosen to construct a 12-dimensional property space. Then the 12-dimensional property space was reduced to a 3-dimensional principle component property space. Under the property space, the multiple unfolding trajectories look like "trees", which have some common characters. The "root of the tree" corresponds to the native state, the "bole" homologizes the partially unfolded conformations, and the "crown" is in correspondence to the unfolded state. These unfolding trajectories can be divided into three types. The first one has the characters of straight "bole" and "crown" corresponding to a fast two-state unfolding pathway of GB1. The second one has the character of "the standstill in the middle tree bole", which may correspond to a three-state unfolding pathway. The third one has the character of "the circuitous bole" corresponding to a slow two-state unfolding pathway. The fast two-state unfolding pathway is a statistically utmost unfolding pathway or preferred pathway of GB1, which occupies 53% of 49 unfolding trajectories. In the property space all the unfolding trajectories construct a thermal unfolding pathway ensemble of GB1. The unfolding pathway ensemble resembles a funnel that is gradually emanative from the native state ensemble to the unfolded state ensemble. In the property space, the thermal unfolded state distribution looks like electronic cloud in quantum mechanics. The unfolded states of the independent unfolding simulation trajectories have substantial overlaps, indicating that the thermal unfolded states are confined by the physical property values, and the number of protein unfolded state are much less than that was believed before.

An Optimized Trajectory Planning for Welding Robot

NASA Astrophysics Data System (ADS)

Chen, Zhilong; Wang, Jun; Li, Shuting; Ren, Jun; Wang, Quan; Cheng, Qunchao; Li, Wentao

2018-03-01

In order to improve the welding efficiency and quality, this paper studies the combined planning between welding parameters and space trajectory for welding robot and proposes a trajectory planning method with high real-time performance, strong controllability and small welding error. By adding the virtual joint at the end-effector, the appropriate virtual joint model is established and the welding process parameters are represented by the virtual joint variables. The trajectory planning is carried out in the robot joint space, which makes the control of the welding process parameters more intuitive and convenient. By using the virtual joint model combined with the B-spline curve affine invariant, the welding process parameters are indirectly controlled by controlling the motion curve of the real joint. To solve the optimal time solution as the goal, the welding process parameters and joint space trajectory joint planning are optimized.

An Overview of a Trajectory-Based Solution for En Route and Terminal Area Self-Spacing: Seventh Revision

NASA Technical Reports Server (NTRS)

Abbott, Terence S.

2015-01-01

This paper presents an overview of the seventh revision to an algorithm specifically designed to support NASA's Airborne Precision Spacing concept. This paper supersedes the previous documentation and presents a modification to the algorithm referred to as the Airborne Spacing for Terminal Arrival Routes version 13 (ASTAR13). This airborne self-spacing concept contains both trajectory-based and state-based mechanisms for calculating the speeds required to achieve or maintain a precise spacing interval. The trajectory-based capability allows for spacing operations prior to the aircraft being on a common path. This algorithm was also designed specifically to support a standalone, non-integrated implementation in the spacing aircraft. This current revision to the algorithm adds the state-based capability in support of evolving industry standards relating to airborne self-spacing.

An Overview of a Trajectory-Based Solution for En Route and Terminal Area Self-Spacing: Eighth Revision

NASA Technical Reports Server (NTRS)

Abbott, Terence S.; Swieringa, Kurt S.

2017-01-01

This paper presents an overview of the eighth revision to an algorithm specifically designed to support NASA's Airborne Precision Spacing concept. This paper supersedes the previous documentation and presents a modification to the algorithm referred to as the Airborne Spacing for Terminal Arrival Routes version 13 (ASTAR13). This airborne self-spacing concept contains both trajectory-based and state-based mechanisms for calculating the speeds required to achieve or maintain a precise spacing interval with another aircraft. The trajectory-based capability allows for spacing operations prior to the aircraft being on a common path. This algorithm was also designed specifically to support a standalone, non-integrated implementation in the spacing aircraft. This current revision to the algorithm supports the evolving industry standards relating to airborne self-spacing.

Dynamic analysis of heartbeat rate signals of epileptics using multidimensional phase space reconstruction approach

NASA Astrophysics Data System (ADS)

Su, Zhi-Yuan; Wu, Tzuyin; Yang, Po-Hua; Wang, Yeng-Tseng

2008-04-01

The heartbeat rate signal provides an invaluable means of assessing the sympathetic-parasympathetic balance of the human autonomic nervous system and thus represents an ideal diagnostic mechanism for detecting a variety of disorders such as epilepsy, cardiac disease and so forth. The current study analyses the dynamics of the heartbeat rate signal of known epilepsy sufferers in order to obtain a detailed understanding of the heart rate pattern during a seizure event. In the proposed approach, the ECG signals are converted into heartbeat rate signals and the embedology theorem is then used to construct the corresponding multidimensional phase space. The dynamics of the heartbeat rate signal are then analyzed before, during and after an epileptic seizure by examining the maximum Lyapunov exponent and the correlation dimension of the attractors in the reconstructed phase space. In general, the results reveal that the heartbeat rate signal transits from an aperiodic, highly-complex behaviour before an epileptic seizure to a low dimensional chaotic motion during the seizure event. Following the seizure, the signal trajectories return to a highly-complex state, and the complex signal patterns associated with normal physiological conditions reappear.

Precise Trajectory Reconstruction of CE-3 Hovering Stage By Landing Camera Images

NASA Astrophysics Data System (ADS)

Yan, W.; Liu, J.; Li, C.; Ren, X.; Mu, L.; Gao, X.; Zeng, X.

2014-12-01

Chang'E-3 (CE-3) is part of the second phase of the Chinese Lunar Exploration Program, incorporating a lander and China's first lunar rover. It was landed on 14 December, 2013 successfully. Hovering and obstacle avoidance stages are essential for CE-3 safety soft landing so that precise spacecraft trajectory in these stages are of great significance to verify orbital control strategy, to optimize orbital design, to accurately determine the landing site of CE-3, and to analyze the geological background of the landing site. Because the time consumption of these stages is just 25s, it is difficult to present spacecraft's subtle movement by Measurement and Control System or by radio observations. Under this background, the trajectory reconstruction based on landing camera images can be used to obtain the trajectory of CE-3 because of its technical advantages such as unaffecting by lunar gravity field spacecraft kinetic model, high resolution, high frame rate, and so on. In this paper, the trajectory of CE-3 before and after entering hovering stage was reconstructed by landing camera images from frame 3092 to frame 3180, which lasted about 9s, under Single Image Space Resection (SISR). The results show that CE-3's subtle changes during hovering stage can be emerged by the reconstructed trajectory. The horizontal accuracy of spacecraft position was up to 1.4m while vertical accuracy was up to 0.76m. The results can be used for orbital control strategy analysis and some other application fields.

Optimal lifting ascent trajectories for the space shuttle

NASA Technical Reports Server (NTRS)

Rau, T. R.; Elliott, J. R.

1972-01-01

The performance gains which are possible through the use of optimal trajectories for a particular space shuttle configuration are discussed. The spacecraft configurations and aerodynamic characteristics are described. Shuttle mission payload capability is examined with respect to the optimal orbit inclination for unconstrained, constrained, and nonlifting conditions. The effects of velocity loss and heating rate on the optimal ascent trajectory are investigated.

Learning and Inferring "Dark Matter" and Predicting Human Intents and Trajectories in Videos.

PubMed

Xie, Dan; Shu, Tianmin; Todorovic, Sinisa; Zhu, Song-Chun

2018-07-01

This paper presents a method for localizing functional objects and predicting human intents and trajectories in surveillance videos of public spaces, under no supervision in training. People in public spaces are expected to intentionally take shortest paths (subject to obstacles) toward certain objects (e.g., vending machine, picnic table, dumpster etc.) where they can satisfy certain needs (e.g., quench thirst). Since these objects are typically very small or heavily occluded, they cannot be inferred by their visual appearance but indirectly by their influence on people's trajectories. Therefore, we call them "dark matter", by analogy to cosmology, since their presence can only be observed as attractive or repulsive "fields" in the public space. A person in the scene is modeled as an intelligent agent engaged in one of the "fields" selected depending his/her intent. An agent's trajectory is derived from an Agent-based Lagrangian Mechanics. The agents can change their intents in the middle of motion and thus alter the trajectory. For evaluation, we compiled and annotated a new dataset. The results demonstrate our effectiveness in predicting human intent behaviors and trajectories, and localizing and discovering distinct types of "dark matter" in wide public spaces.

Space Tug Aerobraking Study. Volume 2: Technical

NASA Technical Reports Server (NTRS)

Corso, C. J.; Eyer, C. L.

1972-01-01

The feasibility and practicality of employing an aerobraking trajectory for return of the reusable Space Tug from geosynchronous and other high energy missions was investigated. The aerobraking return trajectory modes from high orbits employ transfer ellipses which have low perigee altitudes wherein the earth's sensible atmosphere provides drag to reduce the Tug descent delta velocity requirements and thus decrease the required return trip propulsive energy. An aerobraked Space Tug, sized to the Space Shuttle payload capability and dimensional constraints, can accomplish 95 percent of the geosynchronous missions with a single Shuttle/Tug launch per mission. Aerodynamics, aerothermodynamics, trajectory, quidance and control, configuration concepts, materials, weights and performance parameters were identified. Sensitivities to trajectory uncertainties, atmospheric anomalies and re-entry environments were determined. New technology requirements and future studies required to further enhance the aerobraking potential were identified.

Phase space dynamics and control of the quantum particles associated to hypergraph states

NASA Astrophysics Data System (ADS)

Berec, Vesna

2015-05-01

As today's nanotechnology focus becomes primarily oriented toward production and manipulation of materials at the subatomic level, allowing the performance and complexity of interconnects where the device density accepts more than hundreds devices on a single chip, the manipulation of semiconductor nanostructures at the subatomic level sets its prime tasks on preserving and adequate transmission of information encoded in specified (quantum) states. The presented study employs the quantum communication protocol based on the hypergraph network model where the numerical solutions of equations of motion of quantum particles are associated to vertices (assembled with device chip), which follow specific controllable paths in the phase space. We address these findings towards ultimate quest for prediction and selective control of quantum particle trajectories. In addition, presented protocols could represent valuable tool for reducing background noise and uncertainty in low-dimensional and operationally meaningful, scalable complex systems.

Intermittent Fermi-Pasta-Ulam Dynamics at Equilibrium

NASA Astrophysics Data System (ADS)

Campbell, David; Danieli, Carlo; Flach, Sergej

The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body syste. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to measure both the relaxation time of the lowest frequency eigenmode of the Fermi-Pasta-Ulam chain, as well as the fluctuations of the subsequent dynamics in equilibrium. We show that previously obtained scaling laws for equipartition times are modified at low energy density due to an unexpected slowing down of the relaxation. The dynamics in equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. The long excursions arise from sticky dynamics close to regular orbits in the phase space. Our method is generalizable to large classes of many-body systems. The authors acknowledge financial support from IBS (Project Code IBS-R024-D1).

Lunar Prospector Extended Mission

NASA Technical Reports Server (NTRS)

Folta, David; Beckman, Mark; Lozier, David; Galal, Ken

1999-01-01

The National Aeronautics and Space Administration (NASA) selected Lunar Prospector (LP) as one of the discovery missions to conduct solar system exploration science investigations. The mission is NASA's first lunar voyage to investigate key science objectives since Apollo and was launched in January 1998. In keeping with discovery program requirements to reduce total mission cost and utilize new technology, Lunar Prospector's mission design and control focused on the use of innovative and proven trajectory analysis programs. As part of this effort, the Ames Research Center and the Goddard Space Flight Center have become partners in the Lunar Prospector trajectory team to provide the trajectory analysis, maneuver planning, orbit determination support, and product generation. At the end of 1998, Lunar Prospector completed its one-year primary mission at 100 km altitude above the lunar surface. On December 19, 1998, Lunar Prospector entered the extended mission phase. Initially the mission orbit was lowered from 100 km to a mean altitude of 40 km. The altitude of Lunar Prospector varied between 25 and 55 km above the mean lunar geode due to lunar potential effects. After one month, the lunar potential model was updated based upon the new tracking data at 40 km. On January 29, 1999, the altitude was lowered again to a mean altitude of 30 km. This altitude varies between 12 and 48 km above the mean lunar geode. Since the minimum altitude is very close to the mean geode, various approaches were employed to get accurate lunar surface elevation including Clementine altimetry and line of sight analysis. Based upon the best available terrain maps, Lunar Prospector will reach altitudes of 8 km above lunar mountains in the southern polar and far side regions. This extended mission phase of six months will enable LP to obtain science data up to 3 orders of magnitude better than at the mission orbit. This paper details the trajectory design and orbit determination planning and actual results of the Lunar Prospector extended mission including maneuver design, eccentricity & argument of perigee evolution, and lunar potential modeling.

Lunar Prospector Extended Mission

NASA Technical Reports Server (NTRS)

Folta, David; Beckman, Mark; Lozier, David; Galal, Ken

1999-01-01

The National Aeronautics and Space Administration (NASA) selected Lunar Prospector as one of the discovery missions to conduct solar system exploration science investigations. The mission is NASA's first lunar voyage to investigate key science objectives since Apollo and was launched in January 1998. In keeping with discovery program requirements to reduce total mission cost and utilize new technology, Lunar Prospector's mission design and control focused on the use of innovative and proven trajectory analysis programs. As part of this effort, the Ames Research Center and the Goddard Space Flight Center have become partners in the Lunar Prospector trajectory team to provide the trajectory analysis, maneuver planning, orbit determination support, and product generation. At the end of 1998, Lunar Prospector completed its one-year primary mission at 100 km altitude above the lunar surface. On December 19, 1998, Lunar Prospector entered the extended mission phase. Initially the mission orbit was lowered from 100 km to a mean altitude of 40 km. The altitude of Lunar Prospector varied between 25 and 55 km above the mean lunar geode due to lunar potential effects. After one month, the lunar potential model was updated based upon the new tracking data at 40 km. On January 29, 1999, the altitude was lowered again to a mean altitude of 30 km. This altitude varies between 12 and 48 km above the mean lunar geode. Since the minimum altitude is very close to the mean geode, various approaches were employed to get accurate lunar surface elevation including Clementine altimetry and line of sight analysis. Based upon the best available terrain maps, Lunar Prospector will reach altitudes of 8 km above lunar mountains in the southern polar and far side regions. This extended mission phase of six months will enable LP to obtain science data up to 3 orders of magnitude better than at the mission orbit. This paper details the trajectory design and orbit determination planning, and actual results of the the Lunar Prospector extended mission including maneuver design, eccentricity & argument of perigee evolution, and lunar potential modeling.

Lunar Prospector Extended Mission

NASA Astrophysics Data System (ADS)

Folta, David; Beckman, Mark; Lozier, David; Galal, Ken

1999-05-01

The National Aeronautics and Space Administration (NASA) selected Lunar Prospector (LP) as one of the discovery missions to conduct solar system exploration science investigations. The mission is NASA's first lunar voyage to investigate key science objectives since Apollo and was launched in January 1998. In keeping with discovery program requirements to reduce total mission cost and utilize new technology, Lunar Prospector's mission design and control focused on the use of innovative and proven trajectory analysis programs. As part of this effort, the Ames Research Center and the Goddard Space Flight Center have become partners in the Lunar Prospector trajectory team to provide the trajectory analysis, maneuver planning, orbit determination support, and product generation. At the end of 1998, Lunar Prospector completed its one-year primary mission at 100 km altitude above the lunar surface. On December 19, 1998, Lunar Prospector entered the extended mission phase. Initially the mission orbit was lowered from 100 km to a mean altitude of 40 km. The altitude of Lunar Prospector varied between 25 and 55 km above the mean lunar geode due to lunar potential effects. After one month, the lunar potential model was updated based upon the new tracking data at 40 km. On January 29, 1999, the altitude was lowered again to a mean altitude of 30 km. This altitude varies between 12 and 48 km above the mean lunar geode. Since the minimum altitude is very close to the mean geode, various approaches were employed to get accurate lunar surface elevation including Clementine altimetry and line of sight analysis. Based upon the best available terrain maps, Lunar Prospector will reach altitudes of 8 km above lunar mountains in the southern polar and far side regions. This extended mission phase of six months will enable LP to obtain science data up to 3 orders of magnitude better than at the mission orbit. This paper details the trajectory design and orbit determination planning and actual results of the Lunar Prospector extended mission including maneuver design, eccentricity & argument of perigee evolution, and lunar potential modeling.

Efficient Construction of Mesostate Networks from Molecular Dynamics Trajectories.

PubMed

Vitalis, Andreas; Caflisch, Amedeo

2012-03-13

The coarse-graining of data from molecular simulations yields conformational space networks that may be used for predicting the system's long time scale behavior, to discover structural pathways connecting free energy basins in the system, or simply to represent accessible phase space regions of interest and their connectivities in a two-dimensional plot. In this contribution, we present a tree-based algorithm to partition conformations of biomolecules into sets of similar microstates, i.e., to coarse-grain trajectory data into mesostates. On account of utilizing an architecture similar to that of established tree-based algorithms, the proposed scheme operates in near-linear time with data set size. We derive expressions needed for the fast evaluation of mesostate properties and distances when employing typical choices for measures of similarity between microstates. Using both a pedagogically useful and a real-word application, the algorithm is shown to be robust with respect to tree height, which in addition to mesostate threshold size is the main adjustable parameter. It is demonstrated that the derived mesostate networks can preserve information regarding the free energy basins and barriers by which the system is characterized.

Approach to fitting parameters and clustering for characterising measured voltage dips based on two-dimensional polarisation ellipses

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

García-Sánchez, Tania; Gómez-Lázaro, Emilio; Muljadi, E.

An alternative approach to characterise real voltage dips is proposed and evaluated in this study. The proposed methodology is based on voltage-space vector solutions, identifying parameters for ellipses trajectories by using the least-squares algorithm applied on a sliding window along the disturbance. The most likely patterns are then estimated through a clustering process based on the k-means algorithm. The objective is to offer an efficient and easily implemented alternative to characterise faults and visualise the most likely instantaneous phase-voltage evolution during events through their corresponding voltage-space vector trajectories. This novel solution minimises the data to be stored but maintains extensivemore » information about the dips including starting and ending transients. The proposed methodology has been applied satisfactorily to real voltage dips obtained from intensive field-measurement campaigns carried out in a Spanish wind power plant up to a time period of several years. A comparison to traditional minimum root mean square-voltage and time-duration classifications is also included in this study.« less

Multichannel High Resolution Wide Swath SAR Imaging for Hypersonic Air Vehicle with Curved Trajectory.

PubMed

Zhou, Rui; Sun, Jinping; Hu, Yuxin; Qi, Yaolong

2018-01-31

Synthetic aperture radar (SAR) equipped on the hypersonic air vehicle in near space has many advantages over the conventional airborne SAR. However, its high-speed maneuvering characteristics with curved trajectory result in serious range migration, and exacerbate the contradiction between the high resolution and wide swath. To solve this problem, this paper establishes the imaging geometrical model matched with the flight trajectory of the hypersonic platform and the multichannel azimuth sampling model based on the displaced phase center antenna (DPCA) technology. Furthermore, based on the multichannel signal reconstruction theory, a more efficient spectrum reconstruction model using discrete Fourier transform is proposed to obtain the azimuth uniform sampling data. Due to the high complexity of the slant range model, it is difficult to deduce the processing algorithm for SAR imaging. Thus, an approximate range model is derived based on the minimax criterion, and the optimal second-order approximate coefficients of cosine function are obtained using the two-population coevolutionary algorithm. On this basis, aiming at the problem that the traditional Omega-K algorithm cannot compensate the residual phase with the difficulty of Stolt mapping along the range frequency axis, this paper proposes an Exact Transfer Function (ETF) algorithm for SAR imaging, and presents a method of range division to achieve wide swath imaging. Simulation results verify the effectiveness of the ETF imaging algorithm.

Multichannel High Resolution Wide Swath SAR Imaging for Hypersonic Air Vehicle with Curved Trajectory

PubMed Central

Zhou, Rui; Hu, Yuxin; Qi, Yaolong

2018-01-01

Synthetic aperture radar (SAR) equipped on the hypersonic air vehicle in near space has many advantages over the conventional airborne SAR. However, its high-speed maneuvering characteristics with curved trajectory result in serious range migration, and exacerbate the contradiction between the high resolution and wide swath. To solve this problem, this paper establishes the imaging geometrical model matched with the flight trajectory of the hypersonic platform and the multichannel azimuth sampling model based on the displaced phase center antenna (DPCA) technology. Furthermore, based on the multichannel signal reconstruction theory, a more efficient spectrum reconstruction model using discrete Fourier transform is proposed to obtain the azimuth uniform sampling data. Due to the high complexity of the slant range model, it is difficult to deduce the processing algorithm for SAR imaging. Thus, an approximate range model is derived based on the minimax criterion, and the optimal second-order approximate coefficients of cosine function are obtained using the two-population coevolutionary algorithm. On this basis, aiming at the problem that the traditional Omega-K algorithm cannot compensate the residual phase with the difficulty of Stolt mapping along the range frequency axis, this paper proposes an Exact Transfer Function (ETF) algorithm for SAR imaging, and presents a method of range division to achieve wide swath imaging. Simulation results verify the effectiveness of the ETF imaging algorithm. PMID:29385059

Querying databases of trajectories of differential equations 2: Index functions

NASA Technical Reports Server (NTRS)

Grossman, Robert

1991-01-01

Suppose that a large number of parameterized trajectories (gamma) of a dynamical system evolving in R sup N are stored in a database. Let eta is contained R sup N denote a parameterized path in Euclidean space, and let parallel to center dot parallel to denote a norm on the space of paths. A data structures and indices for trajectories are defined and algorithms are given to answer queries of the following forms: Query 1. Given a path eta, determine whether eta occurs as a subtrajectory of any trajectory gamma from the database. If so, return the trajectory; otherwise, return null. Query 2. Given a path eta, return the trajectory gamma from the database which minimizes the norm parallel to eta - gamma parallel.

Trajectory Design Enhancements to Mitigate Risk for the Transiting Exoplanet Survey Satellite (TESS)

NASA Technical Reports Server (NTRS)

Dichmann, Donald; Parker, Joel; Nickel, Craig; Lutz, Stephen

2016-01-01

The Transiting Exoplanet Survey Satellite (TESS) will employ a highly eccentric Earth orbit, in 2:1 lunar resonance, which will be reached with a lunar flyby preceded by 3.5 phasing loops. The TESS mission has limited propellant and several constraints on the science orbit and on the phasing loops. Based on analysis and simulation, we have designed the phasing loops to reduce delta-V (DV) and to mitigate risk due to maneuver execution errors. We have automated the trajectory design process and use distributed processing to generate and optimal nominal trajectories; to check constraint satisfaction; and finally to model the effects of maneuver errors to identify trajectories that best meet the mission requirements.

A navigation and control system for an autonomous rescue vehicle in the space station environment

NASA Technical Reports Server (NTRS)

Merkel, Lawrence

1991-01-01

A navigation and control system was designed and implemented for an orbital autonomous rescue vehicle envisioned to retrieve astronauts or equipment in the case that they become disengaged from the space station. The rescue vehicle, termed the Extra-Vehicular Activity Retriever (EVAR), has an on-board inertial measurement unit ahd GPS receivers for self state estimation, a laser range imager (LRI) and cameras for object state estimation, and a data link for reception of space station state information. The states of the retriever and objects (obstacles and the target object) are estimated by inertial state propagation which is corrected via measurements from the GPS, the LRI system, or the camera system. Kalman filters are utilized to perform sensor fusion and estimate the state propagation errors. Control actuation is performed by a Manned Maneuvering Unit (MMU). Phase plane control techniques are used to control the rotational and translational state of the retriever. The translational controller provides station-keeping or motion along either Clohessy-Wiltshire trajectories or straight line trajectories in the LVLH frame of any sufficiently observed object or of the space station. The software was used to successfully control a prototype EVAR on an air bearing floor facility, and a simulated EVAR operating in a simulated orbital environment. The design of the navigation system and the control system are presented. Also discussed are the hardware systems and the overall software architecture.

Generation of electron Airy beams.

PubMed

Voloch-Bloch, Noa; Lereah, Yossi; Lilach, Yigal; Gover, Avraham; Arie, Ady

2013-02-21

Within the framework of quantum mechanics, a unique particle wave packet exists in the form of the Airy function. Its counterintuitive properties are revealed as it propagates in time or space: the quantum probability wave packet preserves its shape despite dispersion or diffraction and propagates along a parabolic caustic trajectory, even though no force is applied. This does not contradict Newton's laws of motion, because the wave packet centroid propagates along a straight line. Nearly 30 years later, this wave packet, known as an accelerating Airy beam, was realized in the optical domain; later it was generalized to an orthogonal and complete family of beams that propagate along parabolic trajectories, as well as to beams that propagate along arbitrary convex trajectories. Here we report the experimental generation and observation of the Airy beams of free electrons. These electron Airy beams were generated by diffraction of electrons through a nanoscale hologram, which imprinted on the electrons' wavefunction a cubic phase modulation in the transverse plane. The highest-intensity lobes of the generated beams indeed followed parabolic trajectories. We directly observed a non-spreading electron wavefunction that self-heals, restoring its original shape after passing an obstacle. This holographic generation of electron Airy beams opens up new avenues for steering electronic wave packets like their photonic counterparts, because the wave packets can be imprinted with arbitrary shapes or trajectories.

A multicolour graph as a complete topological invariant for \\Omega-stable flows without periodic trajectories on surfaces

NASA Astrophysics Data System (ADS)

Kruglov, V. E.; Malyshev, D. S.; Pochinka, O. V.

2018-01-01

Studying the dynamics of a flow on surfaces by partitioning the phase space into cells with the same limit behaviour of trajectories within a cell goes back to the classical papers of Andronov, Pontryagin, Leontovich and Maier. The types of cells (the number of which is finite) and how the cells adjoin one another completely determine the topological equivalence class of a flow with finitely many special trajectories. If one trajectory is chosen in every cell of a rough flow without periodic orbits, then the cells are partitioned into so-called triangular regions of the same type. A combinatorial description of such a partition gives rise to the three-colour Oshemkov-Sharko graph, the vertices of which correspond to the triangular regions, and the edges to separatrices connecting them. Oshemkov and Sharko proved that such flows are topologically equivalent if and only if the three-colour graphs of the flows are isomorphic, and described an algorithm of distinguishing three-colour graphs. But their algorithm is not efficient with respect to graph theory. In the present paper, we describe the dynamics of Ω-stable flows without periodic trajectories on surfaces in the language of four-colour graphs, present an efficient algorithm for distinguishing such graphs, and develop a realization of a flow from some abstract graph. Bibliography: 17 titles.

A molecular simulation protocol to avoid sampling redundancy and discover new states.

PubMed

Bacci, Marco; Vitalis, Andreas; Caflisch, Amedeo

2015-05-01

For biomacromolecules or their assemblies, experimental knowledge is often restricted to specific states. Ambiguity pervades simulations of these complex systems because there is no prior knowledge of relevant phase space domains, and sampling recurrence is difficult to achieve. In molecular dynamics methods, ruggedness of the free energy surface exacerbates this problem by slowing down the unbiased exploration of phase space. Sampling is inefficient if dwell times in metastable states are large. We suggest a heuristic algorithm to terminate and reseed trajectories run in multiple copies in parallel. It uses a recent method to order snapshots, which provides notions of "interesting" and "unique" for individual simulations. We define criteria to guide the reseeding of runs from more "interesting" points if they sample overlapping regions of phase space. Using a pedagogical example and an α-helical peptide, the approach is demonstrated to amplify the rate of exploration of phase space and to discover metastable states not found by conventional sampling schemes. Evidence is provided that accurate kinetics and pathways can be extracted from the simulations. The method, termed PIGS for Progress Index Guided Sampling, proceeds in unsupervised fashion, is scalable, and benefits synergistically from larger numbers of replicas. Results confirm that the underlying ideas are appropriate and sufficient to enhance sampling. In molecular simulations, errors caused by not exploring relevant domains in phase space are always unquantifiable and can be arbitrarily large. Our protocol adds to the toolkit available to researchers in reducing these types of errors. This article is part of a Special Issue entitled "Recent developments of molecular dynamics". Copyright © 2014 Elsevier B.V. All rights reserved.

STEREO Mission Design Implementation

NASA Technical Reports Server (NTRS)

Guzman, Jose J.; Dunham, David W.; Sharer, Peter J.; Hunt, Jack W.; Ray, J. Courtney; Shapiro, Hongxing S.; Ossing, Daniel A.; Eichstedt, John E.

2007-01-01

STEREO (Solar-TErrestrial RElations Observatory) is the third mission in the Solar Terrestrial Probes program (STP) of the National Aeronautics and Space Administration (NASA) Science Mission Directorate Sun-Earth Connection theme. This paper describes the successful implementation (lunar swingby targeting) of the mission following the first phasing orbit to deployment into the heliocentric mission orbits following the two lunar swingbys. The STEREO Project had to make some interesting trajectory decisions in order to exploit opportunities to image a bright comet and an unusual lunar transit across the Sun.

Dynamical stability of slip-stacking particles

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

Eldred, Jeffrey; Zwaska, Robert

2014-09-01

We study the stability of particles in slip-stacking configuration, used to nearly double proton beam intensity at Fermilab. We introduce universal area factors to calculate the available phase space area for any set of beam parameters without individual simulation. We find perturbative solutions for stable particle trajectories. We establish Booster beam quality requirements to achieve 97% slip-stacking efficiency. We show that slip-stacking dynamics directly correspond to the driven pendulum and to the system of two standing-wave traps moving with respect to each other.

Orbital Tori Construction Using Trajectory Following Spectral Methods

DTIC Science & Technology

2010-09-01

a Walker delta pattern scheme of 18/6/2. Explicitly, this means the 18 satellites were equally spaced in six planes , each inclined at 55 degrees, with...a relative phasing angle parameter of 2 [65]. The planes ’ inclinations were reduced from the original specification of 63 degrees to 55 degrees due...navigation performance specification for the SPS was ≤ 100 meters 8 in the horizontal plane , 95 percent of the time and ≤ 156 meters in the vertical plane

Intermittent many-body dynamics at equilibrium

NASA Astrophysics Data System (ADS)

Danieli, C.; Campbell, D. K.; Flach, S.

2017-06-01

The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body system. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to measure both the relaxation time of the lowest frequency eigenmode of the Fermi-Pasta-Ulam chain, as well as the fluctuations of the subsequent dynamics in equilibrium. The dynamics in equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. Long excursions arise from sticky dynamics close to q -breathers localized in normal mode space. Measuring the exponent allows one to predict the transition into nonergodic dynamics. We generalize our method to Klein-Gordon lattices where the sticky dynamics is due to discrete breathers localized in real space.

Classical trajectory studies of gas phase reaction dynamics and kinetics using ab initio potential energy surfaces

NASA Technical Reports Server (NTRS)

Jaffe, Richard L.; Pattengill, Merle D.; Schwenke, David W.

1989-01-01

Strategies for constructing global potential energy surfaces from a limited number of accurate ab initio electronic energy calculations are discussed. Generally, these data are concentrated in small regions of configuration space (e.g., in the vicinity of saddle points and energy minima) and difficulties arise in generating a potential function that is globally well-behaved. Efficient computer codes for carrying out classical trajectory calculations on vector and parallel processors are also described. Illustrations are given from recent work on the following chemical systems: Ca + HF yields CaF + H, H + H + H2 yields H2 + H2, N + O2 yields NO + O and O + N2 yields NO + N. The dynamics and kinetics of metathesis, dissociation, recombination, energy transfer and complex formation processes will be discussed.

Hybrid Differential Dynamic Programming with Stochastic Search

NASA Technical Reports Server (NTRS)

Aziz, Jonathan; Parker, Jeffrey; Englander, Jacob

2016-01-01

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASAs Dawn mission. The Dawn trajectory was designed with the DDP-based Static Dynamic Optimal Control algorithm used in the Mystic software. Another recently developed method, Hybrid Differential Dynamic Programming (HDDP) is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

Pitch Angle Dependence of Drift Resonant Ions Observed by the Van Allen Probes

NASA Astrophysics Data System (ADS)

Rankin, R.; Wang, C.; Wang, Y.; Zong, Q. G.; Zhou, X.

2017-12-01

Acceleration and modulation of ring current ions by poloidal mode ULF waves is investigated. A simplified MHD model of ULF waves in a dipole magnetic field is presented that includes phase mixing to perpendicular scales determined by the ionospheric Pedersen conductivity. The wave model is combined with a full Lorentz force test particle code to study drift and drift bounce resonance wave-particle interactions. Ion trajectories are traced backward-in-time to an assumed form of the distribution function, and Liouville's method is used to reconstruct the phase space density response (PSD) poloidal mode waves observed by the Van Allen Probes. In spite of its apparent simplicity, simulations using the wave and test particle models are able to explain the acceleration of ions and energy dispersion observed by the Van Allen Probes. The paper focuses on the pitch angle evolution of the initial PSD as it responds to the action of ULF waves. An interesting aspect of the study is the formation of butterfly ion distributions as ions make periodic radial oscillations across L. Ions become trapped in an effective potential well across a limited range of L and follow trajectories that cause them to surf along constant phase fronts. The impications of this new trapping mechanism for both ions and electrons is discussed.

Rare behavior of growth processes via umbrella sampling of trajectories

NASA Astrophysics Data System (ADS)

Klymko, Katherine; Geissler, Phillip L.; Garrahan, Juan P.; Whitelam, Stephen

2018-03-01

We compute probability distributions of trajectory observables for reversible and irreversible growth processes. These results reveal a correspondence between reversible and irreversible processes, at particular points in parameter space, in terms of their typical and atypical trajectories. Thus key features of growth processes can be insensitive to the precise form of the rate constants used to generate them, recalling the insensitivity to microscopic details of certain equilibrium behavior. We obtained these results using a sampling method, inspired by the "s -ensemble" large-deviation formalism, that amounts to umbrella sampling in trajectory space. The method is a simple variant of existing approaches, and applies to ensembles of trajectories controlled by the total number of events. It can be used to determine large-deviation rate functions for trajectory observables in or out of equilibrium.

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.

KSC-2009-5060

NASA Image and Video Library

2009-08-22

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the upper segment of the transportation canister is moved toward the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, spacecraft, at left. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Kim Shiflett

KSC-2009-5050

NASA Image and Video Library

2009-08-20

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers observe as the SV1-SV2 spacecraft is lifted for weighing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5048

NASA Image and Video Library

2009-08-20

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the SV1-SV2 spacecraft is ready to be weighed. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5059

NASA Image and Video Library

2009-08-22

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the upper segment of the transportation canister is lifted to be placed on the top of the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, spacecraft. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Kim Shiflett

KSC-2009-5049

NASA Image and Video Library

2009-08-20

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers observe as the SV1-SV2 spacecraft is lifted for weighing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5066

NASA Image and Video Library

2009-08-27

CAPE CANAVERAL, Fla. – The enclosed Space Tracking and Surveillance System – Demonstrators, or STSS-Demo, spacecraft moves out of the Astrotech payload processing facility. It is being moved to Cape Canaveral Air Force Station's Launch Pad 17-B. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jack Pfaller

KSC-2009-5057

NASA Image and Video Library

2009-08-22

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers maneuver one of the second-row segments of the transportation canister that will be placed around the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, spacecraft. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Kim Shiflett

KSC-2009-5021

NASA Image and Video Library

2009-08-03

CAPE CANAVERAL, Fla. –At the Astrotech payload processing facility in Titusville, Fla., the SV1 spacecraft is lowered onto the SV2 for mating. The two spacecraft are part of the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, Program. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5023

NASA Image and Video Library

2009-08-03

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the SV1 spacecraft is lowered onto the SV2 for mating. The two spacecraft are part of the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, Program. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

Galactic Cosmic-ray Transport in the Global Heliosphere: A Four-Dimensional Stochastic Model

NASA Astrophysics Data System (ADS)

Florinski, V.

2009-04-01

We study galactic cosmic-ray transport in the outer heliosphere and heliosheath using a newly developed transport model based on stochastic integration of the phase-space trajectories of Parker's equation. The model employs backward integration of the diffusion-convection transport equation using Ito calculus and is four-dimensional in space+momentum. We apply the model to the problem of galactic proton transport in the heliosphere during a negative solar minimum. Model results are compared with the Voyager measurements of galactic proton radial gradients and spectra in the heliosheath. We show that the heliosheath is not as efficient in diverting cosmic rays during solar minima as predicted by earlier two-dimensional models.

KSC-2009-5053

NASA Image and Video Library

2009-08-20

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the SV1-SV2 spacecraft sits on the rotation stand after weighing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5042

NASA Image and Video Library

2009-08-20

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers begin center of gravity testing, weighing and balancing on the SV1-SV2 spacecraft. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5061

NASA Image and Video Library

2009-08-22

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the upper segment of the transportation canister is moved toward the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, spacecraft, at bottom left. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Kim Shiflett

KSC-2009-5056

NASA Image and Video Library

2009-08-22

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers place the second row of segments of the transportation canister around the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, spacecraft. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Kim Shiflett

KSC-2009-5020

NASA Image and Video Library

2009-08-03

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the SV1 spacecraft is lowered toward the SV2 for mating. The two spacecraft are part of the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, Program. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5065

NASA Image and Video Library

2009-08-22

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers attach the upper segment of the transportation canister to the lower segments around the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, spacecraft. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Kim Shiflett

KSC-2009-5055

NASA Image and Video Library

2009-08-22

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers place the first segments of the transportation canister around the base of the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, spacecraft. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Kim Shiflett

KSC-2009-5025

NASA Image and Video Library

2009-08-03

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers check the mating of the SV1 spacecraft onto the SV2. The two spacecraft are part of the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, Program. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5194

NASA Image and Video Library

2009-09-23

CAPE CANAVERAL, Fla. – The mobile service tower on Launch Pad 17-B at Cape Canaveral Air Force Station has been rolled back as the countdown proceeds to launch of the United Launch Alliance Delta II rocket with the Space Tracking and Surveillance System - Demonstrator spacecraft aboard. It is being launched by NASA for the Missile Defense System. The hour-long launch window opens at 8 a.m. EDT today. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. Photo credit: NASA/Dimitri Gerondidakis

KSC-2009-5051

NASA Image and Video Library

2009-08-20

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the SV1-SV2 spacecraft is lifted for weighing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5012

NASA Image and Video Library

2009-08-03

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the SV1 and SV2 spacecraft are ready for mating for launch. The two spacecraft are part of the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, Program. STSS-Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. The spacecraft is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5054

NASA Image and Video Library

2009-08-22

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, spacecraft is under a protective cover before being encased in the transportation canister. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Kim Shiflett

KSC-2009-5218

NASA Image and Video Library

2009-09-25

CAPE CANAVERAL, Fla. – The United Launch Alliance Delta II rocket with Space Tracking and Surveillance System - Demonstrator, or STSS-Demo, spacecraft aboard races into the sky leaving a trail of fire and smoke after liftoff from Launch Pad 17-B at Cape Canaveral Air Force Station. It was launched by NASA for the U.S. Missile Defense Agency. Launch was at 8:20:22 a.m. EDT. The STSS-Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. Photo credit: NASA/Jack Pfaller

KSC-2009-5058

NASA Image and Video Library

2009-08-22

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers maneuver one of the second-row segments of the transportation canister that will be placed around the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, spacecraft. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Kim Shiflett

KSC-2009-5013

NASA Image and Video Library

2009-08-03

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers prepare to lift the SV1 and mate it to the SV2 spacecraft for the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, Program. STSS-Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. The spacecraft is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

Trades Between Opposition and Conjunction Class Trajectories for Early Human Missions to Mars

NASA Technical Reports Server (NTRS)

Mattfeld, Bryan; Stromgren, Chel; Shyface, Hilary; Komar, David R.; Cirillo, William; Goodliff, Kandyce

2014-01-01

Candidate human missions to Mars, including NASA's Design Reference Architecture 5.0, have focused on conjunction-class missions with long crewed durations and minimum energy trajectories to reduce total propellant requirements and total launch mass. However, in order to progressively reduce risk and gain experience in interplanetary mission operations, it may be desirable that initial human missions to Mars, whether to the surface or to Mars orbit, have shorter total crewed durations and minimal stay times at the destination. Opposition-class missions require larger total energy requirements relative to conjunction-class missions but offer the potential for much shorter mission durations, potentially reducing risk and overall systems performance requirements. This paper will present a detailed comparison of conjunction-class and opposition-class human missions to Mars vicinity with a focus on how such missions could be integrated into the initial phases of a Mars exploration campaign. The paper will present the results of a trade study that integrates trajectory/propellant analysis, element design, logistics and sparing analysis, and risk assessment to produce a comprehensive comparison of opposition and conjunction exploration mission constructs. Included in the trade study is an assessment of the risk to the crew and the trade offs between the mission duration and element, logistics, and spares mass. The analysis of the mission trade space was conducted using four simulation and analysis tools developed by NASA. Trajectory analyses for Mars destination missions were conducted using VISITOR (Versatile ImpulSive Interplanetary Trajectory OptimizeR), an in-house tool developed by NASA Langley Research Center. Architecture elements were evaluated using EXploration Architecture Model for IN-space and Earth-to-orbit (EXAMINE), a parametric modeling tool that generates exploration architectures through an integrated systems model. Logistics analysis was conducted using NASA's Human Exploration Logistics Model (HELM), and sparing allocation predictions were generated via the Exploration Maintainability Analysis Tool (EMAT), which is a probabilistic simulation engine that evaluates trades in spacecraft reliability and sparing requirements based on spacecraft system maintainability and reparability.

Two-phase framework for near-optimal multi-target Lambert rendezvous

NASA Astrophysics Data System (ADS)

Bang, Jun; Ahn, Jaemyung

2018-03-01

This paper proposes a two-phase framework to obtain a near-optimal solution of multi-target Lambert rendezvous problem. The objective of the problem is to determine the minimum-cost rendezvous sequence and trajectories to visit a given set of targets within a maximum mission duration. The first phase solves a series of single-target rendezvous problems for all departure-arrival object pairs to generate the elementary solutions, which provides candidate rendezvous trajectories. The second phase formulates a variant of traveling salesman problem (TSP) using the elementary solutions prepared in the first phase and determines the final rendezvous sequence and trajectories of the multi-target rendezvous problem. The validity of the proposed optimization framework is demonstrated through an asteroid exploration case study.

Sequential memory: Binding dynamics

NASA Astrophysics Data System (ADS)

Afraimovich, Valentin; Gong, Xue; Rabinovich, Mikhail

2015-10-01

Temporal order memories are critical for everyday animal and human functioning. Experiments and our own experience show that the binding or association of various features of an event together and the maintaining of multimodality events in sequential order are the key components of any sequential memories—episodic, semantic, working, etc. We study a robustness of binding sequential dynamics based on our previously introduced model in the form of generalized Lotka-Volterra equations. In the phase space of the model, there exists a multi-dimensional binding heteroclinic network consisting of saddle equilibrium points and heteroclinic trajectories joining them. We prove here the robustness of the binding sequential dynamics, i.e., the feasibility phenomenon for coupled heteroclinic networks: for each collection of successive heteroclinic trajectories inside the unified networks, there is an open set of initial points such that the trajectory going through each of them follows the prescribed collection staying in a small neighborhood of it. We show also that the symbolic complexity function of the system restricted to this neighborhood is a polynomial of degree L - 1, where L is the number of modalities.

Sequential memory: Binding dynamics.

PubMed

Afraimovich, Valentin; Gong, Xue; Rabinovich, Mikhail

2015-10-01

Temporal order memories are critical for everyday animal and human functioning. Experiments and our own experience show that the binding or association of various features of an event together and the maintaining of multimodality events in sequential order are the key components of any sequential memories-episodic, semantic, working, etc. We study a robustness of binding sequential dynamics based on our previously introduced model in the form of generalized Lotka-Volterra equations. In the phase space of the model, there exists a multi-dimensional binding heteroclinic network consisting of saddle equilibrium points and heteroclinic trajectories joining them. We prove here the robustness of the binding sequential dynamics, i.e., the feasibility phenomenon for coupled heteroclinic networks: for each collection of successive heteroclinic trajectories inside the unified networks, there is an open set of initial points such that the trajectory going through each of them follows the prescribed collection staying in a small neighborhood of it. We show also that the symbolic complexity function of the system restricted to this neighborhood is a polynomial of degree L - 1, where L is the number of modalities.

Generalized gradient algorithm for trajectory optimization

NASA Technical Reports Server (NTRS)

Zhao, Yiyuan; Bryson, A. E.; Slattery, R.

1990-01-01

The generalized gradient algorithm presented and verified as a basis for the solution of trajectory optimization problems improves the performance index while reducing path equality constraints, and terminal equality constraints. The algorithm is conveniently divided into two phases, of which the first, 'feasibility' phase yields a solution satisfying both path and terminal constraints, while the second, 'optimization' phase uses the results of the first phase as initial guesses.

Analytical Evaluation of a Method of Midcourse Guidance for Rendezvous with Earth Satellites

NASA Technical Reports Server (NTRS)

Eggleston, John M.; Dunning, Robert S.

1961-01-01

A digital-computer simulation was made of the midcourse or ascent phase of a rendezvous between a ferry vehicle and a space station. The simulation involved a closed-loop guidance system in which both the relative position and relative velocity between ferry and station are measured (by simulated radar) and the relative-velocity corrections required to null the miss distance are computed and applied. The results are used to study the effectiveness of a particular set of guidance equations and to study the effects of errors in the launch conditions and errors in the navigation data. A number of trajectories were investigated over a variety of initial conditions for cases in which the space station was in a circular orbit and also in an elliptic orbit. Trajectories are described in terms of a rotating coordinate system fixed in the station. As a result of this study the following conclusions are drawn. Successful rendezvous can be achieved even with launch conditions which are substantially less accurate than those obtained with present-day techniques. The average total-velocity correction required during the midcourse phase is directly proportional to the radar accuracy but the miss distance is not. Errors in the time of booster burnout or in the position of the ferry at booster burnout are less important than errors in the ferry velocity at booster burnout. The use of dead bands to account for errors in the navigational (radar) equipment appears to depend upon a compromise between the magnitude of the velocity corrections to be made and the allowable miss distance at the termination of the midcourse phase of the rendezvous. When approximate guidance equations are used, there are limits on their accuracy which are dependent on the angular distance about the earth to the expected point of rendezvous.

ACES: Space shuttle flight software analysis expert system

NASA Technical Reports Server (NTRS)

Satterwhite, R. Scott

1990-01-01

The Analysis Criteria Evaluation System (ACES) is a knowledge based expert system that automates the final certification of the Space Shuttle onboard flight software. Guidance, navigation and control of the Space Shuttle through all its flight phases are accomplished by a complex onboard flight software system. This software is reconfigured for each flight to allow thousands of mission-specific parameters to be introduced and must therefore be thoroughly certified prior to each flight. This certification is performed in ground simulations by executing the software in the flight computers. Flight trajectories from liftoff to landing, including abort scenarios, are simulated and the results are stored for analysis. The current methodology of performing this analysis is repetitive and requires many man-hours. The ultimate goals of ACES are to capture the knowledge of the current experts and improve the quality and reduce the manpower required to certify the Space Shuttle onboard flight software.

Analysis on Tracking Schedule and Measurements Characteristics for the Spacecraft on the Phase of Lunar Transfer and Capture

NASA Astrophysics Data System (ADS)

Song, Young-Joo; Choi, Su-Jin; Ahn, Sang-il; Sim, Eun-Sup

2014-03-01

In this work, the preliminary analysis on both the tracking schedule and measurements characteristics for the spacecraft on the phase of lunar transfer and capture is performed. To analyze both the tracking schedule and measurements characteristics, lunar transfer and capture phases¡¯ optimized trajectories are directly adapted from former research, and eleven ground tracking facilities (three Deep Space Network sties, seven Near Earth Network sites, one Daejeon site) are assumed to support the mission. Under these conceptual mission scenarios, detailed tracking schedules and expected measurement characteristics during critical maneuvers (Trans Lunar Injection, Lunar Orbit Insertion and Apoapsis Adjustment Maneuver), especially for the Deajeon station, are successfully analyzed. The orders of predicted measurements' variances during lunar capture phase according to critical maneuvers are found to be within the order of mm/s for the range and micro-deg/s for the angular measurements rates which are in good agreement with the recommended values of typical measurement modeling accuracies for Deep Space Networks. Although preliminary navigation accuracy guidelines are provided through this work, it is expected to give more practical insights into preparing the Korea's future lunar mission, especially for developing flight dynamics subsystem.

Secondary Payload Opportunities on NASA's Space Launch System (SLS) Enable Science and Deep Space Exploration

NASA Technical Reports Server (NTRS)

Singer, Jody; Pelfrey, Joseph; Norris, George

2016-01-01

For the first time in almost 40 years, a NASA human-rated launch vehicle has completed its Critical Design Review (CDR). With this milestone, NASA's Space Launch System (SLS) and Orion spacecraft are on the path to launch a new era of deep space exploration. This first launch of SLS and the Orion Spacecraft is planned no later than November 2018 and will fly along a trans-lunar trajectory, testing the performance of the SLS and Orion systems for future missions. NASA is making investments to expand the science and exploration capability of the SLS by developing the capability to deploy small satellites during the trans-lunar phase of the mission trajectory. Exploration Mission 1 (EM-1) will include thirteen 6U Cubesat small satellites to be deployed beyond low earth orbit. By providing an earth-escape trajectory, opportunities are created for the advancement of small satellite subsystems, including deep space communications and in-space propulsion. This SLS capability also creates low-cost options for addressing existing Agency strategic knowledge gaps and affordable science missions. A new approach to payload integration and mission assurance is needed to ensure safety of the vehicle, while also maintaining reasonable costs for the small payload developer teams. SLS EM-1 will provide the framework and serve as a test flight, not only for vehicle systems, but also payload accommodations, ground processing, and on-orbit operations. Through developing the requirements and integration processes for EM-1, NASA is outlining the framework for the evolved configuration of secondary payloads on SLS Block upgrades. The lessons learned from the EM-1 mission will be applied to processes and products developed for future block upgrades. In the heavy-lift configuration of SLS, payload accommodations will increase for secondary opportunities including small satellites larger than the traditional Cubesat class payload. The payload mission concept of operations, proposed payload capacity of SLS, and the payload requirements for launch and deployment will be described to provide potential payload users an understanding of this unique exploration capability.

Influence of droplet spacing on drag coefficient in nonevaporating, monodisperse streams

NASA Astrophysics Data System (ADS)

Mulholland, J. A.; Srivastava, R. K.; Wendt, J. O. L.

1988-10-01

Trajectory measurements on single, monodisperse, nonevaporating droplet streams whose droplet size, velocity, and spacing were varied to yield initial Re numbers in the 90-290 range are presently used to ascertain the influence of droplet spacing on the drag coefficient of individual drops injected into a quiescent environment. A trajectory model containing the local drag coefficient was fitted to the experimental data by a nonlinear regression; over 40 additional trajectories were predicted with acceptable accuracy. This formulation will aid the computation of waste-droplet drag in flames for improved combustion-generated pollutant predictions.

Interferometric inverse synthetic aperture radar imaging for space targets based on wideband direct sampling using two antennas

NASA Astrophysics Data System (ADS)

Tian, Biao; Liu, Yang; Xu, Shiyou; Chen, Zengping

2014-01-01

Interferometric inverse synthetic aperture radar (InISAR) imaging provides complementary information to monostatic inverse synthetic aperture radar (ISAR) imaging. This paper proposes a new InISAR imaging system for space targets based on wideband direct sampling using two antennas. The system is easy to realize in engineering since the motion trajectory of space targets can be known in advance, which is simpler than that of three receivers. In the preprocessing step, high speed movement compensation is carried out by designing an adaptive matched filter containing speed that is obtained from the narrow band information. Then, the coherent processing and keystone transform for ISAR imaging are adopted to reserve the phase history of each antenna. Through appropriate collocation of the system, image registration and phase unwrapping can be avoided. Considering the situation not to be satisfied, the influence of baseline variance is analyzed and compensation method is adopted. The corresponding size can be achieved by interferometric processing of the two complex ISAR images. Experimental results prove the validity of the analysis and the three-dimensional imaging algorithm.

Transport of phase space densities through tetrahedral meshes using discrete flow mapping

NASA Astrophysics Data System (ADS)

Bajars, Janis; Chappell, David J.; Søndergaard, Niels; Tanner, Gregor

2017-01-01

Discrete flow mapping was recently introduced as an efficient ray based method determining wave energy distributions in complex built up structures. Wave energy densities are transported along ray trajectories through polygonal mesh elements using a finite dimensional approximation of a ray transfer operator. In this way the method can be viewed as a smoothed ray tracing method defined over meshed surfaces. Many applications require the resolution of wave energy distributions in three-dimensional domains, such as in room acoustics, underwater acoustics and for electromagnetic cavity problems. In this work we extend discrete flow mapping to three-dimensional domains by propagating wave energy densities through tetrahedral meshes. The geometric simplicity of the tetrahedral mesh elements is utilised to efficiently compute the ray transfer operator using a mixture of analytic and spectrally accurate numerical integration. The important issue of how to choose a suitable basis approximation in phase space whilst maintaining a reasonable computational cost is addressed via low order local approximations on tetrahedral faces in the position coordinate and high order orthogonal polynomial expansions in momentum space.

Using sketch-map coordinates to analyze and bias molecular dynamics simulations

PubMed Central

Tribello, Gareth A.; Ceriotti, Michele; Parrinello, Michele

2012-01-01

When examining complex problems, such as the folding of proteins, coarse grained descriptions of the system drive our investigation and help us to rationalize the results. Oftentimes collective variables (CVs), derived through some chemical intuition about the process of interest, serve this purpose. Because finding these CVs is the most difficult part of any investigation, we recently developed a dimensionality reduction algorithm, sketch-map, that can be used to build a low-dimensional map of a phase space of high-dimensionality. In this paper we discuss how these machine-generated CVs can be used to accelerate the exploration of phase space and to reconstruct free-energy landscapes. To do so, we develop a formalism in which high-dimensional configurations are no longer represented by low-dimensional position vectors. Instead, for each configuration we calculate a probability distribution, which has a domain that encompasses the entirety of the low-dimensional space. To construct a biasing potential, we exploit an analogy with metadynamics and use the trajectory to adaptively construct a repulsive, history-dependent bias from the distributions that correspond to the previously visited configurations. This potential forces the system to explore more of phase space by making it desirable to adopt configurations whose distributions do not overlap with the bias. We apply this algorithm to a small model protein and succeed in reproducing the free-energy surface that we obtain from a parallel tempering calculation. PMID:22427357

Fast three-dimensional inner volume excitations using parallel transmission and optimized k-space trajectories.

PubMed

Davids, Mathias; Schad, Lothar R; Wald, Lawrence L; Guérin, Bastien

2016-10-01

To design short parallel transmission (pTx) pulses for excitation of arbitrary three-dimensional (3D) magnetization patterns. We propose a joint optimization of the pTx radiofrequency (RF) and gradient waveforms for excitation of arbitrary 3D magnetization patterns. Our optimization of the gradient waveforms is based on the parameterization of k-space trajectories (3D shells, stack-of-spirals, and cross) using a small number of shape parameters that are well-suited for optimization. The resulting trajectories are smooth and sample k-space efficiently with few turns while using the gradient system at maximum performance. Within each iteration of the k-space trajectory optimization, we solve a small tip angle least-squares RF pulse design problem. Our RF pulse optimization framework was evaluated both in Bloch simulations and experiments on a 7T scanner with eight transmit channels. Using an optimized 3D cross (shells) trajectory, we were able to excite a cube shape (brain shape) with 3.4% (6.2%) normalized root-mean-square error in less than 5 ms using eight pTx channels and a clinical gradient system (Gmax  = 40 mT/m, Smax  = 150 T/m/s). This compared with 4.7% (41.2%) error for the unoptimized 3D cross (shells) trajectory. Incorporation of B0 robustness in the pulse design significantly altered the k-space trajectory solutions. Our joint gradient and RF optimization approach yields excellent excitation of 3D cube and brain shapes in less than 5 ms, which can be used for reduced field of view imaging and fat suppression in spectroscopy by excitation of the brain only. Magn Reson Med 76:1170-1182, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

An instrument for discrimination between orbital debris and natural particles in near-Earth space

NASA Astrophysics Data System (ADS)

Tuzzolino, A. J.; Simpson, J. A.; McKibben, R. B.; Voss, H. D.; Gursky, H.

1993-08-01

We discuss a SPAce DUSt instrument (SPADUS) under development for flight on the USA ARGOS mission to measure the flux, mass, velocity and trajectory of near-Earth dust. Since natural (cosmic) dust and man-made dust particles (orbital debris) have different velocity and trajectory distributions, they are distinguished by means of the SPADUS velocity/trajectory information. Measurements will cover the dust mass range ~5×10-12 g (2 μm diameter) to ~ 1×10-5g (200 μm diameter), with an expected mean error in particle trajectory of ~7° (isotropic flux).

Space tug aerobraking study. Volume 1: Executive summary

NASA Technical Reports Server (NTRS)

Corso, C. J.; Eyer, C. L.

1972-01-01

The feasibility and practicality of employing an aerobraking trajectory for return of the reusable space tug from geosynchronous orbit was investigated. The aerobraking return trajectory modes employ transfer ellipses from high orbits which have low perigee altitudes wherein the earth's sensible atmosphere provides drag to reduce the tug return delta velocity requirements and thus decrease the required return trip propulsive energy. Aerodynamics, aerothermodynamics, trajectories, guidance and control, configuration concepts, materials, weights and performance were considered. Sensitivities to trajectory uncertainties, atmospheric anomalies and reentry environments were determined. New technology requirements and future studies required to further enhance the aerobraking potential were identified.

Dynamic Regimes of El Niño Southern Oscillation and Influenza Pandemic Timing

PubMed Central

Oluwole, Olusegun Steven Ayodele

2017-01-01

El Niño southern oscillation (ENSO) dynamics has been shown to drive seasonal influenza dynamics. Severe seasonal influenza epidemics and the 2009–2010 pandemic were coincident with chaotic regime of ENSO dynamics. ENSO dynamics from 1876 to 2016 were characterized to determine if influenza pandemics are coupled to chaotic regimes. Time-varying spectra of southern oscillation index (SOI) and sea surface temperature (SST) were compared. SOI and SST were decomposed to components using the algorithm of noise-assisted multivariate empirical mode decomposition. The components were Hilbert transformed to generate instantaneous amplitudes and phases. The trajectories and attractors of components were characterized in polar coordinates and state space. Influenza pandemics were mapped to dynamic regimes of SOI and SST joint recurrence of annual components. State space geometry of El Niños lagged by influenza pandemics were characterized and compared with other El Niños. Timescales of SOI and SST components ranged from sub-annual to multidecadal. The trajectories of SOI and SST components and the joint recurrence of annual components were dissipative toward chaotic attractors. Periodic, quasi-periodic, and chaotic regimes were present in the recurrence of trajectories, but chaos–chaos transitions dominated. Influenza pandemics occurred during chaotic regimes of significantly low transitivity dimension (p < 0.0001). El Niños lagged by influenza pandemics had distinct state space geometry (p < 0.0001). Chaotic dynamics explains the aperiodic timing, and varying duration and strength of El Niños. Coupling of all influenza pandemics of the past 140 years to chaotic regimes of low transitivity indicate that ENSO dynamics drives influenza pandemic dynamics. Forecasts models from ENSO dynamics should compliment surveillance for novel influenza viruses. PMID:29218303

Estimating long-term behavior of periodically driven flows without trajectory integration

NASA Astrophysics Data System (ADS)

Froyland, Gary; Koltai, Péter

2017-05-01

Periodically driven flows are fundamental models of chaotic behavior and the study of their transport properties is an active area of research. A well-known analytic construction is the augmentation of phase space with an additional time dimension; in this augmented space, the flow becomes autonomous or time-independent. We prove several results concerning the connections between the original time-periodic representation and the time-extended representation, focusing on transport properties. In the deterministic setting, these include single-period outflows and time-asymptotic escape rates from time-parameterized families of sets. We also consider stochastic differential equations with time-periodic advection term. In this stochastic setting one has a time-periodic generator (the differential operator given by the right-hand-side of the corresponding time-periodic Fokker-Planck equation). We define in a natural way an autonomous generator corresponding to the flow on time-extended phase space. We prove relationships between these two generator representations and use these to quantify decay rates of observables and to determine time-periodic families of sets with slow escape rate. Finally, we use the generator on the time-extended phase space to create efficient numerical schemes to implement the various theoretical constructions. These ideas build on the work of Froyland et al (2013 SIAM J. Numer. Anal. 51 223-47), and no expensive time integration is required. We introduce an efficient new hybrid approach, which treats the space and time dimensions separately.

Wave-Particle Dynamics of Wave Breaking in the Self-Excited Dust Acoustic Wave

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

Teng, L.-W.; Chang, M.-C.; Tseng, Y.-P.

2009-12-11

The wave-particle microdynamics in the breaking of the self-excited dust acoustic wave growing in a dusty plasma liquid is investigated through directly tracking dust micromotion. It is found that the nonlinear wave growth and steepening stop as the mean oscillating amplitude of dust displacement reaches about 1/k (k is the wave number), where the vertical neighboring dust trajectories start to crossover and the resonant wave heating with uncertain crest trapping onsets. The dephased dust oscillations cause the abrupt dropping and broadening of the wave crest after breaking, accompanied by the transition from the liquid phase with coherent dust oscillation tomore » the gas phase with chaotic dust oscillation. Corkscrew-shaped phase-space distributions measured at the fixed phases of the wave oscillation cycle clearly indicate how dusts move in and constitute the evolving waveform through dust-wave interaction.« less

Wave-Particle Dynamics of Wave Breaking in the Self-Excited Dust Acoustic Wave

NASA Astrophysics Data System (ADS)

Teng, Lee-Wen; Chang, Mei-Chu; Tseng, Yu-Ping; I, Lin

2009-12-01

The wave-particle microdynamics in the breaking of the self-excited dust acoustic wave growing in a dusty plasma liquid is investigated through directly tracking dust micromotion. It is found that the nonlinear wave growth and steepening stop as the mean oscillating amplitude of dust displacement reaches about 1/k (k is the wave number), where the vertical neighboring dust trajectories start to crossover and the resonant wave heating with uncertain crest trapping onsets. The dephased dust oscillations cause the abrupt dropping and broadening of the wave crest after breaking, accompanied by the transition from the liquid phase with coherent dust oscillation to the gas phase with chaotic dust oscillation. Corkscrew-shaped phase-space distributions measured at the fixed phases of the wave oscillation cycle clearly indicate how dusts move in and constitute the evolving waveform through dust-wave interaction.

Non-adiabatic dynamics around a conical intersection with surface-hopping coupled coherent states

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

Humeniuk, Alexander; Mitrić, Roland, E-mail: roland.mitric@uni-wuerzburg.de

A surface-hopping extension of the coupled coherent states-method [D. Shalashilin and M. Child, Chem. Phys. 304, 103-120 (2004)] for simulating non-adiabatic dynamics with quantum effects of the nuclei is put forward. The time-dependent Schrödinger equation for the motion of the nuclei is solved in a moving basis set. The basis set is guided by classical trajectories, which can hop stochastically between different electronic potential energy surfaces. The non-adiabatic transitions are modelled by a modified version of Tully’s fewest switches algorithm. The trajectories consist of Gaussians in the phase space of the nuclei (coherent states) combined with amplitudes for an electronicmore » wave function. The time-dependent matrix elements between different coherent states determine the amplitude of each trajectory in the total multistate wave function; the diagonal matrix elements determine the hopping probabilities and gradients. In this way, both interference effects and non-adiabatic transitions can be described in a very compact fashion, leading to the exact solution if convergence with respect to the number of trajectories is achieved and the potential energy surfaces are known globally. The method is tested on a 2D model for a conical intersection [A. Ferretti, J. Chem. Phys. 104, 5517 (1996)], where a nuclear wavepacket encircles the point of degeneracy between two potential energy surfaces and interferes with itself. These interference effects are absent in classical trajectory-based molecular dynamics but can be fully incorpo rated if trajectories are replaced by surface hopping coupled coherent states.« less

Use of Smoothed Measured Winds to Predict and Assess Launch Environments

NASA Technical Reports Server (NTRS)

Cordova, Henry S.; Leahy, Frank; Adelfang, Stanley; Roberts, Barry; Starr, Brett; Duffin, Paul; Pueri, Daniel

2011-01-01

Since many of the larger launch vehicles are operated near their design limits during the ascent phase of flight to optimize payload to orbit, it often becomes necessary to verify that the vehicle will remain within certification limits during the ascent phase as part of the go/no-go review made prior to launch. This paper describes the approach used to predict Ares I-X launch vehicle structural air loads and controllability prior to launch which represents a distinct departure from the methodology of the Space Shuttle and Evolved Expendable Launch Vehicle (EELV) programs. Protection for uncertainty of key environment and trajectory parameters is added to the nominal assessment of launch capability to ensure that critical launch trajectory variables would be within the integrated vehicle certification envelopes. This process was applied by the launch team as a key element of the launch day go/no-go recommendation. Pre-launch assessments of vehicle launch capability for NASA's Space Shuttle and the EELV heavy lift versions require the use of a high-resolution wind profile measurements, which have relatively small sample size compared with low-resolution profile databases (which include low-resolution balloons and radar wind profilers). The approach described in this paper has the potential to allow the pre-launch assessment team to use larger samples of wind measurements from low-resolution wind profile databases that will improve the accuracy of pre-launch assessments of launch availability with no degradation of mission assurance or launch safety.

Fully adaptive propagation of the quantum-classical Liouville equation

NASA Astrophysics Data System (ADS)

Horenko, Illia; Weiser, Martin; Schmidt, Burkhard; Schütte, Christof

2004-05-01

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.

Fully adaptive propagation of the quantum-classical Liouville equation.

PubMed

Horenko, Illia; Weiser, Martin; Schmidt, Burkhard; Schütte, Christof

2004-05-15

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.

Instantons in Self-Organizing Logic Gates

NASA Astrophysics Data System (ADS)

Bearden, Sean R. B.; Manukian, Haik; Traversa, Fabio L.; Di Ventra, Massimiliano

2018-03-01

Self-organizing logic is a recently suggested framework that allows the solution of Boolean truth tables "in reverse"; i.e., it is able to satisfy the logical proposition of gates regardless to which terminal(s) the truth value is assigned ("terminal-agnostic logic"). It can be realized if time nonlocality (memory) is present. A practical realization of self-organizing logic gates (SOLGs) can be done by combining circuit elements with and without memory. By employing one such realization, we show, numerically, that SOLGs exploit elementary instantons to reach equilibrium points. Instantons are classical trajectories of the nonlinear equations of motion describing SOLGs and connect topologically distinct critical points in the phase space. By linear analysis at those points, we show that these instantons connect the initial critical point of the dynamics, with at least one unstable direction, directly to the final fixed point. We also show that the memory content of these gates affects only the relaxation time to reach the logically consistent solution. Finally, we demonstrate, by solving the corresponding stochastic differential equations, that, since instantons connect critical points, noise and perturbations may change the instanton trajectory in the phase space but not the initial and final critical points. Therefore, even for extremely large noise levels, the gates self-organize to the correct solution. Our work provides a physical understanding of, and can serve as an inspiration for, models of bidirectional logic gates that are emerging as important tools in physics-inspired, unconventional computing.

An Evaluation of a Flight Deck Interval Management Algorithm Including Delayed Target Trajectories

NASA Technical Reports Server (NTRS)

Swieringa, Kurt A.; Underwood, Matthew C.; Barmore, Bryan; Leonard, Robert D.

2014-01-01

NASA's first Air Traffic Management (ATM) Technology Demonstration (ATD-1) was created to facilitate the transition of mature air traffic management technologies from the laboratory to operational use. The technologies selected for demonstration are the Traffic Management Advisor with Terminal Metering (TMA-TM), which provides precise timebased scheduling in the terminal airspace; Controller Managed Spacing (CMS), which provides controllers with decision support tools enabling precise schedule conformance; and Interval Management (IM), which consists of flight deck automation that enables aircraft to achieve or maintain precise in-trail spacing. During high demand operations, TMA-TM may produce a schedule and corresponding aircraft trajectories that include delay to ensure that a particular aircraft will be properly spaced from other aircraft at each schedule waypoint. These delayed trajectories are not communicated to the automation onboard the aircraft, forcing the IM aircraft to use the published speeds to estimate the target aircraft's estimated time of arrival. As a result, the aircraft performing IM operations may follow an aircraft whose TMA-TM generated trajectories have substantial speed deviations from the speeds expected by the spacing algorithm. Previous spacing algorithms were not designed to handle this magnitude of uncertainty. A simulation was conducted to examine a modified spacing algorithm with the ability to follow aircraft flying delayed trajectories. The simulation investigated the use of the new spacing algorithm with various delayed speed profiles and wind conditions, as well as several other variables designed to simulate real-life variability. The results and conclusions of this study indicate that the new spacing algorithm generally exhibits good performance; however, some types of target aircraft speed profiles can cause the spacing algorithm to command less than optimal speed control behavior.

Clustering of neural code words revealed by a first-order phase transition

NASA Astrophysics Data System (ADS)

Huang, Haiping; Toyoizumi, Taro

2016-06-01

A network of neurons in the central nervous system collectively represents information by its spiking activity states. Typically observed states, i.e., code words, occupy only a limited portion of the state space due to constraints imposed by network interactions. Geometrical organization of code words in the state space, critical for neural information processing, is poorly understood due to its high dimensionality. Here, we explore the organization of neural code words using retinal data by computing the entropy of code words as a function of Hamming distance from a particular reference codeword. Specifically, we report that the retinal code words in the state space are divided into multiple distinct clusters separated by entropy-gaps, and that this structure is shared with well-known associative memory networks in a recallable phase. Our analysis also elucidates a special nature of the all-silent state. The all-silent state is surrounded by the densest cluster of code words and located within a reachable distance from most code words. This code-word space structure quantitatively predicts typical deviation of a state-trajectory from its initial state. Altogether, our findings reveal a non-trivial heterogeneous structure of the code-word space that shapes information representation in a biological network.

Automation of POST Cases via External Optimizer and "Artificial p2" Calculation

NASA Technical Reports Server (NTRS)

Dees, Patrick D.; Zwack, Mathew R.

2017-01-01

During early conceptual design of complex systems, speed and accuracy are often at odds with one another. While many characteristics of the design are fluctuating rapidly during this phase there is nonetheless a need to acquire accurate data from which to down-select designs as these decisions will have a large impact upon program life-cycle cost. Therefore enabling the conceptual designer to produce accurate data in a timely manner is tantamount to program viability. For conceptual design of launch vehicles, trajectory analysis and optimization is a large hurdle. Tools such as the industry standard Program to Optimize Simulated Trajectories (POST) have traditionally required an expert in the loop for setting up inputs, running the program, and analyzing the output. The solution space for trajectory analysis is in general non-linear and multi-modal requiring an experienced analyst to weed out sub-optimal designs in pursuit of the global optimum. While an experienced analyst presented with a vehicle similar to one which they have already worked on can likely produce optimal performance figures in a timely manner, as soon as the "experienced" or "similar" adjectives are invalid the process can become lengthy. In addition, an experienced analyst working on a similar vehicle may go into the analysis with preconceived ideas about what the vehicle's trajectory should look like which can result in sub-optimal performance being recorded. Thus, in any case but the ideal either time or accuracy can be sacrificed. In the authors' previous work a tool called multiPOST was created which captures the heuristics of a human analyst over the process of executing trajectory analysis with POST. However without the instincts of a human in the loop, this method relied upon Monte Carlo simulation to find successful trajectories. Overall the method has mixed results, and in the context of optimizing multiple vehicles it is inefficient in comparison to the method presented POST's internal optimizer functions like any other gradient-based optimizer. It has a specified variable to optimize whose value is represented as optval, a set of dependent constraints to meet with associated forms and tolerances whose value is represented as p2, and a set of independent variables known as the u-vector to modify in pursuit of optimality. Each of these quantities are calculated or manipulated at a certain phase within the trajectory. The optimizer is further constrained by the requirement that the input u-vector must result in a trajectory which proceeds through each of the prescribed events in the input file. For example, if the input u-vector causes the vehicle to crash before it can achieve the orbital parameters required for a parking orbit, then the run will fail without engaging the optimizer, and a p2 value of exactly zero is returned. This poses a problem, as this "non-connecting" region of the u-vector space is far larger than the "connecting" region which returns a non-zero value of p2 and can be worked on by the internal optimizer. Finding this connecting region and more specifically the global optimum within this region has traditionally required the use of an expert analyst.

Evolution of Space Shuttle Range Safety (RS) Ascent Flight Envelope Design

NASA Technical Reports Server (NTRS)

Brewer, Joan D.

2011-01-01

Ascent flight envelopes are trajectories that define the normal operating region of a space vehicle s position from liftoff until the end of powered flight. They fulfill part of the RS data requirements imposed by the Air Force s 45th Space Wing (45SW) on space vehicles launching from the Eastern Range (ER) in Florida. The 45SW is chartered to protect the public by minimizing risks associated with the inherent hazards of launching a vehicle into space. NASA s Space Shuttle program has launched 130+ manned missions over a 30 year period from the ER. Ascent envelopes were delivered for each of those missions. The 45SW envelope requirements have remained largely unchanged during this time. However, the methodology and design processes used to generate the envelopes have evolved over the years to support mission changes, maintain high data quality, and reduce costs. The evolution of the Shuttle envelope design has yielded lessons learned that can be applied to future endevours. There have been numerous Shuttle ascent design enhancements over the years that have caused the envelope methodology to evolve. One of these Shuttle improvements was the introduction of onboard flight software changes implemented to improve launch probability. This change impacted the preflight nominal ascent trajectory, which is a key element in the RS envelope design. While the early Shuttle nominal trajectories were designed preflight using a representative monthly mean wind, the new software changes involved designing a nominal ascent trajectory on launch day using real-time winds. Because the actual nominal trajectory position was not known until launch day, the envelope analysis had to be customized to account for this nominal trajectory variation in addition to the other envelope components.

An Overview of a Trajectory-Based Solution for En Route and Terminal Area Self-Spacing: Fifth Edition

NASA Technical Reports Server (NTRS)

Abbott, Terence S.

2015-01-01

This paper presents an overview of the fifth revision to an algorithm specifically designed to support NASA's Airborne Precision Spacing concept. This algorithm is referred to as the Airborne Spacing for Terminal Arrival Routes version 12 (ASTAR12). This airborne self-spacing concept is trajectory-based, allowing for spacing operations prior to the aircraft being on a common path. Because this algorithm is trajectory-based, it also has the inherent ability to support required-time-of- arrival (RTA) operations. This algorithm was also designed specifically to support a standalone, non-integrated implementation in the spacing aircraft. This current revision to the algorithm includes a ground speed feedback term to compensate for slower than expected traffic aircraft speeds based on the accepted air traffic control tendency to slow aircraft below the nominal arrival speeds when they are farther from the airport.

NASA Advanced Concepts Office, Earth-To-Orbit Team Design Process and Tools

NASA Technical Reports Server (NTRS)

Waters, Eric D.; Garcia, Jessica; Beers, Benjamin; Philips, Alan; Holt, James B.; Threet, Grady E., Jr.

2013-01-01

The Earth to Orbit (ETO) Team of the Advanced Concepts Office (ACO) at NASA Marshal Space Flight Center (MSFC) is considered the preeminent group to go to for prephase A and phase A concept definition. The ACO team has been at the forefront of a multitude of launch vehicle studies determining the future direction of the Agency as a whole due, in part, to their rapid turnaround time in analyzing concepts and their ability to cover broad trade spaces of vehicles in that limited timeframe. Each completed vehicle concept includes a full mass breakdown of each vehicle to tertiary subsystem components, along with a vehicle trajectory analysis to determine optimized payload delivery to specified orbital parameters, flight environments, and delta v capability. Additionally, a structural analysis of the vehicle based on material properties and geometries is performed as well as an analysis to determine the flight loads based on the trajectory outputs. As mentioned, the ACO Earth to Orbit Team prides themselves on their rapid turnaround time and often need to fulfill customer requests within limited schedule or little advanced notice. Due to working in this fast paced environment, the ETO team has developed some finely honed skills and methods to maximize the delivery capability to meet their customer needs. This paper will describe the interfaces between the 3 primary disciplines used in the design process; weights and sizing, trajectory, and structural analysis, as well as the approach each discipline employs to streamline their particular piece of the design process.

Sensitivity Analysis and Mitigation with Applications to Ballistic and Low-thrust Trajectory Design

NASA Astrophysics Data System (ADS)

Alizadeh, Iman

The ever increasing desire to expand space mission capabilities within the limited budgets of space industries requires new approaches to the old problem of spacecraft trajectory design. For example, recent initiatives for space exploration involve developing new tools to design low-cost, fail-safe trajectories to visit several potential destinations beyond our celestial neighborhood such as Jupiter's moons, asteroids, etc. Designing and navigating spacecraft trajectories to reach these destinations safely are complex and challenging. In particular, fundamental questions of orbital stability imposed by planetary protection requirements are not easily taken into account by standard optimal control schemes. The event of temporary engine loss or an unexpected missed thrust can indeed quickly lead to impact with planetary bodies or other unrecoverable trajectories. While electric propulsion technology provides superior efficiency compared to chemical engines, the very low-control authority and engine performance degradation can impose higher risk to the mission in strongly perturbed orbital environments. The risk is due to the complex gravitational field and its associated chaotic dynamics which causes large navigation dispersions in a short time if left un-controlled. Moreover, in these situations it can be outside the low-thrust propulsion system capability to correct the spacecraft trajectory in a reasonable time frame. These concerns can lead to complete or partial mission failure or even an infeasible mission concept at the early design stage. The goal of this research is to assess and increase orbital stability of ballistic and low-thrust transfer trajectories in multi-body systems. In particular, novel techniques are presented to characterize sensitivity and improve recovery characteristics of ballistic and low-thrust trajectories in unstable orbital environments. The techniques developed are based on perturbation analysis around ballistic trajectories to determine analytically the maximum divergence directions and also optimal control theory with nonstandard cost functions along with inverse dynamics applied to low-thrust trajectories. Several mission scenarios are shown to demonstrate the applicability of the techniques in the Earth-Moon and the Jupiter-Europa system. In addition, the results provide fundamental insight into design, stability analysis and guidance, navigation and control of low-thrust trajectories to meet challenging mission requirements in support of NASA's vision for space exploration.

Mid-Ventilation Concept for Mobile Pulmonary Tumors: Internal Tumor Trajectory Versus Selective Reconstruction of Four-Dimensional Computed Tomography Frames Based on External Breathing Motion

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

Guckenberger, Matthias; Wilbert, Juergen; Krieger, Thomas

2009-06-01

Purpose: To evaluate the accuracy of direct reconstruction of mid-ventilation and peak-phase four-dimensional (4D) computed tomography (CT) frames based on the external breathing signal. Methods and Materials: For 11 patients with 15 pulmonary targets, a respiration-correlated CT study (4D CT) was acquired for treatment planning. After retrospective time-based sorting of raw projection data and reconstruction of eight CT frames equally distributed over the breathing cycle, mean tumor position (P{sub mean}), mid-ventilation frame, and breathing motion were evaluated based on the internal tumor trajectory. Analysis of the external breathing signal (pressure sensor around abdomen) with amplitude-based sorting of projections was performedmore » for direct reconstruction of the mid-ventilation frame and frames at peak phases of the breathing cycle. Results: On the basis of the eight 4D CT frames equally spaced in time, tumor motion was largest in the craniocaudal direction, with 12 {+-} 7 mm on average. Tumor motion between the two frames reconstructed at peak phases was not different in the craniocaudal and anterior-posterior directions but was systematically smaller in the left-right direction by 1 mm on average. The 3-dimensional distance between P{sub mean} and the tumor position in the mid-ventilation frame based on the internal tumor trajectory was 1.2 {+-} 1 mm. Reconstruction of the mid-ventilation frame at the mean amplitude position of the external breathing signal resulted in tumor positions 2.0 {+-} 1.1 mm distant from P{sub mean}. Breathing-induced motion artifacts in mid-ventilation frames caused negligible changes in tumor volume and shape. Conclusions: Direct reconstruction of the mid-ventilation frame and frames at peak phases based on the external breathing signal was reliable. This makes the reconstruction of only three 4D CT frames sufficient for application of the mid-ventilation technique in clinical practice.« less

Linear time-to-space mapping system using double electrooptic beam deflectors.

PubMed

Hisatake, Shintaro; Tada, Keiji; Nagatsuma, Tadao

2008-12-22

We propose and demonstrate a linear time-to-space mapping system, which is based on two times electrooptic sinusoidal beam deflection. The direction of each deflection is set to be mutually orthogonal with the relative deflection phase of pi/2 rad so that the circular optical beam trajectory can be achieved. The beam spot at the observation plane moves with an uniform velocity and as a result linear time-to-space mapping (an uniform temporal resolution through the mapping) can be realized. The proof-of-concept experiment are carried out and the temporal resolution of 5 ps has been demonstrated using traveling-wave type quasi-velosity-matched electrooptic beam deflectors. The developed system is expected to be applied to characterization of ultrafast optical signal or optical arbitrary waveform shaping for modulated microwave/millimeter-wave generation.

A Method of Trajectory Design for Manned Asteroids Exploration

NASA Astrophysics Data System (ADS)

Gan, Q. B.; Zhang, Y.; Zhu, Z. F.; Han, W. H.; Dong, X.

2014-11-01

A trajectory optimization method of the nuclear propulsion manned asteroids exploration is presented. In the case of launching between 2035 and 2065, based on the Lambert transfer orbit, the phases of departure from and return to the Earth are searched at first. Then the optimal flight trajectory in the feasible regions is selected by pruning the flight sequences. Setting the nuclear propulsion flight plan as propel-coast-propel, and taking the minimal mass of aircraft departure as the index, the nuclear propulsion flight trajectory is separately optimized using a hybrid method. With the initial value of the optimized local parameters of each three phases, the global parameters are jointedly optimized. At last, the minimal departure mass trajectory design result is given.

Monte Carlo Analysis as a Trajectory Design Driver for the TESS Mission

NASA Technical Reports Server (NTRS)

Nickel, Craig; Lebois, Ryan; Lutz, Stephen; Dichmann, Donald; Parker, Joel

2016-01-01

The Transiting Exoplanet Survey Satellite (TESS) will be injected into a highly eccentric Earth orbit and fly 3.5 phasing loops followed by a lunar flyby to enter a mission orbit with lunar 2:1 resonance. Through the phasing loops and mission orbit, the trajectory is significantly affected by lunar and solar gravity. We have developed a trajectory design to achieve the mission orbit and meet mission constraints, including eclipse avoidance and a 30-year geostationary orbit avoidance requirement. A parallelized Monte Carlo simulation was performed to validate the trajectory after injecting common perturbations, including launch dispersions, orbit determination errors, and maneuver execution errors. The Monte Carlo analysis helped identify mission risks and is used in the trajectory selection process.

Berry phase dependent quantum trajectories of electron-hole pairs in semiconductors under intense terahertz fields

NASA Astrophysics Data System (ADS)

Yang, Fan; Liu, Ren-Bao

2013-03-01

Quantum evolution of particles under strong fields can be approximated by the quantum trajectories that satisfy the stationary phase condition in the Dirac-Feynmann path integrals. The quantum trajectories are the key concept to understand strong-field optics phenomena, such as high-order harmonic generation (HHG), above-threshold ionization (ATI), and high-order terahertz siedeband generation (HSG). The HSG in semiconductors may have a wealth of physics due to the possible nontrivial ``vacuum'' states of band materials. We find that in a spin-orbit-coupled semiconductor, the cyclic quantum trajectories of an electron-hole pair under a strong terahertz field accumulates nontrivial Berry phases. We study the monolayer MoS2 as a model system and find that the Berry phases are given by the Faraday rotation angles of the pulse emission from the material under short-pulse excitation. This result demonstrates an interesting Berry phase dependent effect in the extremely nonlinear optics of semiconductors. This work is supported by Hong Kong RGC/GRF 401512 and the CUHK Focused Investments Scheme.

Hybrid Differential Dynamic Programming with Stochastic Search

NASA Technical Reports Server (NTRS)

Aziz, Jonathan; Parker, Jeffrey; Englander, Jacob A.

2016-01-01

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASA's Dawn mission. The Dawn trajectory was designed with the DDP-based Static/Dynamic Optimal Control algorithm used in the Mystic software.1 Another recently developed method, Hybrid Differential Dynamic Programming (HDDP),2, 3 is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

Design and Optimization of Low-thrust Orbit Transfers Using Q-law and Evolutionary Algorithms

NASA Technical Reports Server (NTRS)

Lee, Seungwon; vonAllmen, Paul; Fink, Wolfgang; Petropoulos, Anastassios; Terrile, Richard

2005-01-01

Future space missions will depend more on low-thrust propulsion (such as ion engines) thanks to its high specific impulse. Yet, the design of low-thrust trajectories is complex and challenging. Third-body perturbations often dominate the thrust, and a significant change to the orbit requires a long duration of thrust. In order to guide the early design phases, we have developed an efficient and efficacious method to obtain approximate propellant and flight-time requirements (i.e., the Pareto front) for orbit transfers. A search for the Pareto-optimal trajectories is done in two levels: optimal thrust angles and locations are determined by Q-law, while the Q-law is optimized with two evolutionary algorithms: a genetic algorithm and a simulated-annealing-related algorithm. The examples considered are several types of orbit transfers around the Earth and the asteroid Vesta.

Integrating diffusion maps with umbrella sampling: Application to alanine dipeptide

NASA Astrophysics Data System (ADS)

Ferguson, Andrew L.; Panagiotopoulos, Athanassios Z.; Debenedetti, Pablo G.; Kevrekidis, Ioannis G.

2011-04-01

Nonlinear dimensionality reduction techniques can be applied to molecular simulation trajectories to systematically extract a small number of variables with which to parametrize the important dynamical motions of the system. For molecular systems exhibiting free energy barriers exceeding a few kBT, inadequate sampling of the barrier regions between stable or metastable basins can lead to a poor global characterization of the free energy landscape. We present an adaptation of a nonlinear dimensionality reduction technique known as the diffusion map that extends its applicability to biased umbrella sampling simulation trajectories in which restraining potentials are employed to drive the system into high free energy regions and improve sampling of phase space. We then propose a bootstrapped approach to iteratively discover good low-dimensional parametrizations by interleaving successive rounds of umbrella sampling and diffusion mapping, and we illustrate the technique through a study of alanine dipeptide in explicit solvent.

Exact stochastic unraveling of an optical coherence dynamics by cumulant expansion

NASA Astrophysics Data System (ADS)

Olšina, Jan; Kramer, Tobias; Kreisbeck, Christoph; Mančal, Tomáš

2014-10-01

A numerically exact Monte Carlo scheme for calculation of open quantum system dynamics is proposed and implemented. The method consists of a Monte Carlo summation of a perturbation expansion in terms of trajectories in Liouville phase-space with respect to the coupling between the excited states of the molecule. The trajectories are weighted by a complex decoherence factor based on the second-order cumulant expansion of the environmental evolution. The method can be used with an arbitrary environment characterized by a general correlation function and arbitrary coupling strength. It is formally exact for harmonic environments, and it can be used with arbitrary temperature. Time evolution of an optically excited Frenkel exciton dimer representing a molecular exciton interacting with a charge transfer state is calculated by the proposed method. We calculate the evolution of the optical coherence elements of the density matrix and linear absorption spectrum, and compare them with the predictions of standard simulation methods.

Imaging CF3I conical intersection and photodissociation dynamics by ultrafast electron diffraction

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

Yang, Jie

Conical intersections play a critical role in excited state dynamics of polyatomic molecules, as they govern the reaction pathways of many nonadiabatic processes. However, ultrafast probes have lacked sufficient spatial resolution to image wavepacket trajectories through these intersections directly. Here we present the simultaneous experimental characterization of one-photon and two-photon excitation channels in isolated CF3I molecules using ultrafast gas phase electron diffraction. In the two-photon channel, we have mapped out the real space trajectories of a coherent nuclear wavepacket, which bifurcates onto two potential energy surfaces when passing through a conical intersection. In the one-photon channel, we have resolved excitationmore » of both the umbrella and the breathing vibrational modes in the CF3 fragment in multiple nuclear dimensions. These findings benchmark and validate ab-initio nonadiabatic dynamics calculations.« less

Precisely cyclic sand: self-organization of periodically sheared frictional grains.

PubMed

Royer, John R; Chaikin, Paul M

2015-01-06

The disordered static structure and chaotic dynamics of frictional granular matter has occupied scientists for centuries, yet there are few organizational principles or guiding rules for this highly hysteretic, dissipative material. We show that cyclic shear of a granular material leads to dynamic self-organization into several phases with different spatial and temporal order. Using numerical simulations, we present a phase diagram in strain-friction space that shows chaotic dispersion, crystal formation, vortex patterns, and most unusually a disordered phase in which each particle precisely retraces its unique path. However, the system is not reversible. Rather, the trajectory of each particle, and the entire frictional, many-degrees-of-freedom system, organizes itself into a limit cycle absorbing state. Of particular note is that fact that the cyclic states are spatially disordered, whereas the ordered states are chaotic.

Precisely cyclic sand: Self-organization of periodically sheared frictional grains

PubMed Central

Royer, John R.; Chaikin, Paul M.

2015-01-01

The disordered static structure and chaotic dynamics of frictional granular matter has occupied scientists for centuries, yet there are few organizational principles or guiding rules for this highly hysteretic, dissipative material. We show that cyclic shear of a granular material leads to dynamic self-organization into several phases with different spatial and temporal order. Using numerical simulations, we present a phase diagram in strain–friction space that shows chaotic dispersion, crystal formation, vortex patterns, and most unusually a disordered phase in which each particle precisely retraces its unique path. However, the system is not reversible. Rather, the trajectory of each particle, and the entire frictional, many–degrees-of-freedom system, organizes itself into a limit cycle absorbing state. Of particular note is that fact that the cyclic states are spatially disordered, whereas the ordered states are chaotic. PMID:25538298

Massless Particles in Warped Three Spaces

NASA Astrophysics Data System (ADS)

Barros, Manuel; Caballero, Magdalena; Ortega, Miguel

The model governed by an action measuring the total proper acceleration of trajectories provides a nice framework one to describe the dynamics of massless relativistic particles. In high rigidity cases, metrics with constant curvature, the model is consistent only in spherical three spaces and in three-dimensional anti de Sitter backgrounds, according to a Riemannian or a Lorentzian context, respectively. In contrast to flat gravitational fields, the existence of nontrivial trajectories are shown in a family of three spaces whose metrics admit a certain degree of symmetry. Such trajectories are included in regions with real presence of matter. An algorithm to obtain them is also designed.

Of Modeling the Radiation Hazards Along Trajectory Space Vehicles Various Purpose

NASA Astrophysics Data System (ADS)

Grichshenko, Valentina

2016-07-01

The paper discusses the results of the simulation of radiation hazard along trajectory low-orbit spacecraft for various purposes, geostationary and navigation satellites. Developed criteria of reliability of memory cells in Space, including influence of cosmic rays (CR), differences of geophysical and geomagnetic situation on SV orbit are discussed. Numerical value of vertical geomagnetic stiffness, of CR flux and assessment of correlation failures of memory cells along low-orbit spacecrafts trajectory are presented. Obtained results are used to forecasting the radiation situation along SV orbit, reliability of memory cells in the Space and to optimize nominal equipment kit and payload of Kazakhstan SV.

Four-body trajectory optimization

NASA Technical Reports Server (NTRS)

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

1974-01-01

A comprehensive optimization program has been developed for computing fuel-optimal trajectories between the earth and a point in the sun-earth-moon system. It presents methods for generating fuel optimal two-impulse trajectories which may originate at the earth or a point in space and fuel optimal three-impulse trajectories between two points in space. The extrapolation of the state vector and the computation of the state transition matrix are accomplished by the Stumpff-Weiss method. The cost and constraint gradients are computed analytically in terms of the terminal state and the state transition matrix. The 4-body Lambert problem is solved by using the Newton-Raphson method. An accelerated gradient projection method is used to optimize a 2-impulse trajectory with terminal constraint. The Davidon's Variance Method is used both in the accelerated gradient projection method and the outer loop of a 3-impulse trajectory optimization problem.

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.

Radiofrequency pulse design using nonlinear gradient magnetic fields.

PubMed

Kopanoglu, Emre; Constable, R Todd

2015-09-01

An iterative k-space trajectory and radiofrequency (RF) pulse design method is proposed for excitation using nonlinear gradient magnetic fields. The spatial encoding functions (SEFs) generated by nonlinear gradient fields are linearly dependent in Cartesian coordinates. Left uncorrected, this may lead to flip angle variations in excitation profiles. In the proposed method, SEFs (k-space samples) are selected using a matching pursuit algorithm, and the RF pulse is designed using a conjugate gradient algorithm. Three variants of the proposed approach are given: the full algorithm, a computationally cheaper version, and a third version for designing spoke-based trajectories. The method is demonstrated for various target excitation profiles using simulations and phantom experiments. The method is compared with other iterative (matching pursuit and conjugate gradient) and noniterative (coordinate-transformation and Jacobian-based) pulse design methods as well as uniform density spiral and EPI trajectories. The results show that the proposed method can increase excitation fidelity. An iterative method for designing k-space trajectories and RF pulses using nonlinear gradient fields is proposed. The method can either be used for selecting the SEFs individually to guide trajectory design, or can be adapted to design and optimize specific trajectories of interest. © 2014 Wiley Periodicals, Inc.

An LDEF 2 dust instrument for discrimination between orbital debris and natural particles in near-Earth space

NASA Technical Reports Server (NTRS)

Tuzzolino, A. J.; Simpson, J. A.; Mckibben, R. B.; Voss, H. D.; Gursky, H.

1993-01-01

The characteristics of a space dust instrument which would be ideally suited to carry out near-Earth dust measurements on a possible Long Duraction Exposure Facility reflight mission (LDEF 2) is discussed. As a model for the trajectory portion of the instrument proposed for LDEF 2, the characteristics of a SPAce DUSt instrument (SPADUS) currently under development for flight on the USA ARGOS mission to measure the flux, mass, velocity, and trajectory of near-Earth dust is summarized. Since natural (cosmic) dust and man-made dust particles (orbital debris) have different velocity and trajectory distributions, they are distinguished by means of the SPADUS velocity/trajectory information. The SPADUS measurements will cover the dust mass range approximately 5 x 10(exp -12) g (2 microns diameter) to approximately 1 x 10(exp -5) g (200 microns diameter), with an expected mean error in particle trajectory of approximately 7 deg (isotropic flux). Arrays of capture cell devices positioned behind the trajectory instrumentation would provide for Earth-based chemical and isotopic analysis of captured dust. The SPADUS measurement principles, characteristics, its role in the ARGOS mission, and its application to an LDEF 2 mission are summarized.

High-order space charge effects using automatic differentiation

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

Reusch, Michael F.; Bruhwiler, David L.; Computer Accelerator Physics Conference Williamsburg, Virginia 1996

1997-02-01

The Northrop Grumman Topkark code has been upgraded to Fortran 90, making use of operator overloading, so the same code can be used to either track an array of particles or construct a Taylor map representation of the accelerator lattice. We review beam optics and beam dynamics simulations conducted with TOPKARK in the past and we present a new method for modeling space charge forces to high-order with automatic differentiation. This method generates an accurate, high-order, 6-D Taylor map of the phase space variable trajectories for a bunched, high-current beam. The spatial distribution is modeled as the product of amore » Taylor Series times a Gaussian. The variables in the argument of the Gaussian are normalized to the respective second moments of the distribution. This form allows for accurate representation of a wide range of realistic distributions, including any asymmetries, and allows for rapid calculation of the space charge fields with free space boundary conditions. An example problem is presented to illustrate our approach.« less

Dynamical properties and extremes of Northern Hemisphere climate fields over the past 60 years

NASA Astrophysics Data System (ADS)

Faranda, Davide; Messori, Gabriele; Alvarez-Castro, M. Carmen; Yiou, Pascal

2017-12-01

Atmospheric dynamics are described by a set of partial differential equations yielding an infinite-dimensional phase space. However, the actual trajectories followed by the system appear to be constrained to a finite-dimensional phase space, i.e. a strange attractor. The dynamical properties of this attractor are difficult to determine due to the complex nature of atmospheric motions. A first step to simplify the problem is to focus on observables which affect - or are linked to phenomena which affect - human welfare and activities, such as sea-level pressure, 2 m temperature, and precipitation frequency. We make use of recent advances in dynamical systems theory to estimate two instantaneous dynamical properties of the above fields for the Northern Hemisphere: local dimension and persistence. We then use these metrics to characterize the seasonality of the different fields and their interplay. We further analyse the large-scale anomaly patterns corresponding to phase-space extremes - namely time steps at which the fields display extremes in their instantaneous dynamical properties. The analysis is based on the NCEP/NCAR reanalysis data, over the period 1948-2013. The results show that (i) despite the high dimensionality of atmospheric dynamics, the Northern Hemisphere sea-level pressure and temperature fields can on average be described by roughly 20 degrees of freedom; (ii) the precipitation field has a higher dimensionality; and (iii) the seasonal forcing modulates the variability of the dynamical indicators and affects the occurrence of phase-space extremes. We further identify a number of robust correlations between the dynamical properties of the different variables.

Probing periodic potential of crystals via strong-field re-scattering

NASA Astrophysics Data System (ADS)

You, Yong Sing; Cunningham, Eric; Reis, David A.; Ghimire, Shambhu

2018-06-01

Strong-field ionization and re-scattering phenomena have been used to image angstrom-scale structures of isolated molecules in the gas phase. These methods typically make use of the anisotropic response of the participating molecular orbital. Recently, an anisotropic strong-field response has also been observed in high-order harmonic generation (HHG) from bulk crystals (2016 Nat. Phys. 13 345). In a (100) cut magnesium oxide crystal, extreme ultraviolet high-harmonics are found to depend strongly on the crystal structure and inter-atomic bonding. Here, we extend these measurements to other two important crystal orientations: (111) and (110). We find that HHG from these orientations is also strongly anisotropic. The underlying dynamics is understood using a real-space picture, where high-harmonics are produced via coherent collision of strong-field driven electrons from the atomic sites, including from the nearest neighbor atoms. We find that harmonic efficiency is enhanced when semi-classical electron trajectories connect to the concentrated valence charge distribution regions around the atomic cores. Similarly, the efficiency is suppressed when the trajectories miss the atomic cores. These results further support the real-space picture of HHG with implications for retrieving the periodic potential of the crystal, if not the wavefunctions in three-dimensions.

Using Clustering to Establish Climate Regimes from PCM Output

NASA Technical Reports Server (NTRS)

Oglesby, Robert; Arnold, James E. (Technical Monitor); Hoffman, Forrest; Hargrove, W. W.; Erickson, D.

2002-01-01

A multivariate statistical clustering technique--based on the k-means algorithm of Hartigan has been used to extract patterns of climatological significance from 200 years of general circulation model (GCM) output. Originally developed and implemented on a Beowulf-style parallel computer constructed by Hoffman and Hargrove from surplus commodity desktop PCs, the high performance parallel clustering algorithm was previously applied to the derivation of ecoregions from map stacks of 9 and 25 geophysical conditions or variables for the conterminous U.S. at a resolution of 1 sq km. Now applied both across space and through time, the clustering technique yields temporally-varying climate regimes predicted by transient runs of the Parallel Climate Model (PCM). Using a business-as-usual (BAU) scenario and clustering four fields of significance to the global water cycle (surface temperature, precipitation, soil moisture, and snow depth) from 1871 through 2098, the authors' analysis shows an increase in spatial area occupied by the cluster or climate regime which typifies desert regions (i.e., an increase in desertification) and a decrease in the spatial area occupied by the climate regime typifying winter-time high latitude perma-frost regions. The patterns of cluster changes have been analyzed to understand the predicted variability in the water cycle on global and continental scales. In addition, representative climate regimes were determined by taking three 10-year averages of the fields 100 years apart for northern hemisphere winter (December, January, and February) and summer (June, July, and August). The result is global maps of typical seasonal climate regimes for 100 years in the past, for the present, and for 100 years into the future. Using three-dimensional data or phase space representations of these climate regimes (i.e., the cluster centroids), the authors demonstrate the portion of this phase space occupied by the land surface at all points in space and time. Any single spot on the globe will exist in one of these climate regimes at any single point in time. By incrementing time, that same spot will trace out a trajectory or orbit between and among these climate regimes (or atmospheric states) in phase (or state) space. When a geographic region enters a state it never previously visited, a climatic change is said to have occurred. Tracing out the entire trajectory of a single spot on the globe yields a 'manifold' in state space representing the shape of its predicted climate occupancy. This sort of analysis enables a researcher to more easily grasp the multivariate behavior of the climate system.

Application of importance sampling to the computation of large deviations in nonequilibrium processes.

PubMed

Kundu, Anupam; Sabhapandit, Sanjib; Dhar, Abhishek

2011-03-01

We present an algorithm for finding the probabilities of rare events in nonequilibrium processes. The algorithm consists of evolving the system with a modified dynamics for which the required event occurs more frequently. By keeping track of the relative weight of phase-space trajectories generated by the modified and the original dynamics one can obtain the required probabilities. The algorithm is tested on two model systems of steady-state particle and heat transport where we find a huge improvement from direct simulation methods.

Catenaries in viscous fluid

NASA Astrophysics Data System (ADS)

Hanna, James; Chakrabarti, Brato

2015-11-01

Slender structures live in fluid flows across many scales, from towed instruments to plant blades to microfluidic valves. The present work details a simple model of a flexible structure in a uniform flow. We present analytical solutions for the translating, axially flowing equilibria of strings subjected to a uniform body force and linear drag forces. This is an extension of the classical catenaries to a five-parameter family of solutions, represented as trajectories in angle-curvature ``phase space.'' Limiting cases include neutrally buoyant towed cables and freely sedimenting flexible filaments. Now at University of California, San Diego.

Urey Prize Lecture - Chaotic dynamics in the solar system

NASA Technical Reports Server (NTRS)

Wisdom, Jack

1987-01-01

Attention is given to solar system cases in which chaotic solutions of Newton's equations are important, as in chaotic rotation and orbital evolution. Hyperion is noted to be tumbling chaotically; chaotic orbital evolution is suggested to be of fundamental importance to an accounting for the Kirkwood gaps in asteroid distribution and for the phase space boundary of the chaotic zone at the 3/1 mean-motion commensurability with Jupiter. In addition, chaotic trajectories in the 2/1 chaotic zone reach very high eccentricities by a route that carries them to high inclinations temporarily.

KSC-2009-3665

NASA Image and Video Library

2009-05-01

CAPE CANAVERAL, Fla. – At NASA Kennedy Space Center's Shuttle Landing Facility, the shipping container with the STSS Demonstrator SV-2spacecraft is secured on a trailer for transfer to the Astrotech payload processing facility in Titusville, Fla. The spacecraft is a midcourse tracking technology demonstrator, part of an evolving ballistic missile defense system. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency in late summer. Photo credit: NASA/Jack Pfaller (Approved for Public Release 09-MDA-4616 [27 May 09])

KSC-2009-3664

NASA Image and Video Library

2009-05-01

CAPE CANAVERAL, Fla. – At NASA Kennedy Space Center's Shuttle Landing Facility, the shipping container with the STSS Demonstrator SV-2spacecraft is secured on a trailer for transfer to the Astrotech payload processing facility in Titusville, Fla. The spacecraft is a midcourse tracking technology demonstrator, part of an evolving ballistic missile defense system. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency in late summer. Photo credit: NASA/Jack Pfaller (Approved for Public Release 09-MDA-4616 [27 May 09])

KSC-2009-4614

NASA Image and Video Library

2009-06-25

CAPE CANAVERAL, Fla. – At NASA Kennedy Space Center's Shuttle Landing Facility, the SV-1 cargo of the STSS Demonstrator spacecraft is moved onto a flatbed truck for transfer to the Astrotech payload processing facility in Titusville, Fla. The spacecraft is a midcourse tracking technology demonstrator, part of an evolving ballistic missile defense system. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency in late summer. Photo credit: NASA/Kim Shiflett (Approved for Public Release 09-MDA-4804 [4 Aug 09] )

KSC-2009-4615

NASA Image and Video Library

2009-06-25

CAPE CANAVERAL, Fla. – At NASA Kennedy Space Center's Shuttle Landing Facility, the flatbed truck with the SV-1 cargo of the STSS Demonstrator spacecraft begins moving to the Astrotech payload processing facility in Titusville, Fla. The spacecraft is a midcourse tracking technology demonstrator, part of an evolving ballistic missile defense system. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency in late summer. Photo credit: NASA/Kim Shiflett (Approved for Public Release 09-MDA-4804 [4 Aug 09] )

Experimental Validation of Pulse Phase Tracking for X-Ray Pulsar Based

NASA Technical Reports Server (NTRS)

Anderson, Kevin

2012-01-01

Pulsars are a form of variable celestial source that have shown to be usable as aids for autonomous, deep space navigation. Particularly those sources emitting in the X-ray band are ideal for navigation due to smaller detector sizes. In this paper X-ray photons arriving from a pulsar are modeled as a non-homogeneous Poisson process. The method of pulse phase tracking is then investigated as a technique to measure the radial distance traveled by a spacecraft over an observation interval. A maximum-likelihood phase estimator (MLE) is used for the case where the observed frequency signal is constant. For the varying signal frequency case, an algorithm is used in which the observation window is broken up into smaller blocks over which an MLE is used. The outputs of this phase estimation process were then looped through a digital phase-locked loop (DPLL) in order to reduce the errors and produce estimates of the doppler frequency. These phase tracking algorithms were tested both in a computer simulation environment and using the NASA Goddard Space flight Center X-ray Navigation Laboratory Testbed (GXLT). This provided an experimental validation with photons being emitted by a modulated X-ray source and detected by a silicon-drift detector. Models of the Crab pulsar and the pulsar B1821-24 were used in order to generate test scenarios. Three different simulated detector trajectories were used to be tracked by the phase tracking algorithm: a stationary case, one with constant velocity, and one with constant acceleration. All three were performed in one-dimension along the line of sight to the pulsar. The first two had a constant signal frequency and the third had a time varying frequency. All of the constant frequency cases were processed using the MLE, and it was shown that they tracked the initial phase within 0.15% for the simulations and 2.5% in the experiments, based on an average of ten runs. The MLE-DPLL cascade version of the phase tracking algorithm was used in the varying frequency case. This resulted in tracking of the phase and frequency by the DPLL outputs in both the simulation and experimental environments. The crab pulsar was experimentally tested with a trajectory with a higher acceleration. In this case the phase error tended toward zero as the observation extended to 250 seconds and the doppler frequency error tended to zero in under 100 seconds.

An industrial robot singular trajectories planning based on graphs and neural networks

NASA Astrophysics Data System (ADS)

Łęgowski, Adrian; Niezabitowski, Michał

2016-06-01

Singular trajectories are rarely used because of issues during realization. A method of planning trajectories for given set of points in task space with use of graphs and neural networks is presented. In every desired point the inverse kinematics problem is solved in order to derive all possible solutions. A graph of solutions is made. The shortest path is determined to define required nodes in joint space. Neural networks are used to define the path between these nodes.

Potential Cislunar and Interplanetary Proving Ground Excursion Trajectory Concepts

NASA Technical Reports Server (NTRS)

McGuire, Melissa L.; Strange, Nathan J.; Burke, Laura M.; MacDonald, Mark A.; McElrath, Timothy P.; Landau, Damon F.; Lantoine, Gregory; Hack, Kurt J.; Lopez, Pedro

2016-01-01

NASA has been investigating potential translunar excursion concepts to take place in the 2020s that would be used to test and demonstrate long duration life support and other systems needed for eventual Mars missions in the 2030s. These potential trajectory concepts could be conducted in the proving ground, a region of cislunar and near-Earth interplanetary space where international space agencies could cooperate to develop the technologies needed for interplanetary spaceflight. Enabled by high power Solar Electric Propulsion (SEP) technologies, the excursion trajectory concepts studied are grouped into three classes of increasing distance from the Earth and increasing technical difficulty: the first class of excursion trajectory concepts would represent a 90-120 day round trip trajectory with abort to Earth options throughout the entire length, the second class would be a 180-210 day round trip trajectory with periods in which aborts would not be available, and the third would be a 300-400 day round trip trajectory without aborts for most of the length of the trip. This paper provides a top-level summary of the trajectory and mission design of representative example missions of these three classes of excursion trajectory concepts.

KSC-2009-5032

NASA Image and Video Library

2009-08-19

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers remove a cover from around the mated SV1 and SV2 spacecraft before center of gravity testing, weighing and balancing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5033

NASA Image and Video Library

2009-08-19

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the mated SV1 and SV2 spacecraft are largely uncovered before center of gravity testing, weighing and balancing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5062

NASA Image and Video Library

2009-08-22

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the upper segment of the transportation canister is lowered toward the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, spacecraft. It will be installed onto the lower segments already in place. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Kim Shiflett

KSC-2009-5028

NASA Image and Video Library

2009-08-19

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers remove covers around the mated SV1 and SV2 spacecraft before center of gravity testing, weighing and balancing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5039

NASA Image and Video Library

2009-08-19

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the mated SV1 and SV2 spacecraft are on a rotation stand for center of gravity testing, weighing and balancing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5047

NASA Image and Video Library

2009-08-20

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., an overhead crane with a scale is being attached to the SV1-SV2 spacecraft, which will be weighed. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5041

NASA Image and Video Library

2009-08-19

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers check the SV1-SV2 spacecraft that will undergo center of gravity testing, weighing and balancing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5030

NASA Image and Video Library

2009-08-19

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers remove covers around the mated SV1 and SV2 spacecraft before center of gravity testing, weighing and balancing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5045

NASA Image and Video Library

2009-08-20

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., an overhead crane with a scale is being attached to the SV1-SV2 spacecraft, which will be weighed. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5027

NASA Image and Video Library

2009-08-19

CAPE CANAVERAL, Fla. –At the Astrotech payload processing facility in Titusville, Fla., the mated SV1 and SV2 spacecraft are being prepared for center of gravity testing, weighing and balancing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5063

NASA Image and Video Library

2009-08-22

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the upper segment of the transportation canister is lowered over the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, spacecraft. It will be installed onto the lower segments already in place. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Kim Shiflett

KSC-2009-5052

NASA Image and Video Library

2009-08-20

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers observe as the SV1-SV2 spacecraft is lowered again onto the rotation stand after weighing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5015

NASA Image and Video Library

2009-08-03

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., a crane moves the SV1 spacecraft, which will be mated with the SV2 at right. The two spacecraft are part of the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, Program. STSS-Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. The spacecraft is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5017

NASA Image and Video Library

2009-08-03

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., a crane moves the SV1 spacecraft, toward the SV2 at right. The two spacecraft , which will be mated, are part of the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, Program. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5195

NASA Image and Video Library

2009-09-12

CAPE CANAVERAL, Fla. – The two halves of the fairing are moved into the mobile service tower on Launch Pad 17-B at Cape Canaveral Air Force Station in Florida. The two-part fairing will be placed around the Space Tracking and Surveillance System – Demonstrator spacecraft for protection during launch. STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detection, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-4934 (09-22-09) Photo credit: NASA/Cory Huston

KSC-2009-5018

NASA Image and Video Library

2009-08-03

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers help guide the movement of the SV1 spacecraft as it is moved toward the SV2 at right. The two spacecraft are part of the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, Program. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5016

NASA Image and Video Library

2009-08-03

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers help guide the movement of the SV1 spacecraft as it is moved toward the SV2 behind it. The two spacecraft are part of the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, Program. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5040

NASA Image and Video Library

2009-08-19

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., a canister and protective cover are being prepared for placement around the SV1-SV2 spacecraft. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5022

NASA Image and Video Library

2009-08-03

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers observe as the SV1 spacecraft is lowered onto the SV2 for mating. The two spacecraft are part of the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, Program. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5024

NASA Image and Video Library

2009-08-03

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., a worker checks the mating of the SV1 spacecraft onto the SV2. The two spacecraft are part of the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, Program. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5036

NASA Image and Video Library

2009-08-19

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the mated SV1 and SV2 spacecraft are being prepared for center of gravity testing, weighing and balancing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5026

NASA Image and Video Library

2009-08-19

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the mated SV1 and SV2 spacecraft are being prepared for center of gravity testing, weighing and balancing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5046

NASA Image and Video Library

2009-08-20

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., an overhead crane with a scale is being attached to the SV1-SV2 spacecraft, which will be weighed. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5019

NASA Image and Video Library

2009-08-03

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers help guide the movement of the SV1 spacecraft as it is moved toward the SV2 at right. The two spacecraft are part of the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, Program. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5043

NASA Image and Video Library

2009-08-20

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., an overhead crane with a scale is being moved to attach to the SV1-SV2 spacecraft, which will be weighed. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5038

NASA Image and Video Library

2009-08-19

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the mated SV1 and SV2 spacecraft are placed on a rotation stand for center of gravity testing, weighing and balancing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5044

NASA Image and Video Library

2009-08-20

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., an overhead crane with a scale is being moved to attach to the SV1-SV2 spacecraft, which will be weighed. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5031

NASA Image and Video Library

2009-08-19

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers remove covers around the mated SV1 and SV2 spacecraft before center of gravity testing, weighing and balancing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5029

NASA Image and Video Library

2009-08-19

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., workers remove covers around the mated SV1 and SV2 spacecraft before center of gravity testing, weighing and balancing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5064

NASA Image and Video Library

2009-08-22

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the upper segment of the transportation canister is lowered over the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, spacecraft. It will be installed onto the lower segments already in place. The STSS Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Kim Shiflett

Using chaotic forcing to detect damage in a structure

USGS Publications Warehouse

Moniz, L.; Nichols, J.; Trickey, S.; Seaver, M.; Pecora, D.; Pecora, L.

2005-01-01

In this work we develop a numerical test for Holder continuity and apply it and another test for continuity to the difficult problem of detecting damage in structures. We subject a thin metal plate with incremental damage to the plate changes, its filtering properties, and therefore the phase space trajectories of the response chaotic excitation of various bandwidths. Damage to the plate changes its filtering properties and therefore the phase space of the response. Because the data are multivariate (the plate is instrumented with multiple sensors) we use a singular value decomposition of the set of the output time series to reduce the embedding dimension of the response time series. We use two geometric tests to compare an attractor reconstructed from data from an undamaged structure to that reconstructed from data from a damaged structure. These two tests translate to testing for both generalized and differentiable synchronization between responses. We show loss of synchronization of responses with damage to the structure. ?? 2005 American Institute of Physics.

Using chaotic forcing to detect damage in a structure.

USGS Publications Warehouse

Moniz, L.; Nichols, J.; Trickey, S.; Seaver, M.; Pecora, D.; Pecora, L.

2005-01-01

In this work we develop a numerical test for Holder continuity and apply it and another test for continuity to the difficult problem of detecting damage in structures. We subject a thin metal plate with incremental damage to the plate changes, its filtering properties, and therefore the phase space trajectories of the response chaotic excitation of various bandwidths. Damage to the plate changes its filtering properties and therefore the phase space of the response. Because the data are multivariate (the plate is instrumented with multiple sensors) we use a singular value decomposition of the set of the output time series to reduce the embedding dimension of the response time series. We use two geometric tests to compare an attractor reconstructed from data from an undamaged structure to that reconstructed from data from a damaged structure. These two tests translate to testing for both generalized and differentiable synchronization between responses. We show loss of synchronization of responses with damage to the structure.

Anderson localization and Mott insulator phase in the time domain

PubMed Central

Sacha, Krzysztof

2015-01-01

Particles in space periodic potentials constitute standard models for investigation of crystalline phenomena in solid state physics. Time periodicity of periodically driven systems is a close analogue of space periodicity of solid state crystals. There is an intriguing question if solid state phenomena can be observed in the time domain. Here we show that wave-packets localized on resonant classical trajectories of periodically driven systems are ideal elements to realize Anderson localization or Mott insulator phase in the time domain. Uniform superpositions of the wave-packets form stationary states of a periodically driven particle. However, an additional perturbation that fluctuates in time results in disorder in time and Anderson localization effects emerge. Switching to many-particle systems we observe that depending on how strong particle interactions are, stationary states can be Bose-Einstein condensates or single Fock states where definite numbers of particles occupy the periodically evolving wave-packets. Our study shows that non-trivial crystal-like phenomena can be observed in the time domain. PMID:26074169

Locating binding poses in protein-ligand systems using reconnaissance metadynamics

PubMed Central

Söderhjelm, Pär; Tribello, Gareth A.; Parrinello, Michele

2012-01-01

A molecular dynamics-based protocol is proposed for finding and scoring protein-ligand binding poses. This protocol uses the recently developed reconnaissance metadynamics method, which employs a self-learning algorithm to construct a bias that pushes the system away from the kinetic traps where it would otherwise remain. The exploration of phase space with this algorithm is shown to be roughly six to eight times faster than unbiased molecular dynamics and is only limited by the time taken to diffuse about the surface of the protein. We apply this method to the well-studied trypsin–benzamidine system and show that we are able to refind all the poses obtained from a reference EADock blind docking calculation. These poses can be scored based on the length of time the system remains trapped in the pose. Alternatively, one can perform dimensionality reduction on the output trajectory and obtain a map of phase space that can be used in more expensive free-energy calculations. PMID:22440749

Exploring phase space using smartphone acceleration and rotation sensors simultaneously

NASA Astrophysics Data System (ADS)

Monteiro, Martín; Cabeza, Cecilia; Martí, Arturo C.

2014-07-01

A paradigmatic physical system as the physical pendulum is experimentally studied using the acceleration and rotation (gyroscope) sensors available on smartphones and other devices such as iPads and tablets. A smartphone is fixed to the outside of a bicycle wheel whose axis is kept horizontal and fixed. The compound system, wheel plus smartphone, defines a physical pendulum which can rotate, giving full turns in one direction, or oscillate about the equilibrium position (performing either small or large oscillations). Measurements of the radial and tangential acceleration and the angular velocity obtained with smartphone sensors allow a deep insight into the dynamics of the system to be gained. In addition, thanks to the simultaneous use of the acceleration and rotation sensors, trajectories in the phase space are directly obtained. The coherence of the measures obtained with the different sensors and by traditional methods is remarkable. Indeed, due to their low cost and increasing availability, smartphone sensors are valuable tools that can be used in most undergraduate laboratories.

Locating binding poses in protein-ligand systems using reconnaissance metadynamics.

PubMed

Söderhjelm, Pär; Tribello, Gareth A; Parrinello, Michele

2012-04-03

A molecular dynamics-based protocol is proposed for finding and scoring protein-ligand binding poses. This protocol uses the recently developed reconnaissance metadynamics method, which employs a self-learning algorithm to construct a bias that pushes the system away from the kinetic traps where it would otherwise remain. The exploration of phase space with this algorithm is shown to be roughly six to eight times faster than unbiased molecular dynamics and is only limited by the time taken to diffuse about the surface of the protein. We apply this method to the well-studied trypsin-benzamidine system and show that we are able to refind all the poses obtained from a reference EADock blind docking calculation. These poses can be scored based on the length of time the system remains trapped in the pose. Alternatively, one can perform dimensionality reduction on the output trajectory and obtain a map of phase space that can be used in more expensive free-energy calculations.

Trajectory Design to Mitigate Risk on the Transiting Exoplanet Survey Satellite (TESS) Mission

NASA Technical Reports Server (NTRS)

Dichmann, Donald

2016-01-01

The Transiting Exoplanet Survey Satellite (TESS) will employ a highly eccentric Earth orbit, in 2:1 lunar resonance, reached with a lunar flyby preceded by 3.5 phasing loops. The TESS mission has limited propellant and several orbit constraints. Based on analysis and simulation, we have designed the phasing loops to reduce delta-V and to mitigate risk due to maneuver execution errors. We have automated the trajectory design process and use distributed processing to generate and to optimize nominal trajectories, check constraint satisfaction, and finally model the effects of maneuver errors to identify trajectories that best meet the mission requirements.

Low data rate digital space communications

NASA Technical Reports Server (NTRS)

Chen, C. H.

1973-01-01

The low available transmitter power and the large frequency uncertainty constrain the data rate to be low. An all-digital communication receiver is proposed, and its feasibility is established. Although coherent systems should be used whenever practical, the noncoherent MFSK system is more suitable for very low data rates. The effect of Rician fading on the performance of MFSK receiver is studied. Fading characteristics of the Venus channel are examined based on the exponential model and available experimental data on the Venus atmosphere. Because of the requirement of high communication efficiency, three codes are evaluated and compared. The rapidly varying phase error at low data rate has great effects on the tracking loop behaviors which are examined by extensive computer study of the phase plane trajectories.

Pathfinder operations

NASA Technical Reports Server (NTRS)

Wilcher, J.; Stelzried, C.; Finley, S.

1986-01-01

In 1981, the Inter-Agency Consultative Group (composed of European, Soviet, Japanese and American space agency representatives) conceived the idea of using the two Soviet Vega spacecraft as pathfinders for Giotto since they would arrive at Halley's Comet approximately one week before Giotto. The Vega trajectory data and the Halley camera angle data were combined to improve the comet orbit accuracy. This was used to improve the Giotto fly-by targeting. The DSN performed delta DOR (VLBI) and one-way Doppler measurements of the Vega spacecraft for orbit determination. Although the early part-up phase had many problems, the results during the critical November 30, 1985 to March 4, 1986 operational phase had an overall 95 percent success rate, with 59 successes out of 62 two-station passes.

Progress toward a cosmic dust collection facility on space station

NASA Technical Reports Server (NTRS)

Mackinnon, Ian D. R. (Editor); Carey, William C. (Editor)

1987-01-01

Scientific and programmatic progress toward the development of a cosmic dust collection facility (CDCF) for the proposed space station is documented. Topics addressed include: trajectory sensor concepts; trajectory accuracy and orbital evolution; CDCF pointing direction; development of capture devices; analytical techniques; programmatic progress; flight opportunities; and facility development.

Trajectory generation for an on-road autonomous vehicle

NASA Astrophysics Data System (ADS)

Horst, John; Barbera, Anthony

2006-05-01

We describe an algorithm that generates a smooth trajectory (position, velocity, and acceleration at uniformly sampled instants of time) for a car-like vehicle autonomously navigating within the constraints of lanes in a road. The technique models both vehicle paths and lane segments as straight line segments and circular arcs for mathematical simplicity and elegance, which we contrast with cubic spline approaches. We develop the path in an idealized space, warp the path into real space and compute path length, generate a one-dimensional trajectory along the path length that achieves target speeds and positions, and finally, warp, translate, and rotate the one-dimensional trajectory points onto the path in real space. The algorithm moves a vehicle in lane safely and efficiently within speed and acceleration maximums. The algorithm functions in the context of other autonomous driving functions within a carefully designed vehicle control hierarchy.

Monte Carlo Analysis as a Trajectory Design Driver for the Transiting Exoplanet Survey Satellite (TESS) Mission

NASA Technical Reports Server (NTRS)

Nickel, Craig; Parker, Joel; Dichmann, Don; Lebois, Ryan; Lutz, Stephen

2016-01-01

The Transiting Exoplanet Survey Satellite (TESS) will be injected into a highly eccentric Earth orbit and fly 3.5 phasing loops followed by a lunar flyby to enter a mission orbit with lunar 2:1 resonance. Through the phasing loops and mission orbit, the trajectory is significantly affected by lunar and solar gravity. We have developed a trajectory design to achieve the mission orbit and meet mission constraints, including eclipse avoidance and a 30-year geostationary orbit avoidance requirement. A parallelized Monte Carlo simulation was performed to validate the trajectory after injecting common perturbations, including launch dispersions, orbit determination errors, and maneuver execution errors. The Monte Carlo analysis helped identify mission risks and is used in the trajectory selection process.

A simple acquisition strategy to avoid off-resonance blurring in spiral imaging with redundant spiral-in/out k-space trajectories.

PubMed

Fielden, Samuel W; Meyer, Craig H

2015-02-01

The major hurdle to widespread adoption of spiral trajectories has been their poor off-resonance performance. Here we present a self-correcting spiral k-space trajectory that avoids much of the well-known spiral blurring during data acquisition. In comparison with a traditional spiral-out trajectory, the spiral-in/out trajectory has improved off-resonance performance. By combining two spiral-in/out acquisitions, one rotated 180° in k-space compared with the other, multishot spiral-in/out artifacts are eliminated. A phantom was scanned with the center frequency manually tuned 20, 40, 80, and 160 Hz off-resonance with both a spiral-out gradient echo sequence and the redundant spiral-in/out sequence. The phantom was also imaged in an oblique orientation in order to demonstrate improved concomitant gradient field performance of the sequence. Additionally, the trajectory was incorporated into a spiral turbo spin echo sequence for brain imaging. Phantom studies with manually tuned off-resonance agree well with theoretical calculations, showing that moderate off-resonance is well-corrected by this acquisition scheme. Blur due to concomitant fields is reduced, and good results are obtained in vivo. The redundant spiral-in/out trajectory results in less image blur for a given readout length than a traditional spiral-out scan, reducing the need for complex off-resonance correction algorithms. © 2014 Wiley Periodicals, Inc.

Investigation of abort procedures for space shuttle-type vehicles

NASA Technical Reports Server (NTRS)

Powell, R. W.; Eide, D. G.

1974-01-01

An investigation has been made of abort procedures for space shuttle-type vehicles using a point mass trajectory optimization program known as POST. This study determined the minimum time gap between immediate and once-around safe return to the launch site from a baseline due-East launch trajectory for an alternate space shuttle concept which experiences an instantaneous loss of 25 percent of the total main engine thrust.

Singular trajectories: space-time domain topology of developing speckle fields

NASA Astrophysics Data System (ADS)

Vasil'ev, Vasiliy; Soskin, Marat S.

2010-02-01

It is shown the space-time dynamics of optical singularities is fully described by singularities trajectories in space-time domain, or evolution of transverse coordinates(x, y) in some fixed plane z0. The dynamics of generic developing speckle fields was realized experimentally by laser induced scattering in LiNbO3:Fe photorefractive crystal. The space-time trajectories of singularities can be divided topologically on two classes with essentially different scenario and duration. Some of them (direct topological reactions) consist from nucleation of singularities pair at some (x, y, z0, t) point, their movement and annihilation. They possess form of closed loops with relatively short time of existence. Another much more probable class of trajectories are chain topological reactions. Each of them consists from sequence of links, i.e. of singularities nucleation in various points (xi yi, ti) and following annihilation of both singularities in other space-time points with alien singularities of opposite topological indices. Their topology and properties are established. Chain topological reactions can stop on the borders of a developing speckle field or go to infinity. Examples of measured both types of topological reactions for optical vortices (polarization C points) in scalar (elliptically polarized) natural developing speckle fields are presented.

Spiral Imaging in fMRI

PubMed Central

Glover, Gary H.

2011-01-01

T2*-weighted Blood Oxygen Level Dependent (BOLD) functional magnetic resonance imaging (fMRI) requires efficient acquisition methods in order to fully sample the brain in a several second time period. The most widely used approach is Echo Planar Imaging (EPI), which utilizes a Cartesian trajectory to cover k-space. This trajectory is subject to ghosts from off-resonance and gradient imperfections and is intrinsically sensitive to cardiac-induced pulsatile motion from substantial first- and higher order moments of the gradient waveform near the k-space origin. In addition, only the readout direction gradient contributes significant energy to the trajectory. By contrast, the Spiral method samples k-space with an Archimedean or similar trajectory that begins at the k-space center and spirals to the edge (Spiral-out), or its reverse, ending at the origin (Spiral-in). Spiral methods have reduced sensitivity to motion, shorter readout times, improved signal recovery in most frontal and parietal brain regions, and exhibit blurring artifacts instead of ghosts or geometric distortion. Methods combining Spiral-in and Spiral-out trajectories have further advantages in terms of diminished susceptibility-induced signal dropout and increased BOLD signal. In measurements of temporal signal to noise ratio measured in 8 subjects, Spiral-in/out exhibited significant increases over EPI in voxel volumes recovered in frontal and whole brain regions (18% and 10%, respectively). PMID:22036995

Automatic Generation of Indoor Navigable Space Using a Point Cloud and its Scanner Trajectory

NASA Astrophysics Data System (ADS)

Staats, B. R.; Diakité, A. A.; Voûte, R. L.; Zlatanova, S.

2017-09-01

Automatic generation of indoor navigable models is mostly based on 2D floor plans. However, in many cases the floor plans are out of date. Buildings are not always built according to their blue prints, interiors might change after a few years because of modified walls and doors, and furniture may be repositioned to the user's preferences. Therefore, new approaches for the quick recording of indoor environments should be investigated. This paper concentrates on laser scanning with a Mobile Laser Scanner (MLS) device. The MLS device stores a point cloud and its trajectory. If the MLS device is operated by a human, the trajectory contains information which can be used to distinguish different surfaces. In this paper a method is presented for the identification of walkable surfaces based on the analysis of the point cloud and the trajectory of the MLS scanner. This method consists of several steps. First, the point cloud is voxelized. Second, the trajectory is analysing and projecting to acquire seed voxels. Third, these seed voxels are generated into floor regions by the use of a region growing process. By identifying dynamic objects, doors and furniture, these floor regions can be modified so that each region represents a specific navigable space inside a building as a free navigable voxel space. By combining the point cloud and its corresponding trajectory, the walkable space can be identified for any type of building even if the interior is scanned during business hours.

Anatomical nuances of the internal carotid artery in relation to the quadrangular space.

PubMed

Dolci, Ricardo L L; Ditzel Filho, Leo F S; Goulart, Carlos R; Upadhyay, Smita; Buohliqah, Lamia; Lazarini, Paulo R; Prevedello, Daniel M; Carrau, Ricardo L

2018-01-01

OBJECTIVE The aim of this study was to evaluate the anatomical variations of the internal carotid artery (ICA) in relation to the quadrangular space (QS) and to propose a classification system based on the results. METHODS A total of 44 human cadaveric specimens were dissected endonasally under direct endoscopic visualization. During the dissection, the anatomical variations of the ICA and their relationship with the QS were noted. RESULTS The space between the paraclival ICAs (i.e., intercarotid space) can be classified as 1 of 3 different shapes (i.e., trapezoid, square, or hourglass) based on the trajectory of the ICAs. The ICA trajectories also directly influence the volumetric area of the QS. Based on its geometry, the QS was classified as one of the following: 1) Type A has the smallest QS area and is associated with a trapezoid intercarotid space, 2) Type B corresponds to the expected QS area (not minimized or enlarged) and is associated with a square intercarotid space, and 3) Type C has the largest QS area and is associated with an hourglass intercarotid space. CONCLUSIONS The different trajectories of the ICAs can modify the area of the QS and may be an essential parameter to consider for preoperative planning and defining the most appropriate corridor to reach Meckel's cave. In addition, ICA trajectories should be considered prior to surgery to avoid injuring the vessels.

Techniques for shuttle trajectory optimization

NASA Technical Reports Server (NTRS)

Edge, E. R.; Shieh, C. J.; Powers, W. F.

1973-01-01

The application of recently developed function-space Davidon-type techniques to the shuttle ascent trajectory optimization problem is discussed along with an investigation of the recently developed PRAXIS algorithm for parameter optimization. At the outset of this analysis, the major deficiency of the function-space algorithms was their potential storage problems. Since most previous analyses of the methods were with relatively low-dimension problems, no storage problems were encountered. However, in shuttle trajectory optimization, storage is a problem, and this problem was handled efficiently. Topics discussed include: the shuttle ascent model and the development of the particular optimization equations; the function-space algorithms; the operation of the algorithm and typical simulations; variable final-time problem considerations; and a modification of Powell's algorithm.

Program manual for ASTOP, an Arbitrary space trajectory optimization program

NASA Technical Reports Server (NTRS)

Horsewood, J. L.

1974-01-01

The ASTOP program (an Arbitrary Space Trajectory Optimization Program) designed to generate optimum low-thrust trajectories in an N-body field while satisfying selected hardware and operational constraints is presented. The trajectory is divided into a number of segments or arcs over which the control is held constant. This constant control over each arc is optimized using a parameter optimization scheme based on gradient techniques. A modified Encke formulation of the equations of motion is employed. The program provides a wide range of constraint, end conditions, and performance index options. The basic approach is conducive to future expansion of features such as the incorporation of new constraints and the addition of new end conditions.

Global Optimization of N-Maneuver, High-Thrust Trajectories Using Direct Multiple Shooting

NASA Technical Reports Server (NTRS)

Vavrina, Matthew A.; Englander, Jacob A.; Ellison, Donald H.

2016-01-01

The performance of impulsive, gravity-assist trajectories often improves with the inclusion of one or more maneuvers between flybys. However, grid-based scans over the entire design space can become computationally intractable for even one deep-space maneuver, and few global search routines are capable of an arbitrary number of maneuvers. To address this difficulty a trajectory transcription allowing for any number of maneuvers is developed within a multi-objective, global optimization framework for constrained, multiple gravity-assist trajectories. The formulation exploits a robust shooting scheme and analytic derivatives for computational efficiency. The approach is applied to several complex, interplanetary problems, achieving notable performance without a user-supplied initial guess.

Point Clouds to Indoor/outdoor Accessibility Diagnosis

NASA Astrophysics Data System (ADS)

Balado, J.; Díaz-Vilariño, L.; Arias, P.; Garrido, I.

2017-09-01

This work presents an approach to automatically detect structural floor elements such as steps or ramps in the immediate environment of buildings, elements that may affect the accessibility to buildings. The methodology is based on Mobile Laser Scanner (MLS) point cloud and trajectory information. First, the street is segmented in stretches along the trajectory of the MLS to work in regular spaces. Next, the lower region of each stretch (the ground zone) is selected as the ROI and normal, curvature and tilt are calculated for each point. With this information, points in the ROI are classified in horizontal, inclined or vertical. Points are refined and grouped in structural elements using raster process and connected components in different phases for each type of previously classified points. At last, the trajectory data is used to distinguish between road and sidewalks. Adjacency information is used to classify structural elements in steps, ramps, curbs and curb-ramps. The methodology is tested in a real case study, consisting of 100 m of an urban street. Ground elements are correctly classified in an acceptable computation time. Steps and ramps also are exported to GIS software to enrich building models from Open Street Map with information about accessible/inaccessible entrances and their locations.

Analytic Guidance for the First Entry in a Skip Atmospheric Entry

NASA Technical Reports Server (NTRS)

Garcia-Llama, Eduardo

2007-01-01

This paper presents an analytic method to generate a reference drag trajectory for the first entry portion of a skip atmospheric entry. The drag reference, expressed as a polynomial function of the velocity, will meet the conditions necessary to fit the requirements of the complete entry phase. The generic method proposed to generate the drag reference profile is further simplified by thinking of the drag and the velocity as density and cumulative distribution functions respectively. With this notion it will be shown that the reference drag profile can be obtained by solving a linear algebraic system of equations. The resulting drag profile is flown using the feedback linearization method of differential geometric control as guidance law with the error dynamics of a second order homogeneous equation in the form of a damped oscillator. This approach was first proposed as a revisited version of the Space Shuttle Orbiter entry guidance. However, this paper will show that it can be used to fly the first entry in a skip entry trajectory. In doing so, the gains in the error dynamics will be changed at a certain point along the trajectory to improve the tracking performance.

Energy considerations in the partial space elevator

NASA Astrophysics Data System (ADS)

Woo, Pamela; Misra, Arun K.

2014-06-01

The space elevator has been proposed as an alternate method for space transportation. A partial elevator is composed of a tether of several hundreds of kilometres, held vertically in tension between two end masses, with its centre of orbit placed at the geosynchronous orbit. A spacecraft can dock at the lower end, and then use the climber on the elevator to ascend to higher altitudes. In this paper, energy calculations are performed, to determine whether a partial elevator can provide sufficient savings in operational costs, compared to the traditional rocket-powered launch. The energy required to launch a spacecraft from a Low Earth Orbit (LEO) to the geostationary orbit (GEO) is calculated for two trajectories. In the first trajectory, the spacecraft travels from LEO to GEO via a Hohmann transfer. In the second trajectory, the spacecraft travels from LEO to the lower end of the partial space elevator with a Hohmann transfer, and then uses the elevator to climb to GEO. The total energy required is compared between the two trajectories. The effects of tether length, spacecraft-to-climber mass ratio, altitude of LEO, and tether material are investigated.

Robust Task Space Trajectory Tracking Control of Robotic Manipulators

NASA Astrophysics Data System (ADS)

Galicki, M.

2016-08-01

This work deals with the problem of the accurate task space trajectory tracking subject to finite-time convergence. Kinematic and dynamic equations of a redundant manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the end-effector. Furthermore, the movement is to be accomplished in such a way as to reduce both the manipulator torques and their oscillations thus eliminating the potential robot vibrations. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we propose a class of chattering-free robust controllers, based on the estimation of transpose Jacobian, which seem to be effective in counteracting both uncertain kinematics and dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the robot trajectory. The numerical simulations carried out for a redundant manipulator of a SCARA type consisting of the three revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers as well as comparisons with other well known control schemes.

Inviscid and Viscous CFD Analysis of Booster Separation for the Space Launch System Vehicle

NASA Technical Reports Server (NTRS)

Dalle, Derek J.; Rogers, Stuart E.; Chan, William M.; Lee, Henry C.

2016-01-01

This paper presents details of Computational Fluid Dynamic (CFD) simulations of the Space Launch System during solid-rocket booster separation using the Cart3D inviscid and Overflow viscous CFD codes. The discussion addresses the use of multiple data sources of computational aerodynamics, experimental aerodynamics, and trajectory simulations for this critical phase of flight. Comparisons are shown between Cart3D simulations and a wind tunnel test performed at NASA Langley Research Center's Unitary Plan Wind Tunnel, and further comparisons are shown between Cart3D and viscous Overflow solutions for the flight vehicle. The Space Launch System (SLS) is a new exploration-class launch vehicle currently in development that includes two Solid Rocket Boosters (SRBs) modified from Space Shuttle hardware. These SRBs must separate from the SLS core during a phase of flight where aerodynamic loads are nontrivial. The main challenges for creating a separation aerodynamic database are the large number of independent variables (including orientation of the core, relative position and orientation of the boosters, and rocket thrust levels) and the complex flow caused by exhaust plumes of the booster separation motors (BSMs), which are small rockets designed to push the boosters away from the core by firing partially in the direction opposite to the motion of the vehicle.

Patched Conic Trajectory Code

NASA Technical Reports Server (NTRS)

Park, Brooke Anderson; Wright, Henry

2012-01-01

PatCon code was developed to help mission designers run trade studies on launch and arrival times for any given planet. Initially developed in Fortran, the required inputs included launch date, arrival date, and other orbital parameters of the launch planet and arrival planets at the given dates. These parameters include the position of the planets, the eccentricity, semi-major axes, argument of periapsis, ascending node, and inclination of the planets. With these inputs, a patched conic approximation is used to determine the trajectory. The patched conic approximation divides the planetary mission into three parts: (1) the departure phase, in which the two relevant bodies are Earth and the spacecraft, and where the trajectory is a departure hyperbola with Earth at the focus; (2) the cruise phase, in which the two bodies are the Sun and the spacecraft, and where the trajectory is a transfer ellipse with the Sun at the focus; and (3) the arrival phase, in which the two bodies are the target planet and the spacecraft, where the trajectory is an arrival hyperbola with the planet as the focus.

Self-bending elastic waves and obstacle circumventing in wireless power transfer

NASA Astrophysics Data System (ADS)

Tol, S.; Xia, Y.; Ruzzene, M.; Erturk, A.

2017-04-01

We demonstrate self-bending of elastic waves along convex trajectories by means of geometric and phased arrays. Potential applications include ultrasonic imaging and manipulation, wave focusing, and wireless power transfer around obstacles. The basic concept is illustrated through a geometric array, which is designed to implement a phase delay profile among the array elements that leads to self-bending along a specified circular trajectory. Experimental validation is conducted for the lowest asymmetric Lamb wave mode in a thin plate over a range of frequencies to investigate the bandwidth of the approach. Experiments also illustrate the functionality of the array as a transmitter to deliver elastic wave energy to a receiver/harvester located behind a large obstacle for electrical power extraction. It is shown that the trajectory is not distorted by the presence of the obstacle and circumventing is achieved. A linear phased array counterpart of the geometric array is then constructed to illustrate the concept by imposing proper time delays to the array elements, which allows the generation of different trajectories using the same line source. This capability is demonstrated by tailoring the path diameter in the phased array setting, which offers the flexibility and versatility to induce a variety of convex trajectories for self-bending elastic waves.

RF Pulse Design using Nonlinear Gradient Magnetic Fields

PubMed Central

Kopanoglu, Emre; Constable, R. Todd

2014-01-01

Purpose An iterative k-space trajectory and radio-frequency (RF) pulse design method is proposed for Excitation using Nonlinear Gradient Magnetic fields (ENiGMa). Theory and Methods The spatial encoding functions (SEFs) generated by nonlinear gradient fields (NLGFs) are linearly dependent in Cartesian-coordinates. Left uncorrected, this may lead to flip-angle variations in excitation profiles. In the proposed method, SEFs (k-space samples) are selected using a Matching-Pursuit algorithm, and the RF pulse is designed using a Conjugate-Gradient algorithm. Three variants of the proposed approach are given: the full-algorithm, a computationally-cheaper version, and a third version for designing spoke-based trajectories. The method is demonstrated for various target excitation profiles using simulations and phantom experiments. Results The method is compared to other iterative (Matching-Pursuit and Conjugate Gradient) and non-iterative (coordinate-transformation and Jacobian-based) pulse design methods as well as uniform density spiral and EPI trajectories. The results show that the proposed method can increase excitation fidelity significantly. Conclusion An iterative method for designing k-space trajectories and RF pulses using nonlinear gradient fields is proposed. The method can either be used for selecting the SEFs individually to guide trajectory design, or can be adapted to design and optimize specific trajectories of interest. PMID:25203286

Mechanics of the animate.

PubMed Central

Killeen, P R

1992-01-01

Behavior is treated as basic physics. Dimensions are identified and their transformations from physical specification to axes in behavioral space are suggested. Responses are treated as action patterns arrayed along a continuum of activation energy. Behavior is seen as movement along a trajectory through this behavior space. Incentives or reinforcers are attractors in behavior space, at the centers of basins of lowered potential. Trajectories impinging on such basins may be captured; repeated capture will warp the trajectory toward a geodesic, a process called conditioning. Conditioning is enhanced by contiguity, the proximity between the measured behavior and the incentive at the end of the trajectory, and by contingency, the depth of the trajectory below the average level of the potential energy landscape. Motivation is seen as the potential of an organism for motion under the forces impinging on it. Degree of motivation is characterized by the depth of the potential field, with low motivation corresponding to a flat field and a flat gradient of activation energy. Drives are the forces of incentives propagated through behavior space. Different laws for the attenuation of drive with behavioral distance are discussed, as is the dynamics of action. The basic postulate of behavior mechanics is incentive-tracking in behavior space, the energy for which is provided by decreases in potential. The relation of temporal gradients to response differentiation and temporal discrimination is analyzed. Various two-body problems are sketched to illustrate the application of these ideas to association, choice, scalar timing, self-control, and freedom. PMID:1602272

Space Trajectory Error Analysis Program (STEAP) for halo orbit missions. Volume 1: Analytic and user's manual

NASA Technical Reports Server (NTRS)

Byrnes, D. V.; Carney, P. C.; Underwood, J. W.; Vogt, E. D.

1974-01-01

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 is reported. The software consisting of two programs called NOMNAL and ERRAN is part of the Space Trajectories Error Analysis Programs (STEAP). 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. Execution errors at injection, midcourse correction and orbit insertion maneuvers are analyzed along with the navigation uncertainty to determine trajectory control uncertainties and fuel-sizing requirements. The program is also capable of generalized covariance analyses.

HP-9825A HFRMP trajectory processor (#TRAJ), detailed description. [relative motion of the space shuttle orbiter and a free-flying payload

NASA Technical Reports Server (NTRS)

Kindall, S. M.

1980-01-01

The computer code for the trajectory processor (#TRAJ) of the high fidelity relative motion program is described. The #TRAJ processor is a 12-degrees-of-freedom trajectory integrator (6 degrees of freedom for each of two vehicles) which can be used to generate digital and graphical data describing the relative motion of the Space Shuttle Orbiter and a free-flying cylindrical payload. A listing of the code, coding standards and conventions, detailed flow charts, and discussions of the computational logic are included.

Variable Structure Control of a Hand-Launched Glider

NASA Technical Reports Server (NTRS)

Anderson, Mark R.; Waszak, Martin R.

2005-01-01

Variable structure control system design methods are applied to the problem of aircraft spin recovery. A variable structure control law typically has two phases of operation. The reaching mode phase uses a nonlinear relay control strategy to drive the system trajectory to a pre-defined switching surface within the motion state space. The sliding mode phase involves motion along the surface as the system moves toward an equilibrium or critical point. Analysis results presented in this paper reveal that the conventional method for spin recovery can be interpreted as a variable structure controller with a switching surface defined at zero yaw rate. Application of Lyapunov stability methods show that deflecting the ailerons in the direction of the spin helps to insure that this switching surface is stable. Flight test results, obtained using an instrumented hand-launched glider, are used to verify stability of the reaching mode dynamics.

A water bag theory of autoresonant Bernstein-Greene-Kruskal modes

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

Khain, P.; Friedland, L.

2007-08-15

The adiabatic water bag theory describing formation and passage through phase-space of driven, continuously phase-locked (autoresonant) coherent structures in plasmas [L. Friedland et al., Phys. Rev. Lett. 96, 225001 (2006)] and of the associated Bernstein-Greene-Kruskal (BGK) modes is developed. The phase-locking is achieved by using a chirped frequency ponderomotive drive, passing through kinetic Cerenkov-type resonances. The theory uses the adiabatic invariants (conserved actions of limiting trajectories) in the problem and, for a flat-top initial distribution of the electrons, reduces the calculation of the self-field of the driven BGK mode to solution of a few algebraic equations. The adiabatic multiwater bagmore » extension of the theory for applications to autoresonant BGK structures with more general initial distributions is suggested. The results of the theories are in very good agreement with numerical simulations.« less

Calculating tumor trajectory and dose-of-the-day using cone-beam CT projections

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

Jones, Bernard L., E-mail: bernard.jones@ucdenver.edu; Westerly, David; Miften, Moyed

2015-02-15

Purpose: Cone-beam CT (CBCT) projection images provide anatomical data in real-time over several respiratory cycles, forming a comprehensive picture of tumor movement. The authors developed and validated a method which uses these projections to determine the trajectory of and dose to highly mobile tumors during each fraction of treatment. Methods: CBCT images of a respiration phantom were acquired, the trajectory of which mimicked a lung tumor with high amplitude (up to 2.5 cm) and hysteresis. A template-matching algorithm was used to identify the location of a steel BB in each CBCT projection, and a Gaussian probability density function for themore » absolute BB position was calculated which best fit the observed trajectory of the BB in the imager geometry. Two modifications of the trajectory reconstruction were investigated: first, using respiratory phase information to refine the trajectory estimation (Phase), and second, using the Monte Carlo (MC) method to sample the estimated Gaussian tumor position distribution. The accuracies of the proposed methods were evaluated by comparing the known and calculated BB trajectories in phantom-simulated clinical scenarios using abdominal tumor volumes. Results: With all methods, the mean position of the BB was determined with accuracy better than 0.1 mm, and root-mean-square trajectory errors averaged 3.8% ± 1.1% of the marker amplitude. Dosimetric calculations using Phase methods were more accurate, with mean absolute error less than 0.5%, and with error less than 1% in the highest-noise trajectory. MC-based trajectories prevent the overestimation of dose, but when viewed in an absolute sense, add a small amount of dosimetric error (<0.1%). Conclusions: Marker trajectory and target dose-of-the-day were accurately calculated using CBCT projections. This technique provides a method to evaluate highly mobile tumors using ordinary CBCT data, and could facilitate better strategies to mitigate or compensate for motion during stereotactic body radiotherapy.« less

Dawn Orbit Determination Team: Trajectory and Gravity Prediction Performance During Vesta Science Phases

NASA Technical Reports Server (NTRS)

Kennedy, Brian; Abrahamson, Matt; Ardito, Alessandro; Han, Dongsuk; Haw, Robert; Mastrodemos, Nicholas; Nandi, Sumita; Park, Ryan; Rush, Brian; Vaughan, Andrew

2013-01-01

The Dawn spacecraft was launched on September 27th, 2007. Its mission is to consecutively rendezvous with and observe the two largest bodies in the asteroid belt, Vesta and Ceres. It has already completed over a year's worth of direct observations of Vesta (spanning from early 2011 through late 2012) and is currently on a cruise trajectory to Ceres, where it will begin scientific observations in mid-2015. Achieving this data collection required careful planning and execution from all spacecraft teams. Dawn's Orbit Determination (OD) team was tasked with accurately predicting the trajectory of the Dawn spacecraft during the Vesta science phases, and also determining the parameters of Vesta to support future science orbit design. The future orbits included the upcoming science phase orbits as well as the transfer orbits between science phases. In all, five science phases were executed at Vesta, and this paper will describe some of the OD team contributions to the planning and execution of those phases.

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.

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.

Low encounter speed comet COMA sample return missions

NASA Technical Reports Server (NTRS)

Tsou, P.; Yen, C. W.; Albee, A. L.

1994-01-01

Comets, being considered the most primitive bodies in the solar system, command the highest priority among solar-system objects for studying solar nebula evolution and the evolution of life through biogenic elements and compounds. The study of comets, and more especially, of material from them, provides an understanding of the physical, chemical, and mineralogical processes operative in the formation and earliest development of the solar systems. These return samples will provide valuable information on comets and serve as a rosetta stone for the analytical studies conducted on interplanetary dust particles over the past two decades, and will provide much needed extraterrestrial samples for the planetary materials community since the Apollo program. Lander sample return missions require rather complex spacecraft, intricate operations, and costly propulsion systems. By contrast, it is possible to take a highly simplified approach for sample capture and return in the case of a comet. In the past, we have considered Earth free-return trajectory to the comet, in which passive collectors intercept dust and volatiles from the cometary coma. However, standard short period cometary free-return trajectories results in the comet to the spacecraft encounter speeds in the range of 10 km/s. At these speeds the kinetic energy of the capture process can render significant modification of dust structure, change of solid phase as well as the lost of volatiles components. This paper presents a class of new missions with trajectories with significant reduction of encounter speeds by incorporating gravity assists and deep space maneuvering. Low encounter speed cometary flyby sample return will enable a marked increase in the value of the return science. Acquiring thousands of samples from a known comet and thousands of images of a comet nucleus would be space firsts. Applying new approach in flight mechanics to generate a new class of low encounter speed cometary sample return trajectories opens new possibilities in science. A systematic search of trajectories for the first decade of the twenty-first century will be made. The target encounter speed is for less than 7 km/s to short period comets.

An apparent contradiction: increasing variability to achieve greater precision?

PubMed

Rosenblatt, Noah J; Hurt, Christopher P; Latash, Mark L; Grabiner, Mark D

2014-02-01

To understand the relationship between variability of foot placement in the frontal plane and stability of gait patterns, we explored how constraining mediolateral foot placement during walking affects the structure of kinematic variance in the lower-limb configuration space during the swing phase of gait. Ten young subjects walked under three conditions: (1) unconstrained (normal walking), (2) constrained (walking overground with visual guides for foot placement to achieve the measured unconstrained step width) and, (3) beam (walking on elevated beams spaced to achieve the measured unconstrained step width). The uncontrolled manifold analysis of the joint configuration variance was used to quantify two variance components, one that did not affect the mediolateral trajectory of the foot in the frontal plane ("good variance") and one that affected this trajectory ("bad variance"). Based on recent studies, we hypothesized that across conditions (1) the index of the synergy stabilizing the mediolateral trajectory of the foot (the normalized difference between the "good variance" and "bad variance") would systematically increase and (2) the changes in the synergy index would be associated with a disproportionate increase in the "good variance." Both hypotheses were confirmed. We conclude that an increase in the "good variance" component of the joint configuration variance may be an effective method of ensuring high stability of gait patterns during conditions requiring increased control of foot placement, particularly if a postural threat is present. Ultimately, designing interventions that encourage a larger amount of "good variance" may be a promising method of improving stability of gait patterns in populations such as older adults and neurological patients.

The Application of the NASA Advanced Concepts Office, Launch Vehicle Team Design Process and Tools for Modeling Small Responsive Launch Vehicles

NASA Technical Reports Server (NTRS)

Threet, Grady E.; Waters, Eric D.; Creech, Dennis M.

2012-01-01

The Advanced Concepts Office (ACO) Launch Vehicle Team at the NASA Marshall Space Flight Center (MSFC) is recognized throughout NASA for launch vehicle conceptual definition and pre-phase A concept design evaluation. The Launch Vehicle Team has been instrumental in defining the vehicle trade space for many of NASA s high level launch system studies from the Exploration Systems Architecture Study (ESAS) through the Augustine Report, Constellation, and now Space Launch System (SLS). The Launch Vehicle Team s approach to rapid turn-around and comparative analysis of multiple launch vehicle architectures has played a large role in narrowing the design options for future vehicle development. Recently the Launch Vehicle Team has been developing versions of their vetted tools used on large launch vehicles and repackaged the process and capability to apply to smaller more responsive launch vehicles. Along this development path the LV Team has evaluated trajectory tools and assumptions against sounding rocket trajectories and air launch systems, begun altering subsystem mass estimating relationships to handle smaller vehicle components, and as an additional development driver, have begun an in-house small launch vehicle study. With the recent interest in small responsive launch systems and the known capability and response time of the ACO LV Team, ACO s launch vehicle assessment capability can be utilized to rapidly evaluate the vast and opportune trade space that small launch vehicles currently encompass. This would provide a great benefit to the customer in order to reduce that large trade space to a select few alternatives that should best fit the customer s payload needs.

Multi-scale full-orbit analysis on phase-space behavior of runaway electrons in tokamak fields with synchrotron radiation

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

Wang, Yulei; Liu, Jian, E-mail: jliuphy@ustc.edu.cn; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026

In this paper, the secular full-orbit simulations of runaway electrons with synchrotron radiation in tokamak fields are carried out using a relativistic volume-preserving algorithm. Detailed phase-space behaviors of runaway electrons are investigated in different dynamical timescales spanning 11 orders. In the small timescale, i.e., the characteristic timescale imposed by Lorentz force, the severely deformed helical trajectory of energetic runaway electron is witnessed. A qualitative analysis of the neoclassical scattering, a kind of collisionless pitch-angle scattering phenomena, is provided when considering the coupling between the rotation of momentum vector and the background magnetic field. In large timescale up to 1 s,more » it is found that the initial condition of runaway electrons in phase space globally influences the pitch-angle scattering, the momentum evolution, and the loss-gain ratio of runaway energy evidently. However, the initial value has little impact on the synchrotron energy limit. It is also discovered that the parameters of tokamak device, such as the toroidal magnetic field, the loop voltage, the safety factor profile, and the major radius, can modify the synchrotron energy limit and the strength of neoclassical scattering. The maximum runaway energy is also proved to be lower than the synchrotron limit when the magnetic field ripple is considered.« less

Dynamic trajectory-based couch motion for improvement of radiation therapy trajectories in cranial SRT

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

MacDonald, R. Lee; Thomas, Christopher G., E-mail: Chris.Thomas@cdha.nshealth.ca; Department of Medical Physics, Nova Scotia Cancer Centre, Queen Elizabeth II Health Sciences Centre, Halifax, Nova Scotia B3H 1V7

2015-05-15

Purpose: To investigate potential improvement in external beam stereotactic radiation therapy plan quality for cranial cases using an optimized dynamic gantry and patient support couch motion trajectory, which could minimize exposure to sensitive healthy tissue. Methods: Anonymized patient anatomy and treatment plans of cranial cancer patients were used to quantify the geometric overlap between planning target volumes and organs-at-risk (OARs) based on their two-dimensional projection from source to a plane at isocenter as a function of gantry and couch angle. Published dose constraints were then used as weighting factors for the OARs to generate a map of couch-gantry coordinate space,more » indicating degree of overlap at each point in space. A couch-gantry collision space was generated by direct measurement on a linear accelerator and couch using an anthropomorphic solid-water phantom. A dynamic, fully customizable algorithm was written to generate a navigable ideal trajectory for the patient specific couch-gantry space. The advanced algorithm can be used to balance the implementation of absolute minimum values of overlap with the clinical practicality of large-scale couch motion and delivery time. Optimized cranial cancer treatment trajectories were compared to conventional treatment trajectories. Results: Comparison of optimized treatment trajectories with conventional treatment trajectories indicated an average decrease in mean dose to the OARs of 19% and an average decrease in maximum dose to the OARs of 12%. Degradation was seen for homogeneity index (6.14% ± 0.67%–5.48% ± 0.76%) and conformation number (0.82 ± 0.02–0.79 ± 0.02), but neither was statistically significant. Removal of OAR constraints from volumetric modulated arc therapy optimization reveals that reduction in dose to OARs is almost exclusively due to the optimized trajectory and not the OAR constraints. Conclusions: The authors’ study indicated that simultaneous couch and gantry motion during radiation therapy to minimize the geometrical overlap in the beams-eye-view of target volumes and the organs-at-risk can have an appreciable dose reduction to organs-at-risk.« less

Space shuttle launch vehicle performance trajectory, exchange ratios, and dispersion analysis

NASA Technical Reports Server (NTRS)

Toelle, R. G.; Blackwell, D. L.; Lott, L. N.

1973-01-01

A baseline space shuttle performance trajectory for Mission 3A launched from WTR has been generated. Design constraints of maximum dynamic pressure, longitudinal acceleration, and delivered payload were satisfied. Payload exchange ratios are presented with explanation on use. Design envelopes of dynamic pressure, SRB staging point, aerodynamic heating and flight performance reserves are calculated and included.

Latent virus reactivation in astronauts on the international space station.

PubMed

Mehta, Satish K; Laudenslager, Mark L; Stowe, Raymond P; Crucian, Brian E; Feiveson, Alan H; Sams, Clarence F; Pierson, Duane L

2017-01-01

Reactivation of latent herpes viruses was measured in 23 astronauts (18 male and 5 female) before, during, and after long-duration (up to 180 days) spaceflight onboard the international space station . Twenty age-matched and sex-matched healthy ground-based subjects were included as a control group. Blood, urine, and saliva samples were collected before, during, and after spaceflight. Saliva was analyzed for Epstein-Barr virus, varicella-zoster virus, and herpes simplex virus type 1. Urine was analyzed for cytomegalovirus. One astronaut did not shed any targeted virus in samples collected during the three mission phases. Shedding of Epstein-Barr virus, varicella-zoster virus, and cytomegalovirus was detected in 8 of the 23 astronauts. These viruses reactivated independently of each other. Reactivation of Epstein-Barr virus, varicella-zoster virus, and cytomegalovirus increased in frequency, duration, and amplitude (viral copy numbers) when compared to short duration (10 to 16 days) space shuttle missions. No evidence of reactivation of herpes simplex virus type 1, herpes simplex virus type 2, or human herpes virus 6 was found. The mean diurnal trajectory of salivary cortisol changed significantly during flight as compared to before flight ( P  = 0.010). There was no statistically significant difference in levels of plasma cortisol or dehydoepiandosterone concentrations among time points before, during, and after flight for these international space station crew members, although observed cortisol levels were lower at the mid and late-flight time points. The data confirm that astronauts undertaking long-duration spaceflight experience both increased latent viral reactivation and changes in diurnal trajectory of salivary cortisol concentrations.

Coupled Low-thrust Trajectory and System Optimization via Multi-Objective Hybrid Optimal Control

NASA Technical Reports Server (NTRS)

Vavrina, Matthew A.; Englander, Jacob Aldo; Ghosh, Alexander R.

2015-01-01

The optimization of low-thrust trajectories is tightly coupled with the spacecraft hardware. Trading trajectory characteristics with system parameters ton identify viable solutions and determine mission sensitivities across discrete hardware configurations is labor intensive. Local independent optimization runs can sample the design space, but a global exploration that resolves the relationships between the system variables across multiple objectives enables a full mapping of the optimal solution space. A multi-objective, hybrid optimal control algorithm is formulated using a multi-objective genetic algorithm as an outer loop systems optimizer around a global trajectory optimizer. The coupled problem is solved simultaneously to generate Pareto-optimal solutions in a single execution. The automated approach is demonstrated on two boulder return missions.

Tunable Spin dependent beam shift by simultaneously tailoring geometric and dynamical phases of light in inhomogeneous anisotropic medium

PubMed Central

Pal, Mandira; Banerjee, Chitram; Chandel, Shubham; Bag, Ankan; Majumder, Shovan K.; Ghosh, Nirmalya

2016-01-01

Spin orbit interaction and the resulting Spin Hall effect of light are under recent intensive investigations because of their fundamental nature and potential applications. Here, we report an interesting manifestation of spin Hall effect of light and demonstrate its tunability in an inhomogeneous anisotropic medium exhibiting spatially varying retardance level. In our system, the beam shift occurs only for one circular polarization mode keeping the other orthogonal mode unaffected, which is shown to arise due to the combined spatial gradients of the geometric phase and the dynamical phase of light. The constituent two orthogonal circular polarization modes of an input linearly polarized light evolve in different trajectories, eventually manifesting as a large and tunable spin separation. The spin dependent beam shift and the demonstrated principle of simultaneously tailoring space-varying geometric and dynamical phase of light for achieving its tunability (of both magnitude and direction), may provide an attractive route towards development of spin-optical devices. PMID:28004825

The potential influence of Asian and African mineral dust on ice, mixed-phase and liquid water clouds

NASA Astrophysics Data System (ADS)

Wiacek, A.; Peter, T.; Lohmann, U.

2010-02-01

This modelling study explores the availability of mineral dust particles as ice nuclei for interactions with ice, mixed-phase and liquid water clouds, also tracking the particles' history of cloud-processing. We performed 61 320 one-week forward trajectory calculations originating near the surface of major dust emitting regions in Africa and Asia using high-resolution meteorological analysis fields for the year 2007. Without explicitly modelling dust emission and deposition processes, dust-bearing trajectories were assumed to be those coinciding with known dust emission seasons. We found that dust emissions from Asian deserts lead to a higher potential for interactions with high clouds, despite being the climatologically much smaller dust emission source. This is due to Asian regions experiencing significantly more ascent than African regions, with strongest ascent in the Asian Taklimakan desert at ~25%, ~40% and 10% of trajectories ascending to 300 hPa in spring, summer and fall, respectively. The specific humidity at each trajectory's starting point was transported in a Lagrangian manner and relative humidities with respect to water and ice were calculated in 6-h steps downstream, allowing us to estimate the formation of liquid, mixed-phase and ice clouds. Practically none of the simulated air parcels reached regions where homogeneous ice nucleation can take place (T≲-40 °C) along trajectories that have not experienced water saturation first. By far the largest fraction of cloud forming trajectories entered conditions of mixed-phase clouds, where mineral dust will potentially exert the biggest influence. The majority of trajectories also passed through regions supersaturated with respect to ice but subsaturated with respect to water, where "warm" (T≳-40 °C) ice clouds may form prior to supercooled water or mixed-phase clouds. The importance of "warm" ice clouds and the general influence of dust in the mixed-phase cloud region are highly uncertain due to considerable scatter in recent laboratory data from ice nucleation experiments, which we briefly review in this work. For "classical" cirrus-forming temperatures, our results show that only mineral dust IN that underwent mixed-phase cloud-processing previously are likely to be relevant, and, therefore, we recommend further systematic studies of immersion mode ice nucleation on mineral dust suspended in atmospherically relevant coatings.

KSC-2009-5035

NASA Image and Video Library

2009-08-19

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the top of the mated SV1 and SV2 remains covered. The spacecraft are being prepared for center of gravity testing, weighing and balancing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5014

NASA Image and Video Library

2009-08-03

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., a crane is attached to the SV1 spacecraft, part of the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, Program. The SV1 will be lifted and moved to mate with the SV2 on another stand nearby. STSS-Demo is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. The spacecraft is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5034

NASA Image and Video Library

2009-08-19

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., the mated SV1 and SV2 spacecraft retain the covers on the top which are being removed before center of gravity testing, weighing and balancing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

KSC-2009-5037

NASA Image and Video Library

2009-08-19

CAPE CANAVERAL, Fla. – At the Astrotech payload processing facility in Titusville, Fla., this closeup shows part of the mated SV1 and SV2 spacecraft, which is being prepared for center of gravity testing, weighing and balancing. The two spacecraft are known as the Space Tracking and Surveillance System – Demonstrators, or STSS Demo, which is a space-based sensor component of a layered Ballistic Missile Defense System designed for the overall mission of detecting, tracking and discriminating ballistic missiles. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency between 8 and 8:58 a.m. EDT Sept. 18. Approved for Public Release 09-MDA-04886 (10 SEPT 09) Photo credit: NASA/Jim Grossmann

Multi-objective trajectory optimization for the space exploration vehicle

NASA Astrophysics Data System (ADS)

Qin, Xiaoli; Xiao, Zhen

2016-07-01

The research determines temperature-constrained optimal trajectory for the space exploration vehicle by developing an optimal control formulation and solving it using a variable order quadrature collocation method with a Non-linear Programming(NLP) solver. The vehicle is assumed to be the space reconnaissance aircraft that has specified takeoff/landing locations, specified no-fly zones, and specified targets for sensor data collections. A three degree of freedom aircraft model is adapted from previous work and includes flight dynamics, and thermal constraints.Vehicle control is accomplished by controlling angle of attack, roll angle, and propellant mass flow rate. This model is incorporated into an optimal control formulation that includes constraints on both the vehicle and mission parameters, such as avoidance of no-fly zones and exploration of space targets. In addition, the vehicle models include the environmental models(gravity and atmosphere). How these models are appropriately employed is key to gaining confidence in the results and conclusions of the research. Optimal trajectories are developed using several performance costs in the optimal control formation,minimum time,minimum time with control penalties,and maximum distance.The resulting analysis demonstrates that optimal trajectories that meet specified mission parameters and constraints can be quickly determined and used for large-scale space exloration.

Tracking Debris Shed by a Space-Shuttle Launch Vehicle

NASA Technical Reports Server (NTRS)

Stuart, Phillip C.; Rogers, Stuart E.

2009-01-01

The DEBRIS software predicts the trajectories of debris particles shed by a space-shuttle launch vehicle during ascent, to aid in assessing potential harm to the space-shuttle orbiter and crew. The user specifies the location of release and other initial conditions for a debris particle. DEBRIS tracks the particle within an overset grid system by means of a computational fluid dynamics (CFD) simulation of the local flow field and a ballistic simulation that takes account of the mass of the particle and its aerodynamic properties in the flow field. The computed particle trajectory is stored in a file to be post-processed by other software for viewing and analyzing the trajectory. DEBRIS supplants a prior debris tracking code that took .15 minutes to calculate a single particle trajectory: DEBRIS can calculate 1,000 trajectories in .20 seconds on a desktop computer. Other improvements over the prior code include adaptive time-stepping to ensure accuracy, forcing at least one step per grid cell to ensure resolution of all CFD-resolved flow features, ability to simulate rebound of debris from surfaces, extensive error checking, a builtin suite of test cases, and dynamic allocation of memory.

Trajectory Specification for Terminal Air Traffic: Pairwise Conflict Detection and Resolution

NASA Technical Reports Server (NTRS)

Paielli, Russ; Erzberger, Heinz

2017-01-01

Trajectory specification is the explicit bounding and control of aircraft trajectories such that the position at each point in time is constrained to a precisely defined volume of space. The bounding space is defined by cross-track, along-track, and vertical tolerances relative to a reference trajectory that specifies position as a function of time. The tolerances are dynamic and will be based on the aircraft navigation capabilities and the current traffic situation. A standard language will be developed to represent these specifications and to communicate them by datalink. Assuming conformance, trajectory specification can guarantee safe separation for an arbitrary period of time even in the event of an air traffic control (ATC) system or datalink failure, hence it can help to achieve the high level of safety and reliability needed for ATC automation. As a more proactive form of ATC, it can also maximize airspace capacity and reduce the reliance on tactical backup systems during normal operation. It applies to both enroute airspace and the terminal area around airports, but this paper focuses on the terminal area and presents algorithms and software for spacing arrivals and deconflicting both arrivals and departures.

Iterative method of construction of a bifurcation diagram of autorotation motions for a system with one degree of freedom

NASA Astrophysics Data System (ADS)

Klimina, L. A.

2018-05-01

The modification of the Picard approach is suggested that is targeted to the construction of a bifurcation diagram of 2π -periodic motions of mechanical system with a cylindrical phase space. Each iterative step is based on principles of averaging and energy balance similar to the Poincare-Pontryagin approach. If the iterative procedure converges, it provides the periodic trajectory of the system depending on the bifurcation parameter of the model. The method is applied to describe self-sustained rotations in the model of an aerodynamic pendulum.

Hyperbolic geometry of Kuramoto oscillator networks

NASA Astrophysics Data System (ADS)

Chen, Bolun; Engelbrecht, Jan R.; Mirollo, Renato

2017-09-01

Kuramoto oscillator networks have the special property that their trajectories are constrained to lie on the (at most) 3D orbits of the Möbius group acting on the state space T N (the N-fold torus). This result has been used to explain the existence of the N-3 constants of motion discovered by Watanabe and Strogatz for Kuramoto oscillator networks. In this work we investigate geometric consequences of this Möbius group action. The dynamics of Kuramoto phase models can be further reduced to 2D reduced group orbits, which have a natural geometry equivalent to the unit disk \

KSC-2009-3662

NASA Image and Video Library

2009-05-01

CAPE CANAVERAL, Fla. – At NASA Kennedy Space Center's Shuttle Landing Facility, the shipping container with the STSS Demonstrator SV-2spacecraft moves out of the U.S. Air Force C-17 aircraft. The spacecraft will be transferred to the Astrotech payload processing facility in Titusville, Fla. The spacecraft is a midcourse tracking technology demonstrator, part of an evolving ballistic missile defense system. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency in late summer. Photo credit: NASA/Jack Pfaller (Approved for Public Release 09-MDA-4616 [27 May 09])

Space Shuttle Plume and Plume Impingement Study

NASA Technical Reports Server (NTRS)

Tevepaugh, J. A.; Penny, M. M.

1977-01-01

The extent of the influence of the propulsion system exhaust plumes on the vehicle performance and control characteristics is a complex function of vehicle geometry, propulsion system geometry, engine operating conditions and vehicle flight trajectory were investigated. Analytical support of the plume technology test program was directed at the two latter problem areas: (1) definition of the full-scale exhaust plume characteristics, (2) application of appropriate similarity parameters; and (3) analysis of wind tunnel test data. Verification of the two-phase plume and plume impingement models was directed toward the definition of the full-scale exhaust plume characteristics and the separation motor impingement problem.

KSC-2009-3658

NASA Image and Video Library

2009-05-01

CAPE CANAVERAL, Fla. – The U.S. Air Force C-17 aircraft arrives at NASA Kennedy Space Center's Shuttle Landing Facility with its cargo of the STSS Demonstrator SV-2 spacecraft. The spacecraft will be transferred to the Astrotech payload processing facility in Titusville, Fla. The spacecraft is a midcourse tracking technology demonstrator, part of an evolving ballistic missile defense system. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency in late summer. Photo credit: NASA/Jack Pfaller (Approved for Public Release 09-MDA-4616 [27 May 09])

KSC-2009-4611

NASA Image and Video Library

2009-06-25

CAPE CANAVERAL, Fla. – The U.S. Air Force C-17 aircraft arrives at NASA Kennedy Space Center's Shuttle Landing Facility with its SV-1 cargo of the STSS Demonstrator spacecraft. The cargo will be transferred to the Astrotech payload processing facility in Titusville, Fla. The spacecraft is a midcourse tracking technology demonstrator, part of an evolving ballistic missile defense system. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency in late summer. Photo credit: NASA/Kim Shiflett (Approved for Public Release 09-MDA-4804 [4 Aug 09] )

KSC-2009-4612

NASA Image and Video Library

2009-06-25

CAPE CANAVERAL, Fla. – At NASA Kennedy Space Center's Shuttle Landing Facility, the SV-1 cargo of the STSS Demonstrator spacecraft moves out of the U.S. Air Force C-17. The cargo will be transferred to the Astrotech payload processing facility in Titusville, Fla. The spacecraft is a midcourse tracking technology demonstrator, part of an evolving ballistic missile defense system. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency in late summer. Photo credit: NASA/Kim Shiflett (Approved for Public Release 09-MDA-4804 [4 Aug 09] )

KSC-2009-3660

NASA Image and Video Library

2009-05-01

CAPE CANAVERAL, Fla. – At NASA Kennedy Space Center's Shuttle Landing Facility, more equipment for the STSS Demonstrator SV-2 spacecraft is offloaded from the U.S. Air Force C-17 aircraft. The spacecraft will be transferred to the Astrotech payload processing facility in Titusville, Fla.The spacecraft is a midcourse tracking technology demonstrator, part of an evolving ballistic missile defense system. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency in late summer. Photo credit: NASA/Jack Pfaller (Approved for Public Release 09-MDA-4616 [27 May 09])

KSC-2009-4613

NASA Image and Video Library

2009-06-25

CAPE CANAVERAL, Fla. – At NASA Kennedy Space Center's Shuttle Landing Facility, the SV-1 cargo of the STSS Demonstrator spacecraft moves out of the U.S. Air Force C-17. The cargo will be transferred to the Astrotech payload processing facility in Titusville, Fla. The spacecraft is a midcourse tracking technology demonstrator, part of an evolving ballistic missile defense system. STSS is capable of tracking objects after boost phase and provides trajectory information to other sensors. It will be launched by NASA for the Missile Defense Agency in late summer. Photo credit: NASA/Kim Shiflett (Approved for Public Release 09-MDA-4804 [4 Aug 09] )

Sensorimotor coordination and the structure of space.

PubMed

McCollum, Gin

2003-01-01

Embedded in neural and behavioral organization is a structure of sensorimotor space. Both this embedded spatial structure and the structure of physical space inform sensorimotor control. This paper reviews studies in which the gravitational vertical and horizontal are crucial. The mathematical expressions of spatial geometry in these studies indicate methods for investigating sensorimotor control in freefall. In freefall, the spatial structure introduced by gravitation - the distinction between vertical and horizontal - does not exist. However, an astronaut arriving in space carries the physiologically-embedded distinction between horizontal and vertical learned on earth. The physiological organization based on this distinction collapses when the strong otolith activity and other gravitational cues for sensorimotor behavior become unavailable. The mathematical methods in this review are applicable in understanding the changes in physiological organization as an astronaut adapts to sensorimotor control in freefall. Many mathematical languages are available for characterizing the logical structures in physiological organization. Here, group theory is used to characterize basic structure of physical and physiological spaces. Dynamics and topology allow the grouping of trajectory ranges according to the outcomes or attractors. The mathematics of ordered structures express complex orderings, such as in multiphase movements in which different parts of the body are moving in different phase sequences. Conditional dynamics, which combines dynamics with the mathematics of ordered structures, accommodates the parsing of movement sequences into trajectories and transitions. Studies reviewed include those of the sit-to-stand movement and early locomotion, because of the salience of gravitation in those behaviors. Sensorimotor transitions and the conditions leading to them are characterized in conditional dynamic control structures that do not require thinking of an organism as an input-output device. Conditions leading to sensorimotor transitions on earth assume the presence of a gravitational vertical which is lacking in space. Thus, conditions used on earth for sensorimotor transitions may become ambiguous in space. A platform study in which sensorimotor transition conditions are ambiguous and are related to motion sickness is reviewed.

Constrained Multi-Level Algorithm for Trajectory Optimization

NASA Astrophysics Data System (ADS)

Adimurthy, V.; Tandon, S. R.; Jessy, Antony; Kumar, C. Ravi

The emphasis on low cost access to space inspired many recent developments in the methodology of trajectory optimization. Ref.1 uses a spectral patching method for optimization, where global orthogonal polynomials are used to describe the dynamical constraints. A two-tier approach of optimization is used in Ref.2 for a missile mid-course trajectory optimization. A hybrid analytical/numerical approach is described in Ref.3, where an initial analytical vacuum solution is taken and gradually atmospheric effects are introduced. Ref.4 emphasizes the fact that the nonlinear constraints which occur in the initial and middle portions of the trajectory behave very nonlinearly with respect the variables making the optimization very difficult to solve in the direct and indirect shooting methods. The problem is further made complex when different phases of the trajectory have different objectives of optimization and also have different path constraints. Such problems can be effectively addressed by multi-level optimization. In the multi-level methods reported so far, optimization is first done in identified sub-level problems, where some coordination variables are kept fixed for global iteration. After all the sub optimizations are completed, higher-level optimization iteration with all the coordination and main variables is done. This is followed by further sub system optimizations with new coordination variables. This process is continued until convergence. In this paper we use a multi-level constrained optimization algorithm which avoids the repeated local sub system optimizations and which also removes the problem of non-linear sensitivity inherent in the single step approaches. Fall-zone constraints, structural load constraints and thermal constraints are considered. In this algorithm, there is only a single multi-level sequence of state and multiplier updates in a framework of an augmented Lagrangian. Han Tapia multiplier updates are used in view of their special role in diagonalised methods, being the only single update with quadratic convergence. For a single level, the diagonalised multiplier method (DMM) is described in Ref.5. The main advantage of the two-level analogue of the DMM approach is that it avoids the inner loop optimizations required in the other methods. The scheme also introduces a gradient change measure to reduce the computational time needed to calculate the gradients. It is demonstrated that the new multi-level scheme leads to a robust procedure to handle the sensitivity of the constraints, and the multiple objectives of different trajectory phases. Ref. 1. Fahroo, F and Ross, M., " A Spectral Patching Method for Direct Trajectory Optimization" The Journal of the Astronautical Sciences, Vol.48, 2000, pp.269-286 Ref. 2. Phililps, C.A. and Drake, J.C., "Trajectory Optimization for a Missile using a Multitier Approach" Journal of Spacecraft and Rockets, Vol.37, 2000, pp.663-669 Ref. 3. Gath, P.F., and Calise, A.J., " Optimization of Launch Vehicle Ascent Trajectories with Path Constraints and Coast Arcs", Journal of Guidance, Control, and Dynamics, Vol. 24, 2001, pp.296-304 Ref. 4. Betts, J.T., " Survey of Numerical Methods for Trajectory Optimization", Journal of Guidance, Control, and Dynamics, Vol.21, 1998, pp. 193-207 Ref. 5. Adimurthy, V., " Launch Vehicle Trajectory Optimization", Acta Astronautica, Vol.15, 1987, pp.845-850.

The cancellous bone multiscale morphology-elasticity relationship.

PubMed

Agić, Ante; Nikolić, Vasilije; Mijović, Budimir

2006-06-01

The cancellous bone effective properties relations are analysed on multiscale across two aspects; properties of representative volume element on micro scale and statistical measure of trabecular trajectory orientation on mesoscale. Anisotropy of the microstructure is described across fabric tensor measure with trajectory orientation tensor as bridging scale connection. The scatter measured data (elastic modulus, trajectory orientation, apparent density) from compression test are fitted by stochastic interpolation procedure. The engineering constants of the elasticity tensor are estimated by last square fitt procedure in multidimensional space by Nelder-Mead simplex. The multiaxial failure surface in strain space is constructed and interpolated by modified super-ellipsoid.

Reentry trajectories of a space glider, taking acceleration and heating constraints into account

NASA Astrophysics Data System (ADS)

Strauss, Adi

1988-03-01

Three-dimensional trajectories for aerodynamically controlled reentry of an unpowered Space Shuttle-type vehicle from equatorial orbit are investigated analytically, summarizing the results obtained in the author's thesis (Strauss, 1987). Computer programs constructed on the basis of the governing equations of Chern and Yang (1982) and Chern and Vinh (1980) in modified dimensionless Chapman variables are used to optimize the roll angle and lift coefficient of the trajectories. Typical results are presented in graphs and maps and shown to be in good agreement with AVION SPATIAL predictions for the ESA Hermes spacecraft.

Constrained Burn Optimization for the International Space Station

NASA Technical Reports Server (NTRS)

Brown, Aaron J.; Jones, Brandon A.

2017-01-01

In long-term trajectory planning for the International Space Station (ISS), translational burns are currently targeted sequentially to meet the immediate trajectory constraints, rather than simultaneously to meet all constraints, do not employ gradient-based search techniques, and are not optimized for a minimum total deltav (v) solution. An analytic formulation of the constraint gradients is developed and used in an optimization solver to overcome these obstacles. Two trajectory examples are explored, highlighting the advantage of the proposed method over the current approach, as well as the potential v and propellant savings in the event of propellant shortages.

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.

A simple acquisition strategy to avoid off-resonance blurring in spiral imaging with redundant spiral-in/out k-space trajectories

PubMed Central

Fielden, Samuel W.; Meyer, Craig H.

2014-01-01

Purpose The major hurdle to widespread adoption of spiral trajectories has been their poor off-resonance performance. Here we present a self-correcting spiral k-space trajectory that avoids much of the well-known spiral blurring during data acquisition. Theory and Methods In comparison with a traditional spiral-out trajectory, the spiral-in/out trajectory has improved off-resonance performance. By combining two spiral-in/out acquisitions, one rotated 180° in k-space compared to the other, multi-shot spiral-in/out artifacts are eliminated. A phantom was scanned with the center frequency manually tuned 20, 40, 80, and 160 Hz off-resonance with both a spiral-out gradient echo sequence and the redundant spiral-in/out sequence. The phantom was also imaged in an oblique orientation in order to demonstrate improved concomitant gradient field performance of the sequence, and was additionally incorporated into a spiral turbo spin echo sequence for brain imaging. Results Phantom studies with manually-tuned off-resonance agree well with theoretical calculations, showing that moderate off-resonance is well-corrected by this acquisition scheme. Blur due to concomitant fields is reduced, and good results are obtained in vivo. Conclusion The redundant spiral-in/out trajectory results in less image blur for a given readout length than a traditional spiral-out scan, reducing the need for complex off-resonance correction algorithms. PMID:24604539

Interactive orbital proximity operations planning system

NASA Technical Reports Server (NTRS)

Grunwald, Arthur J.; Ellis, Stephen R.

1989-01-01

An interactive, graphical proximity operations planning system was developed which allows on-site design of efficient, complex, multiburn maneuvers in the dynamic multispacecraft environment about the space station. Maneuvering takes place in, as well as out of, the orbital plane. The difficulty in planning such missions results from the unusual and counterintuitive character of relative orbital motion trajectories and complex operational constraints, which are both time varying and highly dependent on the mission scenario. This difficulty is greatly overcome by visualizing the relative trajectories and the relative constraints in an easily interpretable, graphical format, which provides the operator with immediate feedback on design actions. The display shows a perspective bird's-eye view of the space station and co-orbiting spacecraft on the background of the station's orbital plane. The operator has control over two modes of operation: (1) a viewing system mode, which enables him or her to explore the spatial situation about the space station and thus choose and frame in on areas of interest; and (2) a trajectory design mode, which allows the interactive editing of a series of way-points and maneuvering burns to obtain a trajectory which complies with all operational constraints. Through a graphical interactive process, the operator will continue to modify the trajectory design until all operational constraints are met. The effectiveness of this display format in complex trajectory design is presently being evaluated in an ongoing experimental program.

Low Cost Missions Operations on NASA Deep Space Missions

NASA Astrophysics Data System (ADS)

Barnes, R. J.; Kusnierkiewicz, D. J.; Bowman, A.; Harvey, R.; Ossing, D.; Eichstedt, J.

2014-12-01

The ability to lower mission operations costs on any long duration mission depends on a number of factors; the opportunities for science, the flight trajectory, and the cruise phase environment, among others. Many deep space missions employ long cruises to their final destination with minimal science activities along the way; others may perform science observations on a near-continuous basis. This paper discusses approaches employed by two NASA missions implemented by the Johns Hopkins University Applied Physics Laboratory (JHU/APL) to minimize mission operations costs without compromising mission success: the New Horizons mission to Pluto, and the Solar Terrestrial Relations Observatories (STEREO). The New Horizons spacecraft launched in January 2006 for an encounter with the Pluto system.The spacecraft trajectory required no deterministic on-board delta-V, and so the mission ops team then settled in for the rest of its 9.5-year cruise. The spacecraft has spent much of its cruise phase in a "hibernation" mode, which has enabled the spacecraft to be maintained with a small operations team, and minimized the contact time required from the NASA Deep Space Network. The STEREO mission is comprised of two three-axis stabilized sun-staring spacecraft in heliocentric orbit at a distance of 1 AU from the sun. The spacecraft were launched in October 2006. The STEREO instruments operate in a "decoupled" mode from the spacecraft, and from each other. Since STEREO operations are largely routine, unattended ground station contact operations were implemented early in the mission. Commands flow from the MOC to be uplinked, and the data recorded on-board is downlinked and relayed back to the MOC. Tools run in the MOC to assess the health and performance of ground system components. Alerts are generated and personnel are notified of any problems. Spacecraft telemetry is similarly monitored and alarmed, thus ensuring safe, reliable, low cost operations.

Trajectory determinations and collection of micrometeoroids on the space station. Report of the Workshop on Micrometeorite Capture Experiments

NASA Technical Reports Server (NTRS)

Hoerz, F. (Editor)

1986-01-01

Summaries of papers presented at the Workshop on Micrometeorite Capture Experiments are compiled. The goals of the workshop were to define the scientific objectives and the resulting performance requirements of a potential Space Station facility and to identify the major elements of a coherent development program that would generate the desired capabilities within the next decade. Specific topics include cosmic dust and space debris collection techniques, particle trajectory and source determination, and specimen analysis methods.

PTM Along Track Algorithm to Maintain Spacing During Same Direction Pair-Wise Trajectory Management Operations

NASA Technical Reports Server (NTRS)

Carreno, Victor A.

2015-01-01

Pair-wise Trajectory Management (PTM) is a cockpit based delegated responsibility separation standard. When an air traffic service provider gives a PTM clearance to an aircraft and the flight crew accepts the clearance, the flight crew will maintain spacing and separation from a designated aircraft. A PTM along track algorithm will receive state information from the designated aircraft and from the own ship to produce speed guidance for the flight crew to maintain spacing and separation

The Biharmonic Oscillator and Asymmetric Linear Potentials: From Classical Trajectories to Momentum-Space Probability Densities in the Extreme Quantum Limit

ERIC Educational Resources Information Center

Ruckle, L. J.; Belloni, M.; Robinett, R. W.

2012-01-01

The biharmonic oscillator and the asymmetric linear well are two confining power-law-type potentials for which complete bound-state solutions are possible in both classical and quantum mechanics. We examine these problems in detail, beginning with studies of their trajectories in position and momentum space, evaluation of the classical probability…

Does the diffusion dark matter-dark energy interaction model solve cosmological puzzles?

NASA Astrophysics Data System (ADS)

Szydłowski, Marek; Stachowski, Aleksander

2016-08-01

We study dynamics of cosmological models with diffusion effects modeling dark matter and dark energy interactions. We show the simple model with diffusion between the cosmological constant sector and dark matter, where the canonical scaling law of dark matter (ρd m ,0a-3(t )) is modified by an additive ɛ (t )=γ t a-3(t ) to the form ρd m=ρd m ,0a-3(t )+ɛ (t ). We reduced this model to the autonomous dynamical system and investigate it using dynamical system methods. This system possesses a two-dimensional invariant submanifold on which the dark matter-dark energy (DM-DE) interaction can be analyzed on the phase plane. The state variables are density parameter for matter (dark and visible) and parameter δ characterizing the rate of growth of energy transfer between the dark sectors. A corresponding dynamical system belongs to a general class of jungle type of cosmologies represented by coupled cosmological models in a Lotka-Volterra framework. We demonstrate that the de Sitter solution is a global attractor for all trajectories in the phase space and there are two repellers: the Einstein-de Sitter universe and the de Sitter universe state dominating by the diffusion effects. We distinguish in the phase space trajectories, which become in good agreement with the data. They should intersect a rectangle with sides of Ωm ,0∈[0.2724 ,0.3624 ] , δ ∈[0.0000 ,0.0364 ] at the 95% CL. Our model could solve some of the puzzles of the Λ CDM model, such as the coincidence and fine-tuning problems. In the context of the coincidence problem, our model can explain the present ratio of ρm to ρd e, which is equal 0.457 6-0.0831+0.1109 at a 2 σ confidence level.

A New Unified Analysis of Estimate Errors by Model-Matching Phase-Estimation Methods for Sensorless Drive of Permanent-Magnet Synchronous Motors and New Trajectory-Oriented Vector Control, Part I

NASA Astrophysics Data System (ADS)

Shinnaka, Shinji; Sano, Kousuke

This paper presents a new unified analysis of estimate errors by model-matching phase-estimation methods such as rotor-flux state-observers, back EMF state-observers, and back EMF disturbance-observers, for sensorless drive of permanent-magnet synchronous motors. Analytical solutions about estimate errors, whose validity is confirmed by numerical experiments, are rich in universality and applicability. As an example of universality and applicability, a new trajectory-oriented vector control method is proposed, which can realize directly quasi-optimal strategy minimizing total losses with no additional computational loads by simply orienting one of vector-control coordinates to the associated quasi-optimal trajectory. The coordinate orientation rule, which is analytically derived, is surprisingly simple. Consequently the trajectory-oriented vector control method can be applied to a number of conventional vector control systems using one of the model-matching phase-estimation methods.

Interpolating moving least-squares methods for fitting potential energy surfaces: using classical trajectories to explore configuration space.

PubMed

Dawes, Richard; Passalacqua, Alessio; Wagner, Albert F; Sewell, Thomas D; Minkoff, Michael; Thompson, Donald L

2009-04-14

We develop two approaches for growing a fitted potential energy surface (PES) by the interpolating moving least-squares (IMLS) technique using classical trajectories. We illustrate both approaches by calculating nitrous acid (HONO) cis-->trans isomerization trajectories under the control of ab initio forces from low-level HF/cc-pVDZ electronic structure calculations. In this illustrative example, as few as 300 ab initio energy/gradient calculations are required to converge the isomerization rate constant at a fixed energy to approximately 10%. Neither approach requires any preliminary electronic structure calculations or initial approximate representation of the PES (beyond information required for trajectory initial conditions). Hessians are not required. Both approaches rely on the fitting error estimation properties of IMLS fits. The first approach, called IMLS-accelerated direct dynamics, propagates individual trajectories directly with no preliminary exploratory trajectories. The PES is grown "on the fly" with the computation of new ab initio data only when a fitting error estimate exceeds a prescribed tight tolerance. The second approach, called dynamics-driven IMLS fitting, uses relatively inexpensive exploratory trajectories to both determine and fit the dynamically accessible configuration space. Once exploratory trajectories no longer find configurations with fitting error estimates higher than the designated accuracy, the IMLS fit is considered to be complete and usable in classical trajectory calculations or other applications.

High-order space charge effects using automatic differentiation

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

Reusch, M.F.; Bruhwiler, D.L.

1997-02-01

The Northrop Grumman Topkark code has been upgraded to Fortran 90, making use of operator overloading, so the same code can be used to either track an array of particles or construct a Taylor map representation of the accelerator lattice. We review beam optics and beam dynamics simulations conducted with TOPKARK in the past and we present a new method for modeling space charge forces to high-order with automatic differentiation. This method generates an accurate, high-order, 6-D Taylor map of the phase space variable trajectories for a bunched, high-current beam. The spatial distribution is modeled as the product of amore » Taylor Series times a Gaussian. The variables in the argument of the Gaussian are normalized to the respective second moments of the distribution. This form allows for accurate representation of a wide range of realistic distributions, including any asymmetries, and allows for rapid calculation of the space charge fields with free space boundary conditions. An example problem is presented to illustrate our approach. {copyright} {ital 1997 American Institute of Physics.}« less

Quantum trajectory analysis of multimode subsystem-bath dynamics.

PubMed

Wyatt, Robert E; Na, Kyungsun

2002-01-01

The dynamics of a swarm of quantum trajectories is investigated for systems involving the interaction of an active mode (the subsystem) with an M-mode harmonic reservoir (the bath). Equations of motion for the position, velocity, and action function for elements of the probability fluid are integrated in the Lagrangian (moving with the fluid) picture of quantum hydrodynamics. These fluid elements are coupled through the Bohm quantum potential and as a result evolve as a correlated ensemble. Wave function synthesis along the trajectories permits an exact description of the quantum dynamics for the evolving probability fluid. The approach is fully quantum mechanical and does not involve classical or semiclassical approximations. Computational results are presented for three systems involving the interaction on an active mode with M=1, 10, and 15 bath modes. These results include configuration space trajectory evolution, flux analysis of the evolving ensemble, wave function synthesis along trajectories, and energy partitioning along specific trajectories. These results demonstrate the feasibility of using a small number of quantum trajectories to obtain accurate quantum results on some types of open quantum systems that are not amenable to standard quantum approaches involving basis set expansions or Eulerian space-fixed grids.

Integrated Simulation Design Challenges to Support TPS Repair Operations

NASA Technical Reports Server (NTRS)

Quiocho, Leslie J.; Crues, Edwin Z.; Huynh, An; Nguyen, Hung T.; MacLean, John

2005-01-01

During the Orbiter Repair Maneuver (ORM) operations planned for Return to Flight (RTF), the Shuttle Remote Manipulator System (SRMS) must grapple the International Space Station (ISS), undock the Orbiter, maneuver it through a long duration trajectory, and orient it to an EVA crewman poised at the end of the Space Station Remote Manipulator System (SSRMS) to facilitate the repair of the Thermal Protection System (TPS). Once repair has been completed and confirmed, then the SRMS proceeds back through the trajectory to dock the Orbiter to the Orbiter Docking System. In order to support analysis of the complex dynamic interactions of the integrated system formed by the Orbiter, ISS, SRMS, and SSRMS during the ORM, simulation tools used for previous 'nominal' mission support required substantial enhancements. These upgrades were necessary to provide analysts with the capabilities needed to study integrated system performance. This paper discusses the simulation design challenges encountered while developing simulation capabilities to mirror the ORM operations. The paper also describes the incremental build approach that was utilized, starting with the subsystem simulation elements and integration into increasing more complex simulations until the resulting ORM worksite dynamics simulation had been assembled. Furthermore, the paper presents an overall integrated simulation V&V methodology based upon a subsystem level testing, integrated comparisons, and phased checkout.

Simulating a topological transition in a superconducting phase qubit by fast adiabatic trajectories

NASA Astrophysics Data System (ADS)

Wang, Tenghui; Zhang, Zhenxing; Xiang, Liang; Gong, Zhihao; Wu, Jianlan; Yin, Yi

2018-04-01

The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The adiabatic trajectory of a quantum state describes the change of the bulk Bloch eigenstates with the momentum, and this adiabatic simulation method is however practically limited due to quantum dissipation. Here we apply the "shortcut to adiabaticity" (STA) protocol to realize fast adiabatic evolutions in the system of a superconducting phase qubit. The resulting fast adiabatic trajectories illustrate the change of the bulk Bloch eigenstates in the Su-Schrieffer-Heeger (SSH) model. A sharp transition is experimentally determined for the topological invariant of a winding number. Our experiment helps identify the topological Chern number of a two-dimensional toy model, suggesting the applicability of the fast adiabatic simulation method for topological systems.

Performance Analysis and Design Synthesis (PADS) computer program. Volume 1: Formulation

NASA Technical Reports Server (NTRS)

1972-01-01

The program formulation for PADS computer program is presented. It can size launch vehicles in conjunction with calculus-of-variations optimal trajectories and can also be used as a general-purpose branched trajectory optimization program. In the former use, it has the Space Shuttle Synthesis Program as well as a simplified stage weight module for optimally sizing manned recoverable launch vehicles. For trajectory optimization alone or with sizing, PADS has two trajectory modules. The first trajectory module uses the method of steepest descent; the second employs the method of quasilinearization, which requires a starting solution from the first trajectory module.

Operational Concept for Flight Crews to Participate in Merging and Spacing of Aircraft

NASA Technical Reports Server (NTRS)

Baxley, Brian T.; Barmore, Bryan E.; Abbott, Terence S.; Capron, William R.

2006-01-01

The predicted tripling of air traffic within the next 15 years is expected to cause significant aircraft delays and create a major financial burden for the airline industry unless the capacity of the National Airspace System can be increased. One approach to improve throughput and reduce delay is to develop new ground tools, airborne tools, and procedures to reduce the variance of aircraft delivery to the airport, thereby providing an increase in runway throughput capacity and a reduction in arrival aircraft delay. The first phase of the Merging and Spacing Concept employs a ground based tool used by Air Traffic Control that creates an arrival time to the runway threshold based on the aircraft s current position and speed, then makes minor adjustments to that schedule to accommodate runway throughput constraints such as weather and wake vortex separation criteria. The Merging and Spacing Concept also employs arrival routing that begins at an en route metering fix at altitude and continues to the runway threshold with defined lateral, vertical, and velocity criteria. This allows the desired spacing interval between aircraft at the runway to be translated back in time and space to the metering fix. The tool then calculates a specific speed for each aircraft to fly while enroute to the metering fix based on the adjusted land timing for that aircraft. This speed is data-linked to the crew who fly this speed, causing the aircraft to arrive at the metering fix with the assigned spacing interval behind the previous aircraft in the landing sequence. The second phase of the Merging and Spacing Concept increases the timing precision of the aircraft delivery to the runway threshold by having flight crews using an airborne system make minor speed changes during enroute, descent, and arrival phases of flight. These speed changes are based on broadcast aircraft state data to determine the difference between the actual and assigned time interval between the aircraft pair. The airborne software then calculates a speed adjustment to null that difference over the remaining flight trajectory. Follow-on phases still under development will expand the concept to all types of aircraft, arriving from any direction, merging at different fixes and altitudes, and to any airport. This paper describes the implementation phases of the Merging and Spacing Concept, and provides high-level results of research conducted to date.

Conditions for order and chaos in the dynamics of a trapped Bose-Einstein condensate in coordinate and energy space

NASA Astrophysics Data System (ADS)

Sakhel, Roger R.; Sakhel, Asaad R.; Ghassib, Humam B.; Balaz, Antun

2016-03-01

We investigate numerically conditions for order and chaos in the dynamics of an interacting Bose-Einstein condensate (BEC) confined by an external trap cut off by a hard-wall box potential. The BEC is stirred by a laser to induce excitations manifesting as irregular spatial and energy oscillations of the trapped cloud. Adding laser stirring to the external trap results in an effective time-varying trapping frequency in connection with the dynamically changing combined external+laser potential trap. The resulting dynamics are analyzed by plotting their trajectories in coordinate phase space and in energy space. The Lyapunov exponents are computed to confirm the existence of chaos in the latter space. Quantum effects and trap anharmonicity are demonstrated to generate chaos in energy space, thus confirming its presence and implicating either quantum effects or trap anharmonicity as its generator. The presence of chaos in energy space does not necessarily translate into chaos in coordinate space. In general, a dynamic trapping frequency is found to promote chaos in a trapped BEC. An apparent means to suppress chaos in a trapped BEC is achieved by increasing the characteristic scale of the external trap with respect to the condensate size.

Analyzing JAVAD TR-G2 GPS Receiver's Sensitivities to SLS Trajectory

NASA Technical Reports Server (NTRS)

Schuler, Tristan

2017-01-01

Automated guidance and navigation systems are an integral part to successful space missions. Previous researchers created Python tools to receive and parse data from a JAVAD TR-G2 space-capable GPS receiver. I improved the tool by customizing the output for plotting and comparing several simulations. I analyzed position errors, data loss, and signal loss by comparing simulated receiver data from an IFEN GPS simulator to ‘truth data’ from a proposed trajectory. By adjusting the trajectory simulation’s gain, attitude, and start time, NASA can assess the best time to launch the SLS, where to position the antennas on the Block 1-B, and which filter to use. Some additional testing has begun with the Novatel SpaceQuestGPS receiver as well as a GNSS SDR receiver.

Operational space trajectory tracking control of robot manipulators endowed with a primary controller of synthetic joint velocity.

PubMed

Moreno-Valenzuela, Javier; González-Hernández, Luis

2011-01-01

In this paper, a new control algorithm for operational space trajectory tracking control of robot arms is introduced. The new algorithm does not require velocity measurement and is based on (1) a primary controller which incorporates an algorithm to obtain synthesized velocity from joint position measurements and (2) a secondary controller which computes the desired joint acceleration and velocity required to achieve operational space motion control. The theory of singularly perturbed systems is crucial for the analysis of the closed-loop system trajectories. In addition, the practical viability of the proposed algorithm is explored through real-time experiments in a two degrees-of-freedom horizontal planar direct-drive arm. Copyright © 2010 ISA. Published by Elsevier Ltd. All rights reserved.

Trajectories of Identification Across Social Spaces: Intersections Between Home, School and Everyday Spaces

NASA Astrophysics Data System (ADS)

Fields, Deborah Anne

This is a theory-building study taking a wide-angled perspective on youths' development of trajectories of identification across social settings of their everyday lives. I investigated the relationships within and between trajectories of identification across the everyday lives of four youth, studying the conflicts, cohesion, and gaps in their trajectories of identification as they moved across and participated in multiple social settings. I asked how trajectories of identification were built across social settings (i.e. relationships within a trajectory of identification); what kinds of relationships existed between youths' trajectories of identification; and what facilitated the building of trajectories of identification across social settings. To study these questions, I argued for three interrelated lenses on identity: local acting and positioning in practice, the ways one thinks of oneself (self-narratives), and the ways that others think of one (others'-narratives). Using these lenses I shaped a connective ethnography studying four 11-12 year old youth across everyday settings including school, home, hobbies like sports and music, community organizations, and peer groups, following two youth for six months and two youth for one year. I analyzed findings across the four youth. The cases presented in this thesis demonstrate the ways that youth form identities through their travel and not just in a single setting. First, I found that youth build trajectories of identification across social settings and not just in a single setting. As learning is not just within a single mind, so is identity developed beyond a single space. Second, I demonstrated how multiple interacting trajectories of identification within a youth's life may shape each other in inclusive and exclusive ways. Third, throughout the cases I highlighted how traveling artifacts can support building trajectories of identification across social settings, including boundary objects, artifacts created by the youth, and succinct narratives. Their ability to travel depends on how well they encompass values of people from different social settings. In turn, the travel and influence of artifacts are strengthened by certification and brokering.

Definition of two-phase flow behaviors for spacecraft design

NASA Technical Reports Server (NTRS)

Reinarts, Thomas R.; Best, Frederick R.; Miller, Katherine M.; Hill, Wayne S.

1991-01-01

Two-phase flow, thermal management systems are currently being considered as an alternative to conventional, single phase systems for future space missions because of their potential to reduce overall system mass, size, and pumping power requirements. Knowledge of flow regime transitions, heat transfer characteristics, and pressure drop correlations is necessary to design and develop two-phase systems. A boiling and condensing experiment was built in which R-12 was used as the working fluid. A two-phase pump was used to circulate a freon mixture and allow separate measurements of the vapor and liquid flow streams. The experimental package was flown five times aboard the NASA KC-135 aircraft which simulates zero-g conditions by its parabolic flight trajectory. Test conditions included stratified and annual flow regimes in 1-g which became bubbly, slug, or annular flow regimes on 0-g. A portion of this work is the analysis of adiabatic flow regimes. The superficial velocities of liquid and vapor have been obtained from the measured flow rates and are presented along with the observed flow regimes.

Understanding the ion distributions near the boundaries of reconnection outflow region

NASA Astrophysics Data System (ADS)

Zhou, X.; Pan, D.; Angelopoulos, V.; Runov, A.; Zong, Q.; Pu, Z.

2016-12-01

An interesting signature observed shortly after the onset of magnetotail reconnection is the gradual appearance of a local peak of ion phase space density (PSD) in the duskward and downstream direction separated from the colder, nearly-isotropic ion population. Such characteristic ion distributions, well reproduced by a particle-tracing Liouville simulation, are found to appear only near the off-equatorial boundaries of the reconnection outflow region. Further analysis on ion trajectories suggests that the ions at the local peak and at the neighboring PSD cleft both belong to the outflowing population; they both meander across the neutral sheet to exhibit duskward velocities near the off-equatorial boundaries of their trajectories. The difference between them is that the local peak originates from ions previously constituting the pre-onset plasma sheet, whereas the cleft corresponds to the inflowing lobe ions before they are repelled in the downstream direction. As reconnection proceeds, the local PSD peak attenuates and then disappears, which indicates the eventual depletion of thermal ions in the pre-onset plasma sheet.

Advanced design for orbital debris removal in support of solar system exploration

NASA Technical Reports Server (NTRS)

1991-01-01

The development of an Autonomous Space Processor for Orbital Debris (ASPOD) is the ultimate goal. The craft will process, in situ, orbital debris using resources available in low Earth orbit (LEO). The serious problem of orbital debris is briefly described and the nature of the large debris population is outlined. This year, focus was on development of a versatile robotic manipulator to augment an existing robotic arm; incorporation of remote operation of robotic arms; and formulation of optimal (time and energy) trajectory planning algorithms for coordinating robotic arms. The mechanical design of the new arm is described in detail. The versatile work envelope is explained showing the flexibility of the new design. Several telemetry communication systems are described which will enable the remote operation of the robotic arms. The trajectory planning algorithms are fully developed for both the time-optimal and energy-optimal problem. The optimal problem is solved using phase plane techniques while the energy optimal problem is solved using dynamics programming.

PSA: A program to streamline orbit determination for launch support operations

NASA Technical Reports Server (NTRS)

Legerton, V. N.; Mottinger, N. A.

1988-01-01

An interactive, menu driven computer program was written to streamline the orbit determination process during the critical launch support phase of a mission. Residing on a virtual memory minicomputer, this program retains the quantities in-core needed to obtain a least squares estimate of the spacecraft trajectory with interactive displays to assist in rapid radio metric data evaluation. Menu-driven displays allow real time filter and data strategy development. Graphical and tabular displays can be sent to a laser printer for analysis without exiting the program. Products generated by this program feed back to the main orbit determination program in order to further refine the estimate of the trajectory. The final estimate provides a spacecraft ephemeris which is transmitted to the mission control center and used for antenna pointing and frequency predict generation by the Deep Space Network. The development and implementation process of this program differs from that used for most other navigation software by allowing the users to check important operating features during development and have changes made as needed.

Flight Evaluation of Center-TRACON Automation System Trajectory Prediction Process

NASA Technical Reports Server (NTRS)

Williams, David H.; Green, Steven M.

1998-01-01

Two flight experiments (Phase 1 in October 1992 and Phase 2 in September 1994) were conducted to evaluate the accuracy of the Center-TRACON Automation System (CTAS) trajectory prediction process. The Transport Systems Research Vehicle (TSRV) Boeing 737 based at Langley Research Center flew 57 arrival trajectories that included cruise and descent segments; at the same time, descent clearance advisories from CTAS were followed. Actual trajectories of the airplane were compared with the trajectories predicted by the CTAS trajectory synthesis algorithms and airplane Flight Management System (FMS). Trajectory prediction accuracy was evaluated over several levels of cockpit automation that ranged from a conventional cockpit to performance-based FMS vertical navigation (VNAV). Error sources and their magnitudes were identified and measured from the flight data. The major source of error during these tests was found to be the predicted winds aloft used by CTAS. The most significant effect related to flight guidance was the cross-track and turn-overshoot errors associated with conventional VOR guidance. FMS lateral navigation (LNAV) guidance significantly reduced both the cross-track and turn-overshoot error. Pilot procedures and VNAV guidance were found to significantly reduce the vertical profile errors associated with atmospheric and airplane performance model errors.

Transition paths of Met-enkephalin from Markov state modeling of a molecular dynamics trajectory.

PubMed

Banerjee, Rahul; Cukier, Robert I

2014-03-20

Conformational states and their interconversion pathways of the zwitterionic form of the pentapeptide Met-enkephalin (MetEnk) are identified. An explicit solvent molecular dynamics (MD) trajectory is used to construct a Markov state model (MSM) based on dihedral space clustering of the trajectory, and transition path theory (TPT) is applied to identify pathways between open and closed conformers. In the MD trajectory, only four of the eight backbone dihedrals exhibit bistable behavior. Defining a conformer as the string XXXX with X = "+" or "-" denoting, respectively, positive or negative values of a given dihedral angle and obtaining the populations of these conformers shows that only four conformers are highly populated, implying a strong correlation among these dihedrals. Clustering in dihedral space to construct the MSM finds the same four bistable dihedral angles. These state populations are very similar to those found directly from the MD trajectory. TPT is used to obtain pathways, parametrized by committor values, in dihedral state space that are followed in transitioning from closed to open states. Pathway costs are estimated by introducing a kinetics-based procedure that orders pathways from least (shortest) to greater cost paths. The least costly pathways in dihedral space are found to only involve the same XXXX set of dihedral angles, and the conformers accessed in the closed to open transition pathways are identified. For these major pathways, a correlation between reaction path progress (committors) and the end-to-end distance is identified. A dihedral space principal component analysis of the MD trajectory shows that the first three modes capture most of the overall fluctuation, and pick out the same four dihedrals having essentially all the weight in those modes. A MSM based on root-mean-square backbone clustering was also carried out, with good agreement found with dihedral clustering for the static information, but with results that differ significantly for the pathway analysis.

Quantum Dynamics with Short-Time Trajectories and Minimal Adaptive Basis Sets.

PubMed

Saller, Maximilian A C; Habershon, Scott

2017-07-11

Methods for solving the time-dependent Schrödinger equation via basis set expansion of the wave function can generally be categorized as having either static (time-independent) or dynamic (time-dependent) basis functions. We have recently introduced an alternative simulation approach which represents a middle road between these two extremes, employing dynamic (classical-like) trajectories to create a static basis set of Gaussian wavepackets in regions of phase-space relevant to future propagation of the wave function [J. Chem. Theory Comput., 11, 8 (2015)]. Here, we propose and test a modification of our methodology which aims to reduce the size of basis sets generated in our original scheme. In particular, we employ short-time classical trajectories to continuously generate new basis functions for short-time quantum propagation of the wave function; to avoid the continued growth of the basis set describing the time-dependent wave function, we employ Matching Pursuit to periodically minimize the number of basis functions required to accurately describe the wave function. Overall, this approach generates a basis set which is adapted to evolution of the wave function while also being as small as possible. In applications to challenging benchmark problems, namely a 4-dimensional model of photoexcited pyrazine and three different double-well tunnelling problems, we find that our new scheme enables accurate wave function propagation with basis sets which are around an order-of-magnitude smaller than our original trajectory-guided basis set methodology, highlighting the benefits of adaptive strategies for wave function propagation.

Association between mild cognitive impairment and trajectory-based spatial parameters during timed up and go test using a laser range sensor.

PubMed

Nishiguchi, Shu; Yorozu, Ayanori; Adachi, Daiki; Takahashi, Masaki; Aoyama, Tomoki

2017-08-08

The Timed Up and Go (TUG) test may be a useful tool to detect not only mobility impairment but also possible cognitive impairment. In this cross-sectional study, we used the TUG test to investigate the associations between trajectory-based spatial parameters measured by laser range sensor (LRS) and cognitive impairment in community-dwelling older adults. The participants were 63 community-dwelling older adults (mean age, 73.0 ± 6.3 years). The trajectory-based spatial parameters during the TUG test were measured using an LRS. In each forward and backward phase, we calculated the minimum distance from the marker, the maximum distance from the x-axis (center line), the length of the trajectories, and the area of region surrounded by the trajectory of the center of gravity and the x-axis (center line). We measured mild cognitive impairment using the Mini-Mental State Examination score (26/27 was the cut-off score for defining mild cognitive impairment). Compared with participants with normal cognitive function, those with mild cognitive impairment exhibited the following trajectory-based spatial parameters: short minimum distance from the marker (p = 0.044), narrow area of center of gravity in the forward phase (p = 0.012), and a large forward/whole phase ratio of the area of the center of gravity (p = 0.026) during the TUG test. In multivariate logistic regression analyses, a short minimum distance from the marker (odds ratio [OR]: 0.82, 95% confidence interval [CI]: 0.69-0.98), narrow area of the center of gravity in the forward phase (OR: 0.01, 95% CI: 0.00-0.36), and large forward/whole phase ratio of the area of the center of gravity (OR: 0.94, 95% CI: 0.88-0.99) were independently associated with mild cognitive impairment. In conclusion, our results indicate that some of the trajectory-based spatial parameters measured by LRS during the TUG test were independently associated with cognitive impairment in older adults. In particular, older adults with cognitive impairment exhibit shorter minimum distances from the marker and asymmetrical trajectories during the TUG test.

Note on the displacement of a trajectory of hyperbolic motion in curved space-time

NASA Astrophysics Data System (ADS)

Krikorian, R. A.

2012-04-01

The object of this note is to present a physical application of the theory of the infinitesimal deformations or displacements of curves developed by Yano using the concept of Lie derivative. It is shown that an infinitesimal point transformation which carries a given trajectory of hyperbolic motion into a trajectory of the same type, and preserves the affine parametrization of the trajectory, defines a homothetic motion.

Differential Optical Synthetic Aperture Radar

DOEpatents

Stappaerts, Eddy A.

2005-04-12

A new differential technique for forming optical images using a synthetic aperture is introduced. This differential technique utilizes a single aperture to obtain unique (N) phases that can be processed to produce a synthetic aperture image at points along a trajectory. This is accomplished by dividing the aperture into two equal "subapertures", each having a width that is less than the actual aperture, along the direction of flight. As the platform flies along a given trajectory, a source illuminates objects and the two subapertures are configured to collect return signals. The techniques of the invention is designed to cancel common-mode errors, trajectory deviations from a straight line, and laser phase noise to provide the set of resultant (N) phases that can produce an image having a spatial resolution corresponding to a synthetic aperture.

Broken-Plane Maneuver Applications for Earth to Mars Trajectories

NASA Technical Reports Server (NTRS)

Abilleira, Fernando

2007-01-01

Optimization techniques are critical when investigating Earth to Mars trajectories since they have the potential of reducing the total (delta)V of a mission. A deep space maneuver (DSM) executed during the cruise may improve a trajectory by reducing the total mission V. Nonetheless, DSMs not only may improve trajectory performance (from an energetic point of view) but also open up new families of trajectories that would satisfy very specific mission requirements not achievable with ballistic trajectories. In the following pages, various specific examples showing the potential advantages of the usage of broken plane maneuvers will be introduced. These examples correspond to possible scenarios for Earth to Mars trajectories during the next decade (2010-2020).

Romantic Relationships Trajectories of African American Gay/Bisexual Adolescents

ERIC Educational Resources Information Center

Eyre, Stephen L.; Milbrath, Constance; Peacock, Ben

2007-01-01

The interview study reported here sought to identify the perceived trajectory of romantic relationships of a cohort of Oakland African American gay/bisexual adolescents. Biographical interviews were used to identify cultural models of romantic relationships in the study sample and discovered a trajectory of four phases. In the antecedent to the…

Minimum Hamiltonian Ascent Trajectory Evaluation (MASTRE) program (update to automatic flight trajectory design, performance prediction, and vehicle sizing for support of Shuttle and Shuttle derived vehicles) engineering manual

NASA Technical Reports Server (NTRS)

Lyons, J. T.

1993-01-01

The Minimum Hamiltonian Ascent Trajectory Evaluation (MASTRE) program and its predecessors, the ROBOT and the RAGMOP programs, have had a long history of supporting MSFC in the simulation of space boosters for the purpose of performance evaluation. The ROBOT program was used in the simulation of the Saturn 1B and Saturn 5 vehicles in the 1960's and provided the first utilization of the minimum Hamiltonian (or min-H) methodology and the steepest ascent technique to solve the optimum trajectory problem. The advent of the Space Shuttle in the 1970's and its complex airplane design required a redesign of the trajectory simulation code since aerodynamic flight and controllability were required for proper simulation. The RAGMOP program was the first attempt to incorporate the complex equations of the Space Shuttle into an optimization tool by using an optimization method based on steepest ascent techniques (but without the min-H methodology). Development of the complex partial derivatives associated with the Space Shuttle configuration and using techniques from the RAGMOP program, the ROBOT program was redesigned to incorporate these additional complexities. This redesign created the MASTRE program, which was referred to as the Minimum Hamiltonian Ascent Shuttle TRajectory Evaluation program at that time. Unique to this program were first-stage (or booster) nonlinear aerodynamics, upper-stage linear aerodynamics, engine control via moment balance, liquid and solid thrust forces, variable liquid throttling to maintain constant acceleration limits, and a total upgrade of the equations used in the forward and backward integration segments of the program. This modification of the MASTRE code has been used to simulate the new space vehicles associated with the National Launch Systems (NLS). Although not as complicated as the Space Shuttle, the simulation and analysis of the NLS vehicles required additional modifications to the MASTRE program in the areas of providing additional flexibility in the use of the program, allowing additional optimization options, and providing special options for the NLS configuration.

Improved UTE-based attenuation correction for cranial PET-MR using dynamic magnetic field monitoring

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

Aitken, A. P.; Giese, D.; Tsoumpas, C.

2014-01-15

Purpose: Ultrashort echo time (UTE) MRI has been proposed as a way to produce segmented attenuation maps for PET, as it provides contrast between bone, air, and soft tissue. However, UTE sequences require samples to be acquired during rapidly changing gradient fields, which makes the resulting images prone to eddy current artifacts. In this work it is demonstrated that this can lead to misclassification of tissues in segmented attenuation maps (AC maps) and that these effects can be corrected for by measuring the true k-space trajectories using a magnetic field camera. Methods: The k-space trajectories during a dual echo UTEmore » sequence were measured using a dynamic magnetic field camera. UTE images were reconstructed using nominal trajectories and again using the measured trajectories. A numerical phantom was used to demonstrate the effect of reconstructing with incorrect trajectories. Images of an ovine leg phantom were reconstructed and segmented and the resulting attenuation maps were compared to a segmented map derived from a CT scan of the same phantom, using the Dice similarity measure. The feasibility of the proposed method was demonstrated inin vivo cranial imaging in five healthy volunteers. Simulated PET data were generated for one volunteer to show the impact of misclassifications on the PET reconstruction. Results: Images of the numerical phantom exhibited blurring and edge artifacts on the bone–tissue and air–tissue interfaces when nominal k-space trajectories were used, leading to misclassification of soft tissue as bone and misclassification of bone as air. Images of the tissue phantom and thein vivo cranial images exhibited the same artifacts. The artifacts were greatly reduced when the measured trajectories were used. For the tissue phantom, the Dice coefficient for bone in MR relative to CT was 0.616 using the nominal trajectories and 0.814 using the measured trajectories. The Dice coefficients for soft tissue were 0.933 and 0.934 for the nominal and measured cases, respectively. For air the corresponding figures were 0.991 and 0.993. Compared to an unattenuated reference image, the mean error in simulated PET uptake in the brain was 9.16% when AC maps derived from nominal trajectories was used, with errors in the SUV{sub max} for simulated lesions in the range of 7.17%–12.19%. Corresponding figures when AC maps derived from measured trajectories were used were 0.34% (mean error) and −0.21% to +1.81% (lesions). Conclusions: Eddy current artifacts in UTE imaging can be corrected for by measuring the true k-space trajectories during a calibration scan and using them in subsequent image reconstructions. This improves the accuracy of segmented PET attenuation maps derived from UTE sequences and subsequent PET reconstruction.« less

Asteroids as Propulsion Systems of Space Ships

NASA Technical Reports Server (NTRS)

Bolonkin, Alexander

2003-01-01

Currently, rockets are used to change the trajectory of space ships and probes. This method is very expensive and requires a lot of fuel, which limits the feasibility of space stations, interplanetary space ships, and probes. Sometimes space probes use the gravity field of a planet However, there am only nine planets in the Solar System, all separated by great distances. There are tons of millions of asteroids in outer space. This paper offers a revolutionary method for changing the trajectory of space probes. The method uses the kinetic or rotary energy of asteroids, comet nuclei, meteorites or other space bodies (small planets, natural planetary satellites, space debris, etc.) to increase (to decrease) ship (probe) speed up to 1000 m/sec (or more) and to achieve any new direction in outer space. The flight possibilities of space ships and probes are increased by a factor of millions.

High Efficiency Multi-shot Interleaved Spiral-In/Out Acquisition for High Resolution BOLD fMRI

PubMed Central

Jung, Youngkyoo; Samsonov, Alexey A.; Liu, Thomas T.; Buracas, Giedrius T.

2012-01-01

Growing demand for high spatial resolution BOLD functional MRI faces a challenge of the spatial resolution vs. coverage or temporal resolution tradeoff, which can be addressed by methods that afford increased acquisition efficiency. Spiral acquisition trajectories have been shown to be superior to currently prevalent echo-planar imaging in terms of acquisition efficiency, and high spatial resolution can be achieved by employing multiple-shot spiral acquisition. The interleaved spiral in-out trajectory is preferred over spiral-in due to increased BOLD signal CNR and higher acquisition efficiency than that of spiral-out or non-interleaved spiral in/out trajectories (1), but to date applicability of the multi-shot interleaved spiral in-out for high spatial resolution imaging has not been studied. Herein we propose multi-shot interleaved spiral in-out acquisition and investigate its applicability for high spatial resolution BOLD fMRI. Images reconstructed from interleaved spiral-in and -out trajectories possess artifacts caused by differences in T2* decay, off-resonance and k-space errors associated with the two trajectories. We analyze the associated errors and demonstrate that application of conjugate phase reconstruction and spectral filtering can substantially mitigate these image artifacts. After applying these processing steps, the multishot interleaved spiral in-out pulse sequence yields high BOLD CNR images at in-plane resolution below 1x1 mm while preserving acceptable temporal resolution (4 s) and brain coverage (15 slices of 2 mm thickness). Moreover, this method yields sufficient BOLD CNR at 1.5 mm isotropic resolution for detection of activation in hippocampus associated with cognitive tasks (Stern memory task). The multi-shot interleaved spiral in-out acquisition is a promising technique for high spatial resolution BOLD fMRI applications. PMID:23023395

Trajectory-based heating analysis for the European Space Agency/Rosetta Earth Return Vehicle

NASA Technical Reports Server (NTRS)

Henline, William D.; Tauber, Michael E.

1994-01-01

A coupled, trajectory-based flowfield and material thermal-response analysis is presented for the European Space Agency proposed Rosetta comet nucleus sample return vehicle. The probe returns to earth along a hyperbolic trajectory with an entry velocity of 16.5 km/s and requires an ablative heat shield on the forebody. Combined radiative and convective ablating flowfield analyses were performed for the significant heating portion of the shallow ballistic entry trajectory. Both quasisteady ablation and fully transient analyses were performed for a heat shield composed of carbon-phenolic ablative material. Quasisteady analysis was performed using the two-dimensional axisymmetric codes RASLE and BLIMPK. Transient computational results were obtained from the one-dimensional ablation/conduction code CMA. Results are presented for heating, temperature, and ablation rate distributions over the probe forebody for various trajectory points. Comparison of transient and quasisteady results indicates that, for the heating pulse encountered by this probe, the quasisteady approach is conservative from the standpoint of predicted surface recession.

Optimal design of near-Earth asteroid sample-return trajectories in the Sun-Earth-Moon system

NASA Astrophysics Data System (ADS)

He, Shengmao; Zhu, Zhengfan; Peng, Chao; Ma, Jian; Zhu, Xiaolong; Gao, Yang

2016-08-01

In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi-body dynamics, considering the gravitational forces of the Sun, Earth, and Moon. It is proposed that an electric-propulsion spacecraft initially parking in a circular 200-km-altitude low Earth orbit is expected to rendezvous with an asteroid and carry as much sample as possible back to the Earth in a 10-year time frame. The team from the Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences has reported a solution with an asteroid sample mass of 328 tons, which is ranked first in the competition. In this article, we will present our design and optimization methods, primarily including overall analysis, target selection, escape from and capture by the Earth-Moon system, and optimization of impulsive and low-thrust trajectories that are modeled in multi-body dynamics. The orbital resonance concept and lunar gravity assists are considered key techniques employed for trajectory design. The reported solution, preliminarily revealing the feasibility of returning a hundreds-of-tons asteroid or asteroid sample, envisions future space missions relating to near-Earth asteroid exploration.

Effects of space weather on the ionosphere and LEO satellites' orbital trajectory in equatorial, low and middle latitude

NASA Astrophysics Data System (ADS)

Nwankwo, Victor U. J.; Chakrabarti, Sandip K.

2018-04-01

We study the effects of space weather on the ionosphere and low Earth orbit (LEO) satellites' orbital trajectory in equatorial, low- and mid-latitude (EQL, LLT and MLT) regions during (and around) the notable storms of October/November, 2003. We briefly review space weather effects on the thermosphere and ionosphere to demonstrate that such effects are also latitude-dependent and well established. Following the review we simulate the trend in variation of satellite's orbital radius (r), mean height (h) and orbit decay rate (ODR) during 15 October-14 November 2003 in EQL, LLT and MLT. Nominal atmospheric drag on LEO satellite is usually enhanced by space weather or solar-induced variations in thermospheric temperature and density profile. To separate nominal orbit decay from solar-induced accelerated orbit decay, we compute r, h and ODR in three regimes viz. (i) excluding solar indices (or effect), where r =r0, h =h0 and ODR =ODR0 (ii) with mean value of solar indices for the interval, where r =rm, h =hm and ODR =ODRm and (iii) with actual daily values of solar indices for the interval (r, h and ODR). For a typical LEO satellite at h = 450 km, we show that the total decay in r during the period is about 4.20 km, 3.90 km and 3.20 km in EQL, LLT and MLT respectively; the respective nominal decay (r0) is 0.40 km, 0.34 km and 0.22 km, while solar-induced orbital decay (rm) is about 3.80 km, 3.55 km and 2.95 km. h also varied in like manner. The respective nominal ODR0 is about 13.5 m/day, 11.2 m/day and 7.2 m/day, while solar-induced ODRm is about 124.3 m/day, 116.9 m/day and 97.3 m/day. We also show that severe geomagnetic storms can increase ODR by up to 117% (from daily mean value). However, the extent of space weather effects on LEO Satellite's trajectory significantly depends on the ballistic co-efficient and orbit of the satellite, and phase of solar cycles, intensity and duration of driving (or influencing) solar event.

Improved Propulsion Modeling for Low-Thrust Trajectory Optimization

NASA Technical Reports Server (NTRS)

Knittel, Jeremy M.; Englander, Jacob A.; Ozimek, Martin T.; Atchison, Justin A.; Gould, Julian J.

2017-01-01

Low-thrust trajectory design is tightly coupled with spacecraft systems design. In particular, the propulsion and power characteristics of a low-thrust spacecraft are major drivers in the design of the optimal trajectory. Accurate modeling of the power and propulsion behavior is essential for meaningful low-thrust trajectory optimization. In this work, we discuss new techniques to improve the accuracy of propulsion modeling in low-thrust trajectory optimization while maintaining the smooth derivatives that are necessary for a gradient-based optimizer. The resulting model is significantly more realistic than the industry standard and performs well inside an optimizer. A variety of deep-space trajectory examples are presented.

Employment of Asteroids for Movement Space Ship and Probes

NASA Technical Reports Server (NTRS)

Bolonkin, Alexander

2002-01-01

At present, rockets are used to change the trajectory of space ships and probes. This method is very expensive and requires a lot of fuel, which limits the feasibility of space stations, interplanetary space ships, and probes. Sometimes space probes use the gravity field of a planet. However, there are only 9 planets in our solar system and they are separated by great distances. There are tens of millions of asteroids in outer space. The author offers a revolutionary method for changing the trajectory of space probes. This method uses the kinetic or rotary energy of asteroids, meteorites or other space bodies (small planets, natural planet satellites, etc.). to increase (to decrease) ship (probe) speed up to 1000 m/sec (or more) and to get any new direction in outer space. The flight possibilities of space ships and probes are increased by a factor of millions.

Enabling Science and Deep Space Exploration through Space Launch System (LSL) Secondary Payload Opportunities

NASA Technical Reports Server (NTRS)

Singer, Jody; Pelfrey, Joseph; Norris, George

2016-01-01

For the first time in almost 40 years, a NASA human-rated launch vehicle has completed its Critical Design Review (CDR). By reaching this milestone, NASA's Space Launch System (SLS) and Orion spacecraft are on the path to launch a new era of deep space exploration. NASA is making investments to expand science and exploration capability of the SLS by developing the capability to deploy small satellites during the trans-lunar phase of the mission trajectory. Exploration Mission 1 (EM-1), currently planned for launch no earlier than July 2018, will be the first mission to carry such payloads on the SLS. The EM-1 launch will include thirteen 6U Cubesat small satellites that will be deployed beyond low earth orbit. By providing an earth-escape trajectory, opportunities are created for advancement of small satellite subsystems, including deep space communications and in-space propulsion. This SLS capability also creates low-cost options for addressing existing Agency strategic knowledge gaps and affordable science missions. A new approach to payload integration and mission assurance is needed to ensure safety of the vehicle, while also maintaining reasonable costs for the small payload developer teams. SLS EM-1 will provide the framework and serve as a test flight, not only for vehicle systems, but also payload accommodations, ground processing, and on-orbit operations. Through developing the requirements and integration processes for EM-1, NASA is outlining the framework for the evolved configuration of secondary payloads on SLS Block upgrades. The lessons learned from the EM-1 mission will be applied to processes and products developed for future block upgrades. In the heavy-lift configuration of SLS, payload accommodations will increase for secondary opportunities including small satellites larger than the traditional Cubesat class payload. The payload mission concept of operations, proposed payload capacity of SLS, and the payload requirements for launch and deployment will be described to provide potential payload users an understanding of this unique exploration capability.

Interaction of the body, head, and eyes during walking and turning

NASA Technical Reports Server (NTRS)

Imai, T.; Moore, S. T.; Raphan, T.; Cohen, B.

2001-01-01

Body, head, and eye movements were measured in five subjects during straight walking and while turning corners. The purpose was to determine how well the head and eyes followed the linear trajectory of the body in space and whether head orientation followed changes in the gravito-inertial acceleration vector (GIA). Head and body movements were measured with a video-based motion analysis system and horizontal, vertical, and torsional eye movements with video-oculography. During straight walking, there was lateral body motion at the stride frequency, which was at half the frequency of stepping. The GIA oscillated about the direction of heading, according to the acceleration and deceleration associated with heel strike and toe flexion, and the body yawed in concert with stepping. Despite the linear and rotatory motions of the head and body, the head pointed along the forward motion of the body during straight walking. The head pitch/roll component appeared to compensate for vertical and horizontal acceleration of the head rather than orienting to the tilt of the GIA or anticipating it. When turning corners, subjects walked on a 50-cm radius over two steps or on a 200-cm radius in five to seven steps. Maximum centripetal accelerations in sharp turns were ca.0.4 g, which tilted the GIA ca.21 degrees with regard to the heading. This was anticipated by a roll tilt of the head of up to 8 degrees. The eyes rolled 1-1.5 degrees and moved down into the direction of linear acceleration during the tilts of the GIA. Yaw head deviations moved smoothly through the turn, anticipating the shift in lateral body trajectory by as much as 25 degrees. The trunk did not anticipate the change in trajectory. Thus, in contrast to straight walking, the tilt axes of the head and the GIA tended to align during turns. Gaze was stable in space during the slow phases and jumped forward in saccades along the trajectory, leading it by larger angles when the angular velocity of turning was greater. The anticipatory roll head movements during turning are likely to be utilized to overcome inertial forces that would destabilize balance during turning. The data show that compensatory eye, head, and body movements stabilize gaze during straight walking, while orienting mechanisms direct the eyes, head, and body to tilts of the GIA in space during turning.

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.

Galileo 1989 VEEGA trajectory design. [Venus-Earth-Earth-Gravity-Assist

NASA Technical Reports Server (NTRS)

D'Amario, Louis A.; Byrnes, Dennis V.; Johannesen, Jennie R.; Nolan, Brian G.

1989-01-01

The new baseline for the Galileo Mission is a 1989 Venus-earth-earth gravity-assist (VEEGA) trajectory, which utilizes three gravity-assist planetary flybys in order to reduce launch energy requirements significantly compared to other earth-Jupiter transfer modes. The launch period occurs during October-November 1989. The total flight time is about 6 years, with November 1995 as the most likely choice for arrival at Jupiter. Optimal 1989 VEEGA trajectories have been generated for a wide range of earth launch dates and Jupiter arrival dates. Launch/arrival space contour plots are presented for various trajectory parameters, including propellant margin, which is used to measure mission performance. The accessible region of the launch/arrival space is defined by propellant margin and launch energy constraints; the available launch period is approximately 1.5 months long.