Experimental Control of Simple Pendulum Model

ERIC Educational Resources Information Center

Medina, C.

2004-01-01

This paper conveys information about a Physics laboratory experiment for students with some theoretical knowledge about oscillatory motion. Students construct a simple pendulum that behaves as an ideal one, and analyze model assumption incidence on its period. The following aspects are quantitatively analyzed: vanishing friction, small amplitude,…

Development of surface friction guidelines for LADOTD : tech summary.

DOT National Transportation Integrated Search

2012-04-01

The current Louisiana Department of Transportation and Development (LADOTD) surface friction guidelines deal with the polished : stone values (PSV) of coarse aggregates (which is a relative British Pendulum skid-resistance number measured on polished...

Seismic analysis of a LNG storage tank isolated by a multiple friction pendulum system

NASA Astrophysics Data System (ADS)

Zhang, Ruifu; Weng, Dagen; Ren, Xiaosong

2011-06-01

The seismic response of an isolated vertical, cylindrical, extra-large liquefied natural gas (LNG) tank by a multiple friction pendulum system (MFPS) is analyzed. Most of the extra-large LNG tanks have a fundamental frequency which involves a range of resonance of most earthquake ground motions. It is an effective way to decrease the response of an isolation system used for extra-large LNG storage tanks under a strong earthquake. However, it is difficult to implement in practice with common isolation bearings due to issues such as low temperature, soft site and other severe environment factors. The extra-large LNG tank isolated by a MFPS is presented in this study to address these problems. A MFPS is appropriate for large displacements induced by earthquakes with long predominant periods. A simplified finite element model by Malhotra and Dunkerley is used to determine the usefulness of the isolation system. Data reported and statistically sorted include pile shear, wave height, impulsive acceleration, convective acceleration and outer tank acceleration. The results show that the isolation system has excellent adaptability for different liquid levels and is very effective in controlling the seismic response of extra-large LNG tanks.

Development of surface friction guidelines for LADOTD : research project capsule.

DOT National Transportation Integrated Search

2011-02-01

The current friction guideline of the Louisiana Department of : Transportation and Development (LADOTD) for a wearing course mixture : design deals with the polished stone value (PSV) of coarse aggregate : (which is a relative British Pendulum skid-r...

An inexpensive, multipurpose physical pendulum

NASA Astrophysics Data System (ADS)

Schultz, David

2012-10-01

The pendulum is a highly versatile tool for teaching physics. Many special purpose pendula for student experiments have been described.1-4 In this paper, I describe an inexpensive, multipurpose physical pendulum that can function as both a variable gravity and ballistic pendulum. I designed the apparatus for use in a rotational dynamics unit of the AP Physics C mechanics course. The use of a bike wheel hub pivot allows for low-friction, rugged operation that yields results commensurate with those obtained with much more expensive pendula available on the market (typically 500 per unit5), placing these types of experiments within reach of the teacher on a restricted budget.

Coupled oscillators in identification of nonlinear damping of a real parametric pendulum

NASA Astrophysics Data System (ADS)

Olejnik, Paweł; Awrejcewicz, Jan

2018-01-01

A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.

Some new evidence on human joint lubrication.

PubMed Central

Unsworth, A; Dowson, D; Wright, V

1975-01-01

Theoretical consideration has been given to the use of pendulum machines which are used to examine the frictional properties of human joints by incorporating them as fulcra. As a result, a new type of pendulum machine has been built which incorporates the facility to apply sudden loads to the joint on starting the swinging motion, and also the ability to measure directly the frictional torque experienced by the joint. The results obtained from natural hip joints indicate the presence of squeeze film lubrication under conditions of sudden loading of a joint. In addition, a self-generated fluid film process was observed at low loads while at higher loads boundary lubrication appeared to be important. These results have been used to describe the lubrication regimens occurring in a normal activity such as walking. A single experiment carried out on a hip from a patient suffering from severe rheumatoid arthritis has also been reported and the frictional resistance was seen to be increased fifteenfold compared to a normal hip. Images PMID:1190847

Performance of Single Friction Pendulum bearing for isolated buildings subjected to seismic actions in Vietnam

NASA Astrophysics Data System (ADS)

Nguyen, N. V.; Nguyen, C. H.; Hoang, H. P.; Huong, K. T.

2018-04-01

Using structural control technology in earthquake resistant design of buildings in Vietnam is very limited. In this paper, a performance evaluation of using Single Friction Pendulum (SFP) bearing for seismically isolated buildings with earthquake conditions in Vietnam is presented. A two-dimensional (2-D) model of the 5-storey building subjected to earthquakes is analyzed in time domain. Accordingly, the model is analyzed for 2 cases: with and without SFP bearing. The ground acceleration data is selected and scaled to suit the design acceleration in Hanoi followed by the Standard TCVN 9386:2012. It is shown that the seismically isolated buildings gets the performance objectives while achieving an 91% reduction in the base shear, a significant decrease in the inter-story drift and absolute acceleration of each story.

Intelligent clutch control with incremental encoder to improve wear issues of an intercept pendulum in real time

NASA Astrophysics Data System (ADS)

Jalba, C. K.; Diekmann, R.; Epple, S.

2017-01-01

A pendulum impact tester is a technical device which is used to perform plasticity characterizations of metallic materials. Results are calculated based on fracture behavior under pendulum impact loadings according to DIN 50115, DIN 51222/EN 10045. The material is held at the two ends and gets struck in the middle. A mechanical Problem occurs when testing materials with a very high impact toughness. These specimen often do not break when hit by the pendulum. To return the pendulum to its initial position, the operator presses a service button. After a delay of approximately 2 seconds a clutch is activated which connects the arm of the pendulum with an electric motor to return it back upright in start position. At the moment of clutch activation, the pendulum can still swing or bounce with any speed in any direction at any different position. Due to the lack of synchronization between pendulum speed and constant engine speed, the clutch suffers heavy wear of friction. This disadvantage results in considerable service and repair costs for the customer. As a solution to this problem this article presents a customized technical device to significantly increase the lifetime of the clutch. It was accomplished by a precisely controlled activation of the clutch at a point of time when pendulum and motor are at synchronized speed and direction using incremental encoders.

Thrust Stand for Vertically Oriented Electric Propulsion Performance Evaluation

NASA Technical Reports Server (NTRS)

Moeller, Trevor; Polzin, Kurt A.

2010-01-01

A variation of a hanging pendulum thrust stand capable of measuring the performance of an electric thruster operating in the vertical orientation is presented. The vertical orientation of the thruster dictates that the thruster must be horizontally offset from the pendulum pivot arm, necessitating the use of a counterweight system to provide a neutrally-stable system. Motion of the pendulum arm is transferred through a balance mechanism to a secondary arm on which deflection is measured. A non-contact light-based transducer is used to measure displacement of the secondary beam. The members experience very little friction, rotating on twisting torsional pivots with oscillatory motion attenuated by a passive, eddy current damper. Displacement is calibrated using an in situ thrust calibration system. Thermal management and self-leveling systems are incorporated to mitigate thermal and mechanical drifts. Gravitational restoring force and torsional spring constants associated with flexure pivots provide restoring moments. An analysis of the design indicates that the thrust measurement range spans roughly four decades, with the stand capable of measuring thrust up to 12 N for a 200 kg thruster and up to approximately 800 mN for a 10 kg thruster. Data obtained from calibration tests performed using a 26.8 lbm simulated thruster indicated a resolution of 1 mN on 100 mN-level thrusts, while those tests conducted on 200 lbm thruster yielded a resolution of roughly 2.5 micro at thrust levels of 0.5 N and greater.

Thrust stand for vertically oriented electric propulsion performance evaluation

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

Moeller, Trevor; Polzin, Kurt A.

A variation of a hanging pendulum thrust stand capable of measuring the performance of an electric thruster operating in the vertical orientation is presented. The vertical orientation of the thruster dictates that the thruster must be horizontally offset from the pendulum pivot arm, necessitating the use of a counterweight system to provide a neutrally stable system. Motion of the pendulum arm is transferred through a balance mechanism to a secondary arm on which deflection is measured. A noncontact light-based transducer is used to measure displacement of the secondary beam. The members experience very little friction, rotating on twisting torsional pivotsmore » with oscillatory motion attenuated by a passive, eddy-current damper. Displacement is calibrated using an in situ thrust calibration system. Thermal management and self-leveling systems are incorporated to mitigate thermal and mechanical drifts. Gravitational force and torsional spring constants associated with flexure pivots provide restoring moments. An analysis of the design indicates that the thrust measurement range spans roughly four decades, with the stand capable of measuring thrust up to 12 N for a 200 kg thruster and up to approximately 800 mN for a 10 kg thruster. Data obtained from calibration tests performed using a 26.8 lbm simulated thruster indicated a resolution of 1 mN on 100 mN level thrusts, while those tests conducted on a 200 lbm thruster yielded a resolution of roughly 2.5 mN at thrust levels of 0.5 N and greater.« less

Characterization of calculus migration during Ho:YAG laser lithotripsy by high speed camera using suspended pendulum method

NASA Astrophysics Data System (ADS)

Zhang, Jian James; Rajabhandharaks, Danop; Xuan, Jason Rongwei; Chia, Ray W. J.; Hasenberg, Tom

2014-03-01

Calculus migration is a common problem during ureteroscopic laser lithotripsy procedure to treat urolithiasis. A conventional experimental method to characterize calculus migration utilized a hosting container (e.g. a "V" grove or a test tube). These methods, however, demonstrated large variation and poor detectability, possibly attributing to friction between the calculus and the container on which the calculus was situated. In this study, calculus migration was investigated using a pendulum model suspended under water to eliminate the aforementioned friction. A high speed camera was used to study the movement of the calculus which covered zero order (displacement), 1st order (speed) and 2nd order (acceleration). A commercialized, pulsed Ho:YAG laser at 2.1 um, 365-um core fiber, and calculus phantom (Plaster of Paris, 10×10×10mm cube) were utilized to mimic laser lithotripsy procedure. The phantom was hung on a stainless steel bar and irradiated by the laser at 0.5, 1.0 and 1.5J energy per pulse at 10Hz for 1 second (i.e., 5, 10, and 15W). Movement of the phantom was recorded by a high-speed camera with a frame rate of 10,000 FPS. Maximum displacement was 1.25+/-0.10, 3.01+/-0.52, and 4.37+/-0.58 mm for 0.5, 1, and 1.5J energy per pulse, respectively. Using the same laser power, the conventional method showed <0.5 mm total displacement. When reducing the phantom size to 5×5×5mm (1/8 in volume), the displacement was very inconsistent. The results suggested that using the pendulum model to eliminate the friction improved sensitivity and repeatability of the experiment. Detailed investigation on calculus movement and other causes of experimental variation will be conducted as a future study.

Oblique impact and friction of HMX and/or TATB-based PBXs

NASA Astrophysics Data System (ADS)

Picart, Didier; Junqua-Moullet, Alexandra

2017-06-01

Transportation, handling, vibrations can lead to moderate compressive but dynamic loadings requiring the characterization of the safety of PBXs submitted to such scenarios. Knowing that ignition can occur at a lower critical height during a fall on an inclined surface than a normal impact, the attention is focused in this paper on the heating due to the friction between PBXs and surfaces. A lot of experiments have been made using free-falling samples in vertical drop configurations on inclined targets or pendulum (skid) drop configurations (Green et al. 1971; Randolph et al. 1976). Data obtained on our HMX and/or TATB-based plastic-bonded explosives using pendulum drop configurations will be detailed. Evaluation of the heating due to friction requires the determination of the tangential projectile/target relative displacement and the contact pressure. The pressure is related to the normal force during the impact and the evolving contact surface, the latter being evaluated using a series of normal impacts. The aim of our paper is to compare the experimental diameter of the contact zones to (i) the classical Hertz's theory of contacting elastic solids and (ii) a spring-mass description of the impact. Data and models are then used to evaluate the increase of the temperature at the projectile/target interface for our explosives. We highlight the experimental bias which has already been attributed to the grits used to mimic the roughness of the surfaces.

An in vitro simulation method for the tribological assessment of complete natural hip joints

PubMed Central

Fisher, John; Williams, Sophie

2017-01-01

The use of hip joint simulators to evaluate the tribological performance of total hip replacements is widely reported in the literature, however, in vitro simulation studies investigating the tribology of the natural hip joint are limited with heterogeneous methodologies reported. An in vitro simulation system for the complete natural hip joint, enabling the acetabulum and femoral head to be positioned with different orientations whilst maintaining the correct joint centre of rotation, was successfully developed for this study. The efficacy of the simulation system was assessed by testing complete, matched natural porcine hip joints and porcine hip hemiarthroplasty joints in a pendulum friction simulator. The results showed evidence of biphasic lubrication, with a non-linear increase in friction being observed in both groups. Lower overall mean friction factor values in the complete natural joint group that increased at a lower rate over time, suggest that the exudation of fluid and transition to solid phase lubrication occurred more slowly in the complete natural hip joint compared to the hip hemiarthroplasty joint. It is envisaged that this methodology will be used to investigate morphological risk factors for developing hip osteoarthritis, as well as the effectiveness of early interventional treatments for degenerative hip disease. PMID:28886084

Nonlinear analysis of r.c. framed buildings retrofitted with elastomeric and friction bearings under near-fault earthquakes

NASA Astrophysics Data System (ADS)

Mazza, Mirko

2015-12-01

Reinforced concrete (r.c.) framed buildings designed in compliance with inadequate seismic classifications and code provisions present in many cases a high vulnerability and need to be retrofitted. To this end, the insertion of a base isolation system allows a considerable reduction of the seismic loads transmitted to the superstructure. However, strong near-fault ground motions, which are characterised by long-duration horizontal pulses, may amplify the inelastic response of the superstructure and induce a failure of the isolation system. The above considerations point out the importance of checking the effectiveness of different isolation systems for retrofitting a r.c. framed structure. For this purpose, a numerical investigation is carried out with reference to a six-storey r.c. framed building, which, primarily designed (as to be a fixed-base one) in compliance with the previous Italian code (DM96) for a medium-risk seismic zone, has to be retrofitted by insertion of an isolation system at the base for attaining performance levels imposed by the current Italian code (NTC08) in a high-risk seismic zone. Besides the (fixed-base) original structure, three cases of base isolation are studied: elastomeric bearings acting alone (e.g. HDLRBs); in-parallel combination of elastomeric and friction bearings (e.g. high-damping-laminated-rubber bearings, HDLRBs and steel-PTFE sliding bearings, SBs); friction bearings acting alone (e.g. friction pendulum bearings, FPBs). The nonlinear analysis of the fixed-base and base-isolated structures subjected to horizontal components of near-fault ground motions is performed for checking plastic conditions at the potential critical (end) sections of the girders and columns as well as critical conditions of the isolation systems. Unexpected high values of ductility demand are highlighted at the lower floors of all base-isolated structures, while re-centring problems of the base isolation systems under near-fault earthquakes are expected in case of friction bearings acting alone (i.e. FPBs) or that in combination (i.e. SBs) with HDLRBs.

Complex pendulum biomass sensor

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

Hoskinson, Reed L.; Kenney, Kevin L.; Perrenoud, Ben C.

A complex pendulum system biomass sensor having a plurality of pendulums. The plurality of pendulums allow the system to detect a biomass height and density. Each pendulum has an angular deflection sensor and a deflector at a unique height. The pendulums are passed through the biomass and readings from the angular deflection sensors are fed into a control system. The control system determines whether adjustment of machine settings is appropriate and either displays an output to the operator, or adjusts automatically adjusts the machine settings, such as the speed, at which the pendulums are passed through the biomass. In anmore » alternate embodiment, an entanglement sensor is also passed through the biomass to determine the amount of biomass entanglement. This measure of entanglement is also fed into the control system.« less

Relaxation peak near 200 K in NiTi alloy

NASA Astrophysics Data System (ADS)

Zhu, J. S.; Schaller, R.; Benoit, W.

1989-10-01

Internal friction (IF), frequency ( f), electrical resistance ( R) and zero point movement of the torsion pendulum (ɛ) have been measured in near equi-atomic NiTi alloy in order to clarify the mechanism for the relaxation peak near 200 K. The height of the relaxation peak decreases successively with thermal cycling and settles down to a lower stable value in running 15 cycles. However, the electrical resistance of the sample shows a variation in contrast with the internal friction. Both of them will return to the initial state after a single annealing at 773 K for 1 h. The probable mechanism of this relaxation peak was discussed.

Experimental study on synchronization of three coupled mechanical metronomes

NASA Astrophysics Data System (ADS)

Hu, Qiang; Liu, Weiqing; Yang, Hujiang; Xiao, Jinghua; Qian, Xiaolan

2013-03-01

In this paper, a CCD acquisition system is set up to explore the dynamics of three coupled mechanical metronomes in order to compensate for the defects of visual observation. The facility is efficient to observe rich dynamics in an experiment, such as phase synchronization, partial phase synchronization and quasi-periodical oscillation, by accurately recording the trajectory of three coupled metronomes. The parameters, e.g., pendulum length and rolling friction are deemed to significantly influence the dynamics of three coupled mechanical metronomes judging from the experimental phenomena. The experimental results are confirmed by the numerical simulation based on the model with different intrinsic frequencies between three metronomes. The metronome and CCD acquisition systems are excellent demonstration apparatuses for a class and an undergraduate physics laboratory.

Experimental Equipment for Damping Capacity Analyze of High or Low Internal Friction Metallic Materials

NASA Astrophysics Data System (ADS)

Gârnet, I. A.; Stanciu, S.; Hopulele, I.; Zaharia, M. G.; Cimpoesu, N.; Chicet, D. L.; Crăciun, R. C.

2017-06-01

An experimental equipment, type torsion pendulum was made in laboratory in order to analyze the damping capacity of metallic materials. The scheme of the equipment is presented, 2D and 3D visions at real scale. The equipment functioning (mechanical and electrical part) and principles are presented. In this article we present some preliminary experimental results obtained on different materials (aluminium, steel etc.) using two different methods for registration the outputs (one based on optoelectronic device with Arduino acquisition board and second on video analyze (cinematic review: video to jpeg) of the damped motion of the lead pendulum). Steel materials were with shoot penning surface modification with and without heat treatment in order to establish the heat treatment influence on the damping capacity property.

The impact of surface and geometry on coefficient of friction of artificial hip joints.

PubMed

Choudhury, Dipankar; Vrbka, Martin; Mamat, Azuddin Bin; Stavness, Ian; Roy, Chanchal K; Mootanah, Rajshree; Krupka, Ivan

2017-08-01

Coefficient of friction (COF) tests were conducted on 28-mm and 36-mm-diameter hip joint prostheses for four different material combinations, with or without the presence of Ultra High Molecular Weight Polyethylene (UHMWPE) particles using a novel pendulum hip simulator. The effects of three micro dimpled arrays on femoral head against a polyethylene and a metallic cup were also investigated. Clearance played a vital role in the COF of ceramic on polyethylene and ceramic on ceramic artificial hip joints. Micro dimpled metallic femoral heads yielded higher COF against a polyethylene cup; however, with metal on metal prostheses the dimpled arrays significantly reduced the COF. In situ images revealed evidence that the dimple arrays enhanced film formation, which was the main mechanism that contributed to reduced friction. Copyright © 2017 Elsevier Ltd. All rights reserved.

Anelastic behavior of a torsion pendulum with a CuBe fiber at low temperature, and implications for a measurement of the gravitational constant

NASA Astrophysics Data System (ADS)

Bantel, Michael Kurt

1998-07-01

Using a torsion pendulum, we have investigated the anelastic properties of a CuBe torsion fiber for shear strains in the range 4×10-7 to 3×10-3 at temperatures 4.2K, 77K, and 295K. The fiber was 20 μm in diameter and 24 cm long, with a torsion constant of 0.033 dyn/cdot cm/cdot rad-1. It suspended an 11 gram azimuthally symmetric torsion pendulum which loaded the fiber to approximately 25% of its tensile strength at room temperature. The natural torsional oscillation frequency of this system was 6.4 mHz. An autocollimator viewing a set of mirrors on the oscillating pendulum served to measure with great accuracy the times at which the pendulum assumed a large set of discrete angular displacements during each oscillation cycle. This enabled a determination of the angular displacement of the pendulum as a function of time to better than a part in 107 of its oscillation amplitude, from which accurate information was obtained on the pendulum's frequency, damping, and harmonic content as functions of the oscillation amplitude. Analysis yields a determination of the fourth order shear elastic constant of CuBe. Expressing the shear potential energy density as: u(/epsilon)=c2ɛ2+c3ɛ3+ c4ɛ4 where ɛ is the shear strain, the values determined for (c2,/ c3,/ c4) are (25, 0.17, -550) GPa respectively. A striking feature of the fiber's internal friction Q-1 is that it appears to be the sum of two independent components: Q-1=Q I-1(T)+ Q II-1(A) where Q I-1(T) is temperature-dependent, varying by a factor of 3 between 4.2 and 77K, and Q II-1(A) is linearly dependent on amplitude and virtually independent of temperature; its linear dependence on amplitude varied by less than 4% between 4.2K and 77K. Interestingly the measurements of: the linear amplitude-dependent Q II-1, the linear component of the amplitude-dependent frequency shift, and the harmonic content associated with a dissipative hysteresis loop, are consistent with the motion generated by a simple stick-slip mechanism. Such a mechanism may be the result of microplastic behavior associated with the motion of dislocations and/or point defects. For a measurement of the gravitational constant using a torsion pendulum, these fiber-related properties may create a maximal 2-5 ppm systematic error assuming a comprehensive analysis is employed.

A Personal Navigation System Based on Inertial and Magnetic Field Measurements

DTIC Science & Technology

2010-09-01

MATLAB IMPLEMENTATION.................................................................74 G. A MODEL FOR PENDULUM MOTION SENSOR DATA...76 1. Pendulum Model for MATLAB Simulation....................................76 2. Sensor Data Generated with the Pendulum Model... PENDULUM ..................................................................................................88 I. FILTER PERFORMANCE WITH REAL PENDULUM DATA

Apparatus for measuring internal friction Q factors in brittle materials. [applied to lunar samples

NASA Technical Reports Server (NTRS)

Tittmann, B. R.; Curnow, J. M.

1976-01-01

A flexural analog of the torsion pendulum for measuring the Young's modulus and the internal friction Q factor of brittle materials has been developed for Q greater than 10 to the 3rd measurements at a zero static stress and at 10 to the -7th strains of brittle materials in the Hz frequency range. The present design was motivated by the desire to measure Q in fragile lunar return samples at zero static stress to shed light on the anomalously low attenuation of seismic waves on the moon. The use of the apparatus is demonstrated with data on fused silica and on a terrestrial analog of lunar basalt.

Assessment of energy harvesting and vibration mitigation of a pendulum dynamic absorber

NASA Astrophysics Data System (ADS)

Kecik, Krzysztof

2018-06-01

The paper presents a novel system for simultaneous energy harvesting and vibration mitigation. The system consists of two main parts: an autoparametric pendulum vibration absorber and an energy harvester device. The recovered energy is from oscillation of a levitating magnet in a coil. The energy harvesting system is mounted in a pendulum structure. The system allows energy recovery from a semi-trivial solution (pendulum in rest) or/and swinging of a pendulum. The influence of harvester parameters on the system response and energy harvesting in a parametric resonance is studied in detail. The harvester device does not decrease vibration reduction effectiveness.

Measure synchronization in a Huygens's non-dissipative two-pendulum clocks system

NASA Astrophysics Data System (ADS)

Tian, Jing; Chen, ZiChen; Qiu, HaiBo; Xi, XiaoQiang

2018-01-01

In this paper, we characterize measure synchronization (MS) in a four-degrees-of-freedom Huygens's two-pendulum clocks system. The two-pendulum clocks are connected by a massless spring with stiffness constant k. We find that with the stiffness constant k increasing, the coupled pendulums system achieves MS above a threshold value of k c . The energy characteristics of measure synchronization have been discussed, it is found that averaged energy of each pendulum system provide us an easy way to characterize MS transition. Furthermore, we discuss the dependence of the critical value for MS transition on initial conditions and the characteristic parameters of the system.

Energy behavior of an electromechanical system with internal impacts and uncertainties

NASA Astrophysics Data System (ADS)

Lima, Roberta; Sampaio, Rubens

2016-07-01

This paper analyzes the maximal energy stored in an elastic barrier due to the impacts of a pendulum fitted within a vibro-impact electromechanical system considering the existence of epistemic uncertainties in the system parameters. The vibro-impact electromechanical system is composed of two subsystems. The first subsystem is the electromechanical system composed by a motor, cart and pendulum, and the second is an elastic barrier. The first will be called striker system. The pendulum is fitted within the cart. Its suspension point is fixed in the cart, so that it may exist a relative motion between cart and pendulum. The influence of the DC motor in the dynamic behavior of the pendulum is considered. The coupling between the motor and the cart is made by a scotch yoke mechanism, so that the motor rotational motion is transformed in horizontal cart motion over a rail. The pendulum is modeled as a mathematical pendulum (bar without mass and particle of mass mp at the end). A flexible barrier, placed inside the cart, constrains the pendulum motion. Due to the relative motion between the cart and the pendulum, impacts may occur between these two elements. The objective of the paper is to analyze the energy stored in the barrier due to impacts as a function of some parameters of the electromechanical system from a deterministic and from a stochastic viewpoint. The system is designed as an aid in drilling. The impacts damage or fracture the rock and facilitate the conventional drilling.

Mechanical response of the flux lines in ceramic YBa2Cu3O7-δ

NASA Astrophysics Data System (ADS)

Luzuriaga, J.; André, M.-O.; Benoit, W.

1992-06-01

We have studied the mechanical response of the flux-line lattice (FLL) in ceramic samples of YBa2Cu3O7 by means of a low-frequency forced pendulum. The internal friction and elastic modulus variation of the FLL have been measured as a function of temperature for different values of the applied stress. A somewhat different behavior was observed whether a zero-field-cooling or field-cooling procedure was followed. Measurements of the internal friction and elastic modulus as a function of the applied stress at constant temperature show amplitude-dependent dissipation, with a maximum dissipation at intermediate values of the stress. This dependence is well fitted by a rheological model of extended dry friction, if we restrict ourselves to the dissipation and modulus at fixed temperature. The agreement is not so good when attempting to extend the model to fit the temperature dependence.

Desktop chaotic systems: Intuition and visualization

NASA Technical Reports Server (NTRS)

Bright, Michelle M.; Melcher, Kevin J.; Qammar, Helen K.; Hartley, Tom T.

1993-01-01

This paper presents a dynamic study of the Wildwood Pendulum, a commercially available desktop system which exhibits a strange attractor. The purpose of studying this chaotic pendulum is twofold: to gain insight in the paradigmatic approach of modeling, simulating, and determining chaos in nonlinear systems; and to provide a desktop model of chaos as a visual tool. For this study, the nonlinear behavior of this chaotic pendulum is modeled, a computer simulation is performed, and an experimental performance is measured. An assessment of the pendulum in the phase plane shows the strange attractor. Through the use of a box-assisted correlation dimension methodology, the attractor dimension is determined for both the model and the experimental pendulum systems. Correlation dimension results indicate that the pendulum and the model are chaotic and their fractal dimensions are similar.

Dynamic stabilization of an optomechanical oscillator

DTIC Science & Technology

2014-10-20

respectively. The proper frequency of the pendulum is ω0 = √ g/, where g is the gravitational acceleration and is the length of the pendulum . The...controlled experiments. In this paper we discuss one such situation, the dynamic stabilization of a mechanical system such as an inverted pendulum . The...quantumoptomechanics, macroscopic quantum system, dynamic stabilization, Kapitza pendulum REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S

Apparatus for Investigating Momentum and Energy Conservation With MBL and Video Analysis

NASA Astrophysics Data System (ADS)

George, Elizabeth; Vazquez-Abad, Jesus

1998-04-01

We describe the development and use of a laboratory setup that is appropriate for computer-aided student investigation of the principles of conservation of momentum and mechanical energy in collisions. The setup consists of two colliding carts on a low-friction track, with one of the carts (the target) attached to a spring, whose extension or compression takes the place of the pendulum's rise in the traditional ballistic pendulum apparatus. Position vs. time data for each cart are acquired either by using two motion sensors or by digitizing images obtained with a video camera. This setup allows students to examine the time history of momentum and mechanical energy during the entire collision process, rather than simply focusing on the before and after regions. We believe that this setup is suitable for helping students gain understanding as the processes involved are simple to follow visually, to manipulate, and to analyze.

Calculus migration characterization during Ho:YAG laser lithotripsy by high-speed camera using suspended pendulum method.

PubMed

Zhang, Jian James; Rajabhandharaks, Danop; Xuan, Jason Rongwei; Chia, Ray W J; Hasenberg, Thomas

2017-07-01

Calculus migration is a common problem during ureteroscopic laser lithotripsy procedure to treat urolithiasis. A conventional experimental method to characterize calculus migration utilized a hosting container (e.g., a "V" grove or a test tube). These methods, however, demonstrated large variation and poor detectability, possibly attributed to the friction between the calculus and the container on which the calculus was situated. In this study, calculus migration was investigated using a pendulum model suspended underwater to eliminate the aforementioned friction. A high-speed camera was used to study the movement of the calculus which covered zero order (displacement), first order (speed), and second order (acceleration). A commercialized, pulsed Ho:YAG laser at 2.1 μm, a 365-μm core diameter fiber, and a calculus phantom (Plaster of Paris, 10 × 10 × 10 mm 3 ) was utilized to mimic laser lithotripsy procedure. The phantom was hung on a stainless steel bar and irradiated by the laser at 0.5, 1.0, and 1.5 J energy per pulse at 10 Hz for 1 s (i.e., 5, 10, and 15 W). Movement of the phantom was recorded by a high-speed camera with a frame rate of 10,000 FPS. The video data files are analyzed by MATLAB program by processing each image frame and obtaining position data of the calculus. With a sample size of 10, the maximum displacement was 1.25 ± 0.10, 3.01 ± 0.52, and 4.37 ± 0.58 mm for 0.5, 1, and 1.5 J energy per pulse, respectively. Using the same laser power, the conventional method showed <0.5 mm total displacement. When reducing the phantom size to 5 × 5 × 5 mm 3 (one eighth in volume), the displacement was very inconsistent. The results suggested that using the pendulum model to eliminate the friction improved sensitivity and repeatability of the experiment. A detailed investigation on calculus movement and other causes of experimental variation will be conducted as a future study.

A new class of compact high sensitive tiltmeter based on the UNISA folded pendulum mechanical architecture

NASA Astrophysics Data System (ADS)

Barone, Fabrizio; Giordano, Gerardo

2018-02-01

We present the Extended Folded Pendulum Model (EFPM), a model developed for a quantitative description of the dynamical behavior of a folded pendulum generically oriented in space. This model, based on the Tait-Bryan angular reference system, highlights the relationship between the folded pendulum orientation in the gravitational field and its natural resonance frequency. Tis model validated by tests performed with a monolithic UNISA Folded Pendulum, highlights a new technique of implementation of folded pendulum based tiltmeters.

Translation of time-reversal violation in the neutral K-meson system into a table-top mechanical system

NASA Astrophysics Data System (ADS)

Reiser, Andreas; Schubert, Klaus R.; Stiewe, Jürgen

2012-08-01

Weak interactions break time-reversal (T) symmetry in the two-state system of neutral K-mesons. We present and discuss a two-state mechanical system, i.e. a Foucault-type pendulum on a rotating table, for a full representation of {K^0}{{\\overlineK}{}^0} transitions by the pendulum motions including T violation. The pendulum moves with two different oscillation frequencies and two different magnetic dampings. Its equation of motion is identical to the differential equation for the real part of the CPT-symmetric K-meson wavefunction. The pendulum is able to represent microscopic CP and T violation with CPT symmetry owing to the macroscopic Coriolis force, which breaks the symmetry under reversal-of-motion. Video clips of the pendulum motions are given as supplementary material.

Experimental Uncertainty Associated with Traveling Wave Excitation

DTIC Science & Technology

2014-09-15

20 2.9 Schematic of the Lumped Model [6] . . . . . . . . . . . . . . . . . . . . . . . 21 2.10 Multiple Coupled Pendulum [7...model to describe the physical system, the authors chose to employ a coupled pendulum model to represent a rotor. This system is shown in Figure 2.10...System mistuning is introduced by altering pendulum lengths. All other system parameters are equal. A linear viscous proportional damping force is

A Laboratory Experiment on Coupled Non-Identical Pendulums

ERIC Educational Resources Information Center

Li, Ang; Zeng, Jingyi; Yang, Hujiang; Xiao, Jinghua

2011-01-01

In this paper, coupled pendulums with different lengths are studied. Through steel magnets, each pendulum is coupled with others, and a stepping motor is used to drive the whole system. To record the data automatically, we designed a data acquisition system with a CCD camera connected to a computer. The coupled system shows in-phase, locked-phase…

[Determination of a Friction Coefficient for THA Bearing Couples].

PubMed

Vrbka, M; Nečas, D; Bartošík, J; Hartl, M; Křupka, I; Galandáková, A; Gallo, J

2015-01-01

The wear of articular surfaces is considered one of the most important factors limiting the life of total hip arthroplasty (THA). It is assumed that the particles released from the surface of a softer material induce a complex inflammatory response, which will eventually result in osteolysis and aseptic loosening. Implant wear is related to a friction coefficient which depends on combination of the materials used, roughness of the articulating surfaces, internal clearance, and dimensions of the prosthesis. The selected parameters of the bearing couples tested were studied using an experimental device based on the principle of a pendulum. Bovine serum was used as a lubricant and the load corresponded to a human body mass of 75 kg. The friction coefficient was derived from a curve of slowdown of pendulum oscillations. Roughness was measured with a device working on the principle of interferometry. Clearance was assessed by measuring diameters of the acetabular and femoral heads with a 3D optical scanner. The specimens tested included unused metal-on-highly cross-linked polyethylene, ceramic-on-highly cross-linked polyethylene and ceramic-on-ceramic bearing couples with the diameters of 28 mm and 36 mm. For each measured parameter, an arithmetic mean was calculated from 10 measurements. 1) The roughness of polyethylene surfaces was higher by about one order of magnitude than the roughness of metal and ceramic components. The Protasul metal head had the least rough surface (0.003 μm). 2) The ceramic-on-ceramic couples had the lowest clearance. Bearing couples with polyethylene acetabular liners had markedly higher clearances ranging from 150 μm to 545 μm. A clearance increased with large femoral heads (up to 4-fold in one of the couple tested). 3) The friction coefficient was related to the combination of materials; it was lowest in ceramic-on-ceramic surfaces (0.11 to 0.12) and then in ceramic-on-polyethylene implants (0.13 to 0.14). The friction coefficient is supposed to increase with a decreasing femoral head diameter. However, in the bearing couples with polyethylene liners manufactured by one company, paradoxically, the friction coefficient slightly increased with an increase in femoral head size from 28 mm to 36 mm. 4) The lowest friction moment (< 3.5 Nm) was found for ceramic-on-ceramic implants 28 mm in diameter; the highest values were recorded in metal-on-polyethylene bearing couples 36 mm in diameter (> 7 Nm). Although our study confirmed that the bearing couples produced by different manufacturers varied to some extent in the parameters studied, in our opinion, this variability was not significant because it was not within an order of magnitude in any of the tests. The study showed that both the friction coefficient and the friction moment are affected more by the combination of materials than by the diameter of a femoral head. The best results were achieved in ceramic-on-ceramic implants.

Cyclic loading increases friction and changes cartilage surface integrity in lubricin-mutant mouse knees

PubMed Central

Drewniak, Elizabeth I; Jay, Gregory D; Fleming, Braden C; Zhang, Ling; Warman, Matthew L; Crisco, Joseph J

2012-01-01

Objective To investigate the effects of lubricin gene dosage and cyclic loading on whole joint coefficient of friction and articular cartilage surface integrity in mouse knee joints. Methods Joints from mice with 2 (Prg4+/+), 1 (Prg4+/−), or no (Prg4−/−) functioning lubricin alleles were subjected to 26 hours of cyclic loading using a custom-built pendulum. Coefficient of friction values were measured at multiple time points. Contralateral control joints were left unloaded. Following testing, joints were examined for histologic evidence of damage and cell viability. Results At baseline, the coefficient of friction values in Prg4−/− mice were significantly higher than those in Prg4+/+ and Prg4+/− mice (P < 0.001). Cyclic loading continuously increased the coefficient of friction in Prg4−/− mouse joints. In contrast, Prg4+/− and Prg4+/+ mouse joints had no coefficient of friction increases during the first 4 hours of loading. After 26 hours of loading, joints from all genotypes had increased coefficient of friction values compared to baseline and unloaded controls. Significantly greater increases occurred in Prg4−/− and Prg4+/− mouse joints compared to Prg4+/+ mouse joints. The coefficient of friction values were not significantly associated with histologic evidence of damage or loss of cell viability. Conclusion Our findings indicate that mice lacking lubricin have increased baseline coefficient of friction values and are not protected against further increases caused by loading. Prg4+/− mice are indistinguishable from Prg4+/+ mice at baseline, but have significantly greater coefficient of friction values following 26 hours of loading. Lubricin dosage affects joint properties during loading, and may have clinical implications in patients for whom injury or illness alters lubricin abundance. PMID:21905020

Dropping a Particle Out of a Roller Coaster

DTIC Science & Technology

2014-04-24

of the kinetic energy gained from the gravitational potential energy lost. Both friction and air drag are neglected. Point P marks a local minimum of...be that of a person swinging on the end of a rope like a simple pendulum and then releasing it and flying through the air [3]. • Reminiscent of a...shape described by functions such as a clothoid [7] to minimize any abrupt changes in the centripetal acceleration of the riders. The analysis can be

Development of Gravity Acceleration Measurement Using Simple Harmonic Motion Pendulum Method Based on Digital Technology and Photogate Sensor

NASA Astrophysics Data System (ADS)

Yulkifli; Afandi, Zurian; Yohandri

2018-04-01

Development of gravitation acceleration measurement using simple harmonic motion pendulum method, digital technology and photogate sensor has been done. Digital technology is more practical and optimizes the time of experimentation. The pendulum method is a method of calculating the acceleration of gravity using a solid ball that connected to a rope attached to a stative pole. The pendulum is swung at a small angle resulted a simple harmonic motion. The measurement system consists of a power supply, Photogate sensors, Arduino pro mini and seven segments. The Arduino pro mini receives digital data from the photogate sensor and processes the digital data into the timing data of the pendulum oscillation. The calculation result of the pendulum oscillation time is displayed on seven segments. Based on measured data, the accuracy and precision of the experiment system are 98.76% and 99.81%, respectively. Based on experiment data, the system can be operated in physics experiment especially in determination of the gravity acceleration.

Broadband pendulum energy harvester

NASA Astrophysics Data System (ADS)

Liang, Changwei; Wu, You; Zuo, Lei

2016-09-01

A novel electromagnetic pendulum energy harvester with mechanical motion rectifier (MMR) is proposed and investigated in this paper. MMR is a mechanism which rectifies the bidirectional swing motion of the pendulum into unidirectional rotation of the generator by using two one-way clutches in the gear system. In this paper, two prototypes of pendulum energy harvester with MMR and without MMR are designed and fabricated. The dynamic model of the proposed MMR pendulum energy harvester is established by considering the engagement and disengagement of the one way clutches. The simulation results show that the proposed MMR pendulum energy harvester has a larger output power at high frequencies comparing with non-MMR pendulum energy harvester which benefits from the disengagement of one-way clutch during pendulum vibration. Moreover, the proposed MMR pendulum energy harvester is broadband compare with non-MMR pendulum energy harvester, especially when the equivalent inertia is large. An experiment is also conducted to compare the energy harvesting performance of these two prototypes. A flywheel is attached at the end of the generator to make the disengagement more significant. The experiment results also verify that MMR pendulum energy harvester is broadband and has a larger output power at high frequency over the non-MMR pendulum energy harvester.

Optical Kapitza pendulum

NASA Astrophysics Data System (ADS)

Jones, Philip H.; Smart, Thomas J.; Richards, Christopher J.; Cubero, David

2016-09-01

The Kapitza pendulum is the paradigm for the phenomenon of dynamical stabilization, whereby an otherwise unstable system achieves a stability that is induced by fast modulation of a control parameter. In the classic, macroscopic Kapitza pendulum, a rigid pendulum is stabilized in the upright, inverted pendulum using a particle confined in a ring-shaped optical trap, subject to a drag force via fluid flow and driven via oscillating the potential in a direction parallel to the fluid flow. In the regime of vanishing Reynold's number with high-frequency driving the inverted pendulum is no longer stable, but new equilibrium positions appear that depend on the amplitude of driving. As the driving frequency is decreased a yet different behavior emerges where stability of the pendulum depends also on the details of the pendulum hydrodynamics. We present a theory for the observed induced stability of the overdamped pendulum based on the separation of timescales in the pendulum motion as formulated by Kapitza, but with the addition of a viscous drag. Excellent agreement is found between the predicted behavior from the analytical theory and the experimental results across the range of pendulum driving frequencies. We complement these results with Brownian motion simulations, and we characterize the stabilized pendulum by both time- and frequency-domain analyses of the pendulum Brownian motion.

Design and Experimental Implementation of Optimal Spacecraft Antenna Slews

DTIC Science & Technology

2013-12-01

LINK PENDULUM MODEL ............................................................58  C.  AZIMUTH-ELEVATION SYSTEM...BOUNDARY VALUE PROBLEM ......................77  B.  DOUBLE PENDULUM EXAMPLE............................................................82  C.  SOLVING THE...Figure 15.  Two-link Pendulum .........................................................................................58  Figure 16.  Double

Autonomous navigation system. [gyroscopic pendulum for air navigation

NASA Technical Reports Server (NTRS)

Merhav, S. J. (Inventor)

1981-01-01

An inertial navigation system utilizing a servo-controlled two degree of freedom pendulum to obtain specific force components in the locally level coordinate system is described. The pendulum includes a leveling gyroscope and an azimuth gyroscope supported on a two gimbal system. The specific force components in the locally level coordinate system are converted to components in the geographical coordinate system by means of a single Euler transformation. The standard navigation equations are solved to determine longitudinal and lateral velocities. Finally, vehicle position is determined by a further integration.

Recent development of the passive vibration control method

NASA Astrophysics Data System (ADS)

Ishida, Yukio

2012-05-01

This paper introduces new passive vibration suppression methods developed recently in our laboratory. First, two methods used to suppress steady-state resonances are explained. One is the improvement of the efficiency of a ball balancer. A simple method to eliminate the influence of friction of balls and to improve its efficiency is introduced. The other is an effective method that utilizes the discontinuous spring characteristics. Secondly, a method to eliminate unstable ranges in rotor systems is explained. Unstable ranges in an asymmetrical shaft, and in a hollow rotor partially filled with liquid, are eliminated by the discontinuous spring characteristics. Thirdly, a method to suppress self-excited oscillations is explained. Self-excited oscillations due to internal damping and rubbing are discussed. Finally, the methods of using a pendulum or roller type absorbers to suppress torsional vibrations are explained.

Control of Torsional Vibrations by Pendulum Masses

NASA Technical Reports Server (NTRS)

Stieglitz, Albert

1942-01-01

Various versions of pendulum masses have been developed abroad within the past few years by means of which resonant vibrations of rotating shafts can be eliminated at a given tuning. They are already successfully employed on radial engines in the form of pendulous counterweights. Compared with the commonly known torsional vibration dampers, the pendulum masses have the advantage of being structurally very simple, requiring no internal damping and being capable of completely eliminating certain vibrations. Unexplained, so far, remains the problem of behavior of pendulum masses in other critical zones to which they are not tuned, their dynamic behavior at some tuning other than in resonance, and their effect within a compound vibration system and at simultaneous application of several differently tuned pendulous masses. These problems are analyzed in the present report. The results constitute an enlargement of the scope of application of pendulum masses, especially for in-line engines. Among other things it is found that the natural frequency of a system can be raised by means of a correspondingly tuned pendulum mass. The formulas necessary for the design of any practical version are developed, and a pendulum mass having two different natural frequencies simultaneously is described.

Modeling and Model Identification of Autonomous Underwater Vehicles

DTIC Science & Technology

2015-06-01

setup, based on a quadrifilar pendulum , is developed to measure the moments of inertia of the vehicle. System identification techniques, based on...parametric models of the platforms: an individual channel excitation approach and a free decay pendulum test. The former is applied to THAUS, which can...excite the system in individual channels in four degrees of freedom. These results are verified in the free decay pendulum setup, which has the

Electronic system for the complex measurement of a Wilberforce pendulum

NASA Astrophysics Data System (ADS)

Kos, B.; Grodzicki, M.; Wasielewski, R.

2018-05-01

The authors present a novel application of a micro-electro-mechanical measurement system to the description of basic physical phenomena in a model Wilberforce pendulum. The composition of the kit includes a tripod with a mounted spring with freely hanging bob, a module GY-521 on the MPU 6050 coupled with an Arduino Uno, which in conjunction with a PC acts as measuring set. The system allows one to observe the swing of the pendulum in real time. Obtained data stays in good agreement with both theoretical predictions and previous works. The aim of this article is to introduce the study of a Wilberforce pendulum to the canon of physical laboratory exercises due to its interesting properties and multifaceted method of measurement.

Thrust Measurements in Ballistic Pendulum Ablative Laser Propulsion Experiments

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

Brazolin, H.; Rodrigues, N. A. S.; Minucci, M. A. S.

This paper describes a setup for thrust measurement in ablative laser propulsion experiments, based on a simple ballistic pendulum associated to an imaging system, which is being assembled at IEAv. A light aluminium pendulum holding samples is placed inside a 100 liters vacuum chamber with two optical windows: the first (in ZnSe) for the laser beam and the second (in fused quartz) for the pendulum visualization. A TEA-CO{sub 2} laser beam is focused to the samples providing ablation and transferring linear moment to the pendulum as a whole. A CCD video camera captures the oscillatory movement of the pendulum andmore » the its trajectory is obtained by image processing. By fitting the trajectory of the pendulum to a dumped sinusoidal curve is possible to obtain the amplitude of the movement which is directly related to the momentum transfered to the sample.« less

Reliability and validity of pendulum test measures of spasticity obtained with the Polhemus tracking system from patients with chronic stroke

PubMed Central

Bohannon, Richard W; Harrison, Steven; Kinsella-Shaw, Jeffrey

2009-01-01

Background Spasticity is a common impairment accompanying stroke. Spasticity of the quadriceps femoris muscle can be quantified using the pendulum test. The measurement properties of pendular kinematics captured using a magnetic tracking system has not been studied among patients who have experienced a stroke. Therefore, this study describes the test-retest reliability and known groups and convergent validity of the pendulum test measures obtained with the Polhemus tracking system. Methods Eight patients with chronic stroke underwent pendulum tests with their affected and unaffected lower limbs, with and without the addition of a 2.2 kg cuff weight at the ankle, using the Polhemus magnetic tracking system. Also measured bilaterally were knee resting angles, Ashworth scores (grades 0–4) of quadriceps femoris muscles, patellar tendon (knee jerk) reflexes (grades 0–4), and isometric knee extension force. Results Three measures obtained from pendular traces of the affected side were reliable (intraclass correlation coefficient ≥ .844). Known groups validity was confirmed by demonstration of a significant difference in the measurements between sides. Convergent validity was supported by correlations ≥ .57 between pendulum test measures and other measures reflective of spasticity. Conclusion Pendulum test measures obtained with the Polhemus tracking system from the affected side of patients with stroke have good test-retest reliability and both known groups and convergent validity. PMID:19642989

Reliability and validity of pendulum test measures of spasticity obtained with the Polhemus tracking system from patients with chronic stroke.

PubMed

Bohannon, Richard W; Harrison, Steven; Kinsella-Shaw, Jeffrey

2009-07-30

Spasticity is a common impairment accompanying stroke. Spasticity of the quadriceps femoris muscle can be quantified using the pendulum test. The measurement properties of pendular kinematics captured using a magnetic tracking system has not been studied among patients who have experienced a stroke. Therefore, this study describes the test-retest reliability and known groups and convergent validity of the pendulum test measures obtained with the Polhemus tracking system. Eight patients with chronic stroke underwent pendulum tests with their affected and unaffected lower limbs, with and without the addition of a 2.2 kg cuff weight at the ankle, using the Polhemus magnetic tracking system. Also measured bilaterally were knee resting angles, Ashworth scores (grades 0-4) of quadriceps femoris muscles, patellar tendon (knee jerk) reflexes (grades 0-4), and isometric knee extension force. Three measures obtained from pendular traces of the affected side were reliable (intraclass correlation coefficient > or = .844). Known groups validity was confirmed by demonstration of a significant difference in the measurements between sides. Convergent validity was supported by correlations > or = .57 between pendulum test measures and other measures reflective of spasticity. Pendulum test measures obtained with the Polhemus tracking system from the affected side of patients with stroke have good test-retest reliability and both known groups and convergent validity.

Experiments with a Magnetically Controlled Pendulum

ERIC Educational Resources Information Center

Kraftmakher, Yaakov

2007-01-01

A magnetically controlled pendulum is used for observing free and forced oscillations, including nonlinear oscillations and chaotic motion. A data-acquisition system stores the data and displays time series of the oscillations and related phase plane plots, Poincare maps, Fourier spectra and histograms. The decay constant of the pendulum can be…

An analytical approach to the external force-free motion of pendulums on surfaces of constant curvature

NASA Astrophysics Data System (ADS)

Rubio, Rafael M.; Salamanca, Juan J.

2018-07-01

The dynamics of external force free motion of pendulums on surfaces of constant Gaussian curvature is addressed when the pivot moves along a geodesic obtaining the Lagrangian of the system. As an application it is possible the study of elastic and quantum pendulums.

Dynamic modelling of a double-pendulum gantry crane system incorporating payload

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

Ismail, R. M. T. Raja; Ahmad, M. A.; Ramli, M. S.

The natural sway of crane payloads is detrimental to safe and efficient operation. Under certain conditions, the problem is complicated when the payloads create a double pendulum effect. This paper presents dynamic modelling of a double-pendulum gantry crane system based on closed-form equations of motion. The Lagrangian method is used to derive the dynamic model of the system. A dynamic model of the system incorporating payload is developed and the effects of payload on the response of the system are discussed. Extensive results that validate the theoretical derivation are presented in the time and frequency domains.

Explicit Analytical Solution of a Pendulum with Periodically Varying Length

ERIC Educational Resources Information Center

Yang, Tianzhi; Fang, Bo; Li, Song; Huang, Wenhu

2010-01-01

A pendulum with periodically varying length is an interesting physical system. It has been studied by some researchers using traditional perturbation methods (for example, the averaging method). But due to the limitation of the conventional perturbation methods, the solutions are not valid for long-term prediction of the pendulum. In this paper,…

The Multiple Pendulum Problem via Maple[R

ERIC Educational Resources Information Center

Salisbury, K. L.; Knight, D. G.

2002-01-01

The way in which computer algebra systems, such as Maple, have made the study of physical problems of some considerable complexity accessible to mathematicians and scientists with modest computational skills is illustrated by solving the multiple pendulum problem. A solution is obtained for four pendulums with no restriction on the size of the…

Bound Motion of Bodies and Paticles in the Rotating Systems

NASA Astrophysics Data System (ADS)

Pardy, Miroslav

2007-04-01

The Lagrange theory of particle motion in the noninertial systems is applied to the Foucault pendulum, isosceles triangle pendulum and the general triangle pendulum swinging on the rotating Earth. As an analogue, planet orbiting in the rotating galaxy is considered as the giant galactic gyroscope. The Lorentz equation and the Bargmann-Michel-Telegdi equations are generalized for the rotation system. The knowledge of these equations is inevitable for the construction of LHC where each orbital proton “feels” the Coriolis force caused by the rotation of the Earth.

Tidal evolution of the Galilean satellites - A linearized theory

NASA Technical Reports Server (NTRS)

Greenberg, R.

1981-01-01

The Laplace resonance among the Galilean satellites Io, Europa, and Ganymede is traditionally reduced to a pendulum-like dynamical problem by neglecting short-period variations of several orbital elements. However, some of these variations that can now be neglected may once have had longer periods, comparable to the 'pendulum' period, if the system was formerly in deep resonance (pairs of periods even closer to the ratio 2:1 than they are now). In that case, the dynamical system cannot be reduced to fewer than nine dimensions. The nine-dimensional system is linearized here in order to study small variations about equilibrium. When tidal effects are included, the resulting evolution is substantially the same as was indicated by the pendulum approach, except that evolution out of deep resonance is found to be somewhat slower than suggested by extrapolation of the pendulum results. This slower rate helps support the hypothesis that the system may have evolved from deep resonance.

Implementation of Push Recovery Strategy Using Triple Linear Inverted Pendulum Model in “T-FloW” Humanoid Robot

NASA Astrophysics Data System (ADS)

Dimas Pristovani, R.; Raden Sanggar, D.; Dadet, Pramadihanto.

2018-04-01

Push recovery is one of humanbehaviorwhich is a strategy to defend the body from anexternal force in any environment. This paper describes push recovery strategy which usesMIMO decoupled control system method. The dynamics system uses aquasi-dynamic system based on triple linear inverted pendulum model (TLIPM). The analysis of TLIPMuses zero moment point (ZMP) calculation from ZMP simplification in last research. By using this simplification of dynamics system, the control design can be simplified into 3 serial SISOwith known and uncertain disturbance models in each inverted pendulum. Each pendulum has different plan to damp the external force effect. In this experiment, PID controller (closed- loop)is used to arrange the damp characteristic.The experiment result shows thatwhen using push recovery control strategy (closed-loop control) is about 85.71% whilewithout using push recovery control strategy (open-loop control) it is about 28.57%.

Radial forcing and Edgar Allan Poe's lengthening pendulum

NASA Astrophysics Data System (ADS)

McMillan, Matthew; Blasing, David; Whitney, Heather M.

2013-09-01

Inspired by Edgar Allan Poe's The Pit and the Pendulum, we investigate a radially driven, lengthening pendulum. We first show that increasing the length of an undriven pendulum at a uniform rate does not amplify the oscillations in a manner consistent with the behavior of the scythe in Poe's story. We discuss parametric amplification and the transfer of energy (through the parameter of the pendulum's length) to the oscillating part of the system. In this manner, radial driving can easily and intuitively be understood, and the fundamental concept applied in many other areas. We propose and show by a numerical model that appropriately timed radial forcing can increase the oscillation amplitude in a manner consistent with Poe's story. Our analysis contributes a computational exploration of the complex harmonic motion that can result from radially driving a pendulum and sheds light on a mechanism by which oscillations can be amplified parametrically. These insights should prove especially valuable in the undergraduate physics classroom, where investigations into pendulums and oscillations are commonplace.

Integrated Reconfigurable Intelligent Systems (IRIS) for Complex Naval Systems

DTIC Science & Technology

2011-02-23

INTRODUCTION 35 2.2 GENERAL MODEL SETUP 36 2.2.1 Co-Simulation Principles 36 2.2.2 Double pendulum : a simple example 38 2.2.3 Description of numerical... pendulum sample problem 45 2.3 DISCUSSION OF APPROACH WITH RESPECT TO PROPOSED SUBTASKS 49 2.4 RESULTS DISCUSSION AND FUTURE WORK 49 TASK 3...Kim and Praehofer 2000]. 2.2.2 Double pendulum : a simple example In order to be able to evaluate co-simulation principles, specifically an

A composite controller for trajectory tracking applied to the Furuta pendulum.

PubMed

Aguilar-Avelar, Carlos; Moreno-Valenzuela, Javier

2015-07-01

In this paper, a new composite scheme is proposed, where the total control action is composed of the sum of a feedback-linearization-based controller and an energy-based compensation. This new proposition is applied to the rotary inverted pendulum or Furuta pendulum. The Furuta pendulum is a well-known underactuated mechanical system with two degrees of freedom. The control objective in this case is the tracking of a desired periodic trajectory in the actuated joint, while the unactuated link is regulated at the upward position. The closed-loop system is analyzed showing uniformly ultimately boundedness of the error trajectories. The design procedure is shown in a constructive form, such that it may be applied to other underactuated mechanical systems, with the proper definitions of the output function and the energy function. Numerical simulations and real-time experiments show the practical viability of the controller. Finally, the proposed algorithm is compared with a tracking controller previously reported in the literature. The new algorithm shows better performance in both arm trajectory tracking and pendulum regulation. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Design and Flight Test of a Cable Angle Feedback Control System for Improving Helicopter Slung Load Operations at Low Speed

DTIC Science & Technology

2014-04-01

improve the damping of the load pendulum motions, but the load feedback generally had the effect of making the load feel heavier to the pilot [28...0.25 2 1000lbs 16,000lbs 0.06 Another important parameter is the slung load pendulum frequency. Using a simple pendulum model, this natural...the expected yaw and heave modes. The presence of the load adds oscillatory pendulum modes in the pitch and roll axes, as expected. Table 2-3

Computer simulation of multigrid body dynamics and control

NASA Technical Reports Server (NTRS)

Swaminadham, M.; Moon, Young I.; Venkayya, V. B.

1990-01-01

The objective is to set up and analyze benchmark problems on multibody dynamics and to verify the predictions of two multibody computer simulation codes. TREETOPS and DISCOS have been used to run three example problems - one degree-of-freedom spring mass dashpot system, an inverted pendulum system, and a triple pendulum. To study the dynamics and control interaction, an inverted planar pendulum with an external body force and a torsional control spring was modeled as a hinge connected two-rigid body system. TREETOPS and DISCOS affected the time history simulation of this problem. System state space variables and their time derivatives from two simulation codes were compared.

Foot trajectory approximation using the pendulum model of walking.

PubMed

Fang, Juan; Vuckovic, Aleksandra; Galen, Sujay; Conway, Bernard A; Hunt, Kenneth J

2014-01-01

Generating a natural foot trajectory is an important objective in robotic systems for rehabilitation of walking. Human walking has pendular properties, so the pendulum model of walking has been used in bipedal robots which produce rhythmic gait patterns. Whether natural foot trajectories can be produced by the pendulum model needs to be addressed as a first step towards applying the pendulum concept in gait orthosis design. This study investigated circle approximation of the foot trajectories, with focus on the geometry of the pendulum model of walking. Three able-bodied subjects walked overground at various speeds, and foot trajectories relative to the hip were analysed. Four circle approximation approaches were developed, and best-fit circle algorithms were derived to fit the trajectories of the ankle, heel and toe. The study confirmed that the ankle and heel trajectories during stance and the toe trajectory in both the stance and the swing phases during walking at various speeds could be well modelled by a rigid pendulum. All the pendulum models were centred around the hip with pendular lengths approximately equal to the segment distances from the hip. This observation provides a new approach for using the pendulum model of walking in gait orthosis design.

Response of Pendulums to Translational and Rotational Components of Ground Motion

NASA Astrophysics Data System (ADS)

Graizer, V.; Kalkan, E.

2008-12-01

Dynamic response of most seismological instruments and many engineering structures to ground shaking can be represented via response of a pendulum (single-degree-of-freedom oscillator). Pendulum response is usually simplified by considering the input from uni-axial translational motion only. Complete ground motion however, includes not only translational components but also rotations (tilt and torsion). We consider complete equations of motion for three following types of pendulum: (i) conventional mass-on-rod, (ii) mass- on-spring type, and (iii) inverted (astatic), then their response sensitivities to each component of complex ground motion are examined. Inverted pendulums are used in seismology for more than 100 years, for example, classical Wiechert's horizontal seismograph built around 1905 and still used at some seismological observatories, and recent Guralp's horizontal seismometers CMG-40T and CMG-3T. Inverted pendulums also have significant importance for engineering applications where they are often used to simulate the dynamic response of various structural systems. The results of this study show that a horizontal pendulum similar to a modern accelerometer used in strong motion measurements is practically sensitive to translational motion and tilt only, while inverted pendulum is sensitive not only to translational components, but also to angular accelerations and tilt. For better understanding of the inverted pendulum's dynamic behavior under complex ground excitation, relative contribution of each component of motion on response variants is carefully isolated. The responses of pendulums are calculated in time-domain using close-form solution Duhamel's integral with complex input forcing functions. As compared to a common horizontal pendulum, response of an inverted pendulum is sensitive to acceleration of gravity and vertical acceleration when it reaches the level close to 1.0 g. Gravity effect introduces nonlinearity into the differential equation of motion, and results in shift of the frequency response to lower frequencies. The equations of inverted pendulum represent elastic response of pendulums (as material behavior), with nonlinearity created by time and amplitude dependence of equation coefficients. Sensitivity of inverted pendulum to angular acceleration of tilt is proportional to the length of a pendulum, and should be taken into consideration since it can produce significant effect especially for long pendulums, idealizing for instance, bridge piers, bents, elevated water tanks, telecommunication towers, etc.

On the Stable Limit Cycle of a Weight-Driven Pendulum Clock

ERIC Educational Resources Information Center

Llibre, J; Teixeira, M. A.

2010-01-01

In a recent paper (Denny 2002 Eur. J. Phys. 23 449-58), entitled "The pendulum clock: a venerable dynamical system", Denny showed that in a first approximation the steady-state motion of a weight-driven pendulum clock is shown to be a stable limit cycle. He placed the problem in a historical context and obtained an approximate solution using the…

Working Model of a Foucault Pendulum at Intermediate Latitudes

ERIC Educational Resources Information Center

Sears, Francis W.

1969-01-01

Describes a working model of a Foucault pendulum at intermediate latitudes constructed of a steel drill rod with a steel ball attached at one end. The rod makes an angle of 45 degrees with the rotation axis of a horizontal turntable. The vibrating system is the same as that which led Foucault to construct his first gravity pendulum. (LC)

Orion GN&C Detection and Mitigation of Parachute Pendulosity

NASA Technical Reports Server (NTRS)

Kane, Mark A.; Wacker, Roger

2016-01-01

New techniques being employed by Orion guidance, navigation, and control (GN&C) using a reaction control system (RCS) under parachutes are described. Pendulosity refers to a pendulum-oscillatory mode that can occur during descent under main parachutes and that has been observed during Orion parachute drop tests. The pendulum mode reduces the ability of GN&C to maneuver the suspended vehicle resulting in undesirable increases to structural loads at touchdown. Parachute redesign efforts have been unsuccessful in reducing the pendulous behavior necessitating GN&C mitigation options. An observer has been developed to estimate the pendulum motion as well as the underlying wind velocity vector. Using this knowledge, the control system maneuvers the vehicle using two separate strategies determined by wind velocity magnitude and pendulum energy thresholds; at high wind velocities the vehicle is aligned with the wind direction and for cases with lower wind velocities and large pendulum amplitudes the vehicle is aligned such that it is perpendicular to the swing plane. Pendulum damping techniques using RCS thrusters are discussed but have not been selected for use onboard the Orion spacecraft. The techniques discussed in this paper will be flown on Exploration Mission 1 (EM-1).

Measurement of Motion Transfer Functions for Mirror Suspensions

NASA Astrophysics Data System (ADS)

Stuver, Amber; Beilby, Mark; Glancy, Aran; Gonzalez, Gabriela

2001-04-01

Interferometric gravitational wave detectors, such as LIGO, use mirrors suspended in pendulums. The current LIGO dectors use simple pendulums, but advanced LIGO detectors will use multiple pendulums with some stages on soft vertical springs. A drawback of the a multiple pendulum design is that it is difficult to model and predict cross couplings from one vibrational mode to another due to slight unavoidable asymmetries in the real system. Of most concern are the couplings to motion along the optical axis and into angular motions, which have the most potential to contaminate data. Our research focuses on the experimental testing of the pendulum designs for cross couplings with a special dedicated shaking stage. The cross couplings in each degree of freedom, their isolation and damping are investigated in this research though the measurement of transfer functions as filtered though the suspension system. This research is supported by The Pennsylvania State University, the NSF Grant no. PHY-9870032, and the REU program at The Pennsylvania State University.

Science Projects from Astronomy to Zoology.

ERIC Educational Resources Information Center

Learning, 1983

1983-01-01

Activities for teaching about the solar system, the earth's rotation, plants, pendulums, and animal adaptation are described. Included are suggestions for building scale models to illustrate the solar system's proportions and the earth's rotation speed, and for using playground swings to demonstrate pendulum motion. (PP)

Electromagnetic energy harvesting from a dual-mass pendulum oscillator

NASA Astrophysics Data System (ADS)

Wang, Hongyan; Tang, Jiong

2016-04-01

This paper presents the analysis of a type of vibration energy harvester composed of an electromagnetic pendulum oscillator combined to an elastic main structure. In this study, the elastic main structure connected to the base is considered as a single degree-of-freedom (DOF) spring-mass-damper subsystem. The electromagnetic pendulum oscillator is considered as a dual-mass two-frequency subsystem, which is composed of a hollow bar with a tip winded coil and a magnetic mass with a spring located in the hollow bar. As the pendulum swings, the magnetic mass can move along the axial direction of the bar. Thus, the relative motion between the magnet and the coil induces a wire current. A mathematical model of the coupled system is established. The system dynamics a 1:2:1 internal resonance. Parametric analysis is carried out to demonstrate the effect of the excitation acceleration, excitation frequency, load resistance, and frequency tuning parameters on system performance.

Mechanical characterisation of the TorPeDO: a low frequency gravitational force sensor

NASA Astrophysics Data System (ADS)

McManus, D. J.; Forsyth, P. W. F.; Yap, M. J.; Ward, R. L.; Shaddock, D. A.; McClelland, D. E.; Slagmolen, B. J. J.

2017-07-01

Newtonian noise is likely to be a future challenge at low frequencies for Advanced LIGO and other second generation gravitational wave detectors. We present the TorPeDO system: a dual torsion pendulum sensor designed to measure local gravitational forces to high precision. Gravitational forces induce a differential rotation between the two torsion beams, which is measured with an optical read-out. Both torsion pendulums have a common suspension point, tunable centre of mass, and resonant frequency. This produces a high level of mechanical common mode noise cancellation. We report on a controls prototype of the TorPeDO system, presenting the frequency response and tuning range of both pendulums. A noise budget and mechanical cross-coupling model for this system are also presented. We demonstrate frequency tuning of the two torsion pendulums to a difference of 4.3 μHz.

Combined input shaping and feedback control for double-pendulum systems

NASA Astrophysics Data System (ADS)

Mar, Robert; Goyal, Anurag; Nguyen, Vinh; Yang, Tianle; Singhose, William

2017-02-01

A control system combining input shaping and feedback is developed for double-pendulum systems subjected to external disturbances. The proposed control method achieves fast point-to-point response similar to open-loop input-shaping control. It also minimizes transient deflections during the motion of the system, and disturbance-induced residual swing using the feedback control. Effects of parameter variations such as the mass ratio of the double pendulum, the suspension length ratio, and the move distance were studied via numerical simulation. The most important results were also verified with experiments on a small-scale crane. The controller effectively suppresses the disturbances and is robust to modelling uncertainties and task variations.

A simple, low-cost, data logging pendulum built from a computer mouse

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

Gintautas, Vadas; Hubler, Alfred

Lessons and homework problems involving a pendulum are often a big part of introductory physics classes and laboratory courses from high school to undergraduate levels. Although laboratory equipment for pendulum experiments is commercially available, it is often expensive and may not be affordable for teachers on fixed budgets, particularly in developing countries. We present a low-cost, easy-to-build rotary sensor pendulum using the existing hardware in a ball-type computer mouse. We demonstrate how this apparatus may be used to measure both the frequency and coefficient of damping of a simple physical pendulum. This easily constructed laboratory equipment makes it possible formore » all students to have hands-on experience with one of the most important simple physical systems.« less

Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems

NASA Astrophysics Data System (ADS)

Pritula, G. M.; Petrenko, E. V.; Usatenko, O. V.

2018-02-01

A linearized plane pendulum with the slowly varying mass and length of string and the suspension point moving at a slowly varying speed is presented as an example of a simple 1D mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. The expression for the pendulum geometric phase is obtained by three different methods. The pendulum is shown to be canonically equivalent to the damped harmonic oscillator. This supports the mathematical conclusion, not widely accepted in physical community, of no difference between the dissipative and Hamiltonian 1D systems.

State Estimation for Humanoid Robots

DTIC Science & Technology

2015-07-01

21 2.2.1 Linear Inverted Pendulum Model . . . . . . . . . . . . . . . . . . . 21 2.2.2 Planar Five-link Model...Linear Inverted Pendulum Model. LVDT Linear Variable Differential Transformers. MEMS Microelectromechanical Systems. MHE Moving Horizon Estimator. QP...

Response of pendulums to complex input ground motion

USGS Publications Warehouse

Graizer, V.; Kalkan, E.

2008-01-01

Dynamic response of most seismological instruments and many engineering structures to ground shaking can be represented via response of a pendulum (single-degree-of-freedom oscillator). In most studies, pendulum response is simplified by considering the input from uni-axial translational motion alone. Complete ground motion however, includes not only translational components but also rotations (tilt and torsion). In this paper, complete equations of motion for three following types of pendulum are described: (i) conventional (mass-on-rod), (ii) mass-on-spring type, and (iii) inverted (astatic), then their response sensitivities to each component of complex ground motion are examined. The results of this study show that a horizontal pendulum similar to an accelerometer used in strong motion measurements is practically sensitive to translational motion and tilt only, while inverted pendulum commonly utilized to idealize multi-degree-of-freedom systems is sensitive not only to translational components, but also to angular accelerations and tilt. For better understanding of the inverted pendulum's dynamic behavior under complex ground excitation, relative contribution of each component of motion on response variants is carefully isolated. The systematically applied loading protocols indicate that vertical component of motion may create time-dependent variations on pendulum's oscillation period; yet most dramatic impact on response is produced by the tilting (rocking) component. ?? 2007 Elsevier Ltd. All rights reserved.

A Clinically Realistic Large Animal Model of Intra-Articular Fracture

DTIC Science & Technology

2014-12-01

pendulum system for measuring energy absorption during fracture insult to large animal joints in vivo. J Biomech Eng. 2014 Jun;136(6):064502. PMID:24760051...Model 4. Yucatan Minipig 5. Impact 6. Pendulum 7. Mankin Scoring 8. Inflammatory Cytokines 9. Gait Analysis 10. Incongruity 3. OVERALL...primarily hardware upgrades and ex-vivo experimentation of the pendulum . 3.2.a Device Upgrades The primary hardware upgrade was to instrument the

Bulk Viscoelastic Contribution to the Wet Sliding Friction of Rubber Compounds

NASA Astrophysics Data System (ADS)

Pan, Xiao-Dong

2002-03-01

An efficient stopping of an automobile on a wet highway in a rainy day is of obvious importance to the safety of the driving public. Here tire tread made of filled rubber compounds plays an essential role in detremining the wet traction performance. Even though significant progress has been made in improving this tire performance character and much knowledge has been accumulated, there still lacks a coherent fundamental understanding on this dynamic process. Consequently there currently exist no accurate guidelines for designing rubber compounds for better wet traction, and for predicting the wet traction performance of a rubber compound. In this experimental study, a portable British Pendulum Skid Tester has been employed to examine in the laboratory how the rubber compound material properties affect its wet sliding friction on a concrete surface. A dramatic dispaly of the impacts from the compound bulk viscoelastic properties has been observed for the first time. This observation will be discussed in relation to previous results discussed in the literature.

Development of a two-dimensional dual pendulum thrust stand for Hall thrusters.

PubMed

Nagao, N; Yokota, S; Komurasaki, K; Arakawa, Y

2007-11-01

A two-dimensional dual pendulum thrust stand was developed to measure thrust vectors [axial and horizontal (transverse) direction thrusts] of a Hall thruster. A thruster with a steering mechanism is mounted on the inner pendulum, and thrust is measured from the displacement between inner and outer pendulums, by which a thermal drift effect is canceled out. Two crossover knife-edges support each pendulum arm: one is set on the other at a right angle. They enable the pendulums to swing in two directions. Thrust calibration using a pulley and weight system showed that the measurement errors were less than 0.25 mN (1.4%) in the main thrust direction and 0.09 mN (1.4%) in its transverse direction. The thrust angle of the thrust vector was measured with the stand using the thruster. Consequently, a vector deviation from the main thrust direction of +/-2.3 degrees was measured with the error of +/-0.2 degrees under the typical operating conditions for the thruster.

Mechanics

NASA Astrophysics Data System (ADS)

Cox, John

2014-05-01

Part 1. The Winning of the Principles: 1. Introduction; 2. The beginnings of statics. Archimedes. Problem of the lever and of the centre of gravity; 2. Experimental verification and applications of the principle of the lever; 3. The centre of gravity; 4. The balance; 5. Stevinus of Bruges. The principle of the inclined plane; 6. The parallelogram of forces; 7. The principle of virtual work; 8. Review of the principles of statics; 9. The beginnings of dynamics. Galileo. The problem of falling bodies; 10. Huyghens. The problem of uniform motion in a circle. 'Centrifugal force'; 11. Final statement of the principles of dynamics. Extension to the motions of the heavenly bodies. The law of universal gravitation. Newton; Part II. Mathematical Statement of the Principles: Introduction; 12. Kinematics; 13. Kinetics of a particle moving in a straight line. The laws of motion; 14. Experimental verification of the laws of motion. Atwood's machine; 15. Work and energy; 16. The parallelogram law; 17. The composition and resolution of forces. Resultant. Component. Equilibrium; 18. Forces in one plane; 19. Friction; Part III. Application to Various Problems: 20. Motion on an inclined plane. Brachistochrones; 21. Projectiles; 22. Simple harmonic motion; 23. The simple pendulum; 24. Central forces. The law of gravitation; 25. Impact and impulsive forces; Part IV. The Elements of Rigid Dynamics: 26. The compound pendulum. Huyghens' solution; 27. D'alembert's principle; 28. Moment of inertia; 29. Experimental determination of moments of inertia; 30. Determination of the value of gravity by Kater's pendulum; 31. The constant of gravitation, or weighing the Earth. The Cavendish experiment; Answers to the examples; Index.

The Impact of Pictorial Display on Operator Learning and Performance. M.S. Thesis

NASA Technical Reports Server (NTRS)

Miller, R. A.; Messing, L. J.; Jagacinski, R. J.

1984-01-01

The effects of pictorially displayed information on human learning and performance of a simple control task were investigated. The controlled system was a harmonic oscillator and the system response was displayed to subjects as either an animated pendulum or a horizontally moving dot. Results indicated that the pendulum display did not effect performance scores but did significantly effect the learning processes of individual operators. The subjects with the pendulum display demonstrated more vertical internal models early in the experiment and the manner in which their internal models were tuned with practice showed increased variability between subjects.

Frequency and amplitude response of the flux-line lattice to mechanical perturbation in ceramic YBa 2Cu 3O 7

NASA Astrophysics Data System (ADS)

Luzuriaga, J.; André, M.-O.; Benoit, W.

1992-10-01

The mechanical response of the flux-line lattice has been measured with a low-frequency forced pendulum in ceramic YBa 2Cu 3O 7. A dissipation peak observed in temperature sweeps is frequency-independent between 1 mHz and 5 Hz. Dissipation depends strongly on applied torque, and for fixed temperatures this dependence is well fitted by a rheological model of extended dry friction. If the model is extended to take account of thermal activation, however, it does not agree with the measured frequency independence, which is hard to explain within simple models of thermal activation.

Quantum Simulation and Quantum Sensing with Ultracold Strontium

DTIC Science & Technology

2015-09-18

quantum Kapitza pendulum , a novel Floquet system which we are investigating using modulated optical lattices. We have proposed and are developing...another goal of our AFOSR YIP project. To this end, we have developed the first theoretical treatment of a lattice-based quantum Kapitza pendulum . We have...classical single-particle analogue of this phase occurs in a rigid pendulum with an oscillating support (known as a Kapitza pendu- lum [9]). To prepare for

Two-Pendulum Model of Propellant Slosh in Europa Clipper PMD Tank

NASA Technical Reports Server (NTRS)

Ng, Wanyi; Benson, David

2017-01-01

Model propellant slosh for Europa Clipper using two pendulums such that controls engineers can predict slosh behavior during the mission. Importance of predicting propellant slosh; (1) Sloshing changes CM (center of mass) of spacecraft and exerts forces and torques on spacecraft. (2) Avoid natural frequencies of structures. (3) Size ACS (Attitude Control Systems) thrusters to counteract forces and torques. Can model sloshing fluid as two pendulums with specific parameters (mass, length, damping),

Seismic isolation of nuclear power plants using sliding isolation bearings

NASA Astrophysics Data System (ADS)

Kumar, Manish

Nuclear power plants (NPP) are designed for earthquake shaking with very long return periods. Seismic isolation is a viable strategy to protect NPPs from extreme earthquake shaking because it filters a significant fraction of earthquake input energy. This study addresses the seismic isolation of NPPs using sliding bearings, with a focus on the single concave Friction Pendulum(TM) (FP) bearing. Friction at the sliding surface of an FP bearing changes continuously during an earthquake as a function of sliding velocity, axial pressure and temperature at the sliding surface. The temperature at the sliding surface, in turn, is a function of the histories of coefficient of friction, sliding velocity and axial pressure, and the travel path of the slider. A simple model to describe the complex interdependence of the coefficient of friction, axial pressure, sliding velocity and temperature at the sliding surface is proposed, and then verified and validated. Seismic hazard for a seismically isolated nuclear power plant is defined in the United States using a uniform hazard response spectrum (UHRS) at mean annual frequencies of exceedance (MAFE) of 10-4 and 10 -5. A key design parameter is the clearance to the hard stop (CHS), which is influenced substantially by the definition of the seismic hazard. Four alternate representations of seismic hazard are studied, which incorporate different variabilities and uncertainties. Response-history analyses performed on single FP-bearing isolation systems using ground motions consistent with the four representations at the two shaking levels indicate that the CHS is influenced primarily by whether the observed difference between the two horizontal components of ground motions in a given set is accounted for. The UHRS at the MAFE of 10-4 is increased by a design factor (≥ 1) for conventional (fixed base) nuclear structure to achieve a target annual frequency of unacceptable performance. Risk oriented calculations are performed for eight sites across the United States to show that the factor is equal to 1.0 for seismically isolated NPPs, if the risk is dominated by horizontal earthquake shaking. Response-history analyses using different models of seismically isolated NPPs are performed to understand the importance of the choice of friction model, model complexity and vertical ground motion for calculating horizontal displacement response across a wide range of sites and shaking intensities. A friction model for the single concave FP bearing should address heating. The pressure- and velocity-dependencies were not important for the models and sites studied. Isolation-system displacements can be computed using a macro model comprising a single FP bearing.

The friction coefficient of shoulder joints remains remarkably low over 24 h of loading.

PubMed

Jones, Brian K; Durney, Krista M; Hung, Clark T; Ateshian, Gerard A

2015-11-05

The frictional response of whole human joints over durations spanning activities of daily living has not been reported previously. This study measured the friction of human glenohumeral joints during 24 h of reciprocal loading in a pendulum testing device, at moderate (0.2 mm/s, 4320 cycles) and low (0.02 mm/s, 432 cycles) sliding speeds, under a 200 N load. The effect of joint congruence was also investigated by testing human humeral heads against significantly larger mature bovine glenoids. Eight human joints and six bovine joints were tested in four combinations: human joints tested at moderate (hHCMS, n=6) and low speed (hHCLS, n=3), human humeral heads tested against bovine glenoids at moderate speed (LCMS, n=3), and bovine joints tested at moderate speed (bHCMS, n=3). In the first half hour the mean±standard deviation of the friction coefficient was hHCMS: 0.0016±0.0011, hHCLS: 0.0012±0.0002, LCMS: 0.0008±0.0002 and bHCMS: 0.0024±0.0008; in the last four hours it was hHCMS: 0.0057±0.0025, hHCLS: 0.0047±0.0017, LCMS: 0.0012±0.0003 and bHCMS: 0.0056±0.0016. The initial value was lower than the final value (p<0.0001). The value in LCMS was significantly lower than in hHCMS and bHCMS (p<0.01). No visual damage was observed in any of the specimens. These are the first results to demonstrate that the friction coefficient of natural human shoulders remains remarkably low (averaging as little as 0.0015 and no greater than 0.006) for up to 24 h of continuous loading. The sustained low friction coefficients observed in incongruent joints (~0.001) likely represent rolling rather than sliding friction. Copyright © 2015. Published by Elsevier Ltd.

Tuned mass damping system for a pendulum in gravity and microgravity fields

NASA Astrophysics Data System (ADS)

Atour, Farah

2016-07-01

An electrodynamic tether is a simple idea, but one with an amazing number of uses. Electrodynamic tether is a long conductor wire that is attached to the satellite, which can act as a generator or motor, from its motion through the earth's magnetic field. And it has the potential to make space travel significantly cheaper. The lack of electrodynamic tether's widespread in common applications can be attributed to the variable Lorentz forces occuring on the tethers, which will cause them to oscillate and may go out of control, de-orbit the satellite and fall to Earth. A tuned mass damper system, for short refered as tilger, is suggested as damper of oscillations of tethers. A system composed of a tuned mass damper and a simple pendulum simulating the tether was therefore constructed. 350 sets of experimental trials were done on the system, while it was installed inside a drop tower capsule resting on the ground, in order to pick four optimum setup experiments that will undergo a series of microgravity experiments at the Bremen Drop Tower in Bremen, Germany. The GJU Bachelor Research students found that the oscillations of the simple pendulum will not be affected by the tilger during the free fall experiment, except if a feedback mechanism is installed between the simple pendulum and the tilger. In this case, the tilger will dampen the simple pendulum oscillations during free fall.

Robust Control Algorithm for a Two Cart System and an Inverted Pendulum

NASA Technical Reports Server (NTRS)

Wilson, Chris L.; Capo-Lugo, Pedro

2011-01-01

The Rectilinear Control System can be used to simulate a launch vehicle during liftoff. Several control schemes have been developed that can control different dynamic models of the rectilinear plant. A robust control algorithm was developed that can control a pendulum to maintain an inverted position. A fluid slosh tank will be attached to the pendulum in order to test robustness in the presence of unknown slosh characteristics. The rectilinear plant consists of a DC motor and three carts mounted in series. Each cart s weight can be adjusted with brass masses and the carts can be coupled with springs. The pendulum is mounted on the first cart and an adjustable air damper can be attached to the third cart if desired. Each cart and the pendulum have a quadrature encoder to determine position. Full state feedback was implemented in order to develop the control algorithm along with a state estimator to determine the velocity states of the system. A MATLAB program was used to convert the state space matrices from continuous time to discrete time. This program also used a desired phase margin and damping ratio to determine the feedback gain matrix that would be used in the LabVIEW program. This experiment will allow engineers to gain a better understanding of liquid propellant slosh dynamics, therefore enabling them to develop more robust control algorithms for launch vehicle systems

Predictor-based control for an inverted pendulum subject to networked time delay.

PubMed

Ghommam, J; Mnif, F

2017-03-01

The inverted pendulum is considered as a special class of underactuated mechanical systems with two degrees of freedom and a single control input. This mechanical configuration allows to transform the underactuated system into a nonlinear system that is referred to as the normal form, whose control design techniques for stabilization are well known. In the presence of time delays, these control techniques may result in inadequate behavior and may even cause finite escape time in the controlled system. In this paper, a constructive method is presented to design a controller for an inverted pendulum characterized by a time-delayed balance control. First, the partial feedback linearization control for the inverted pendulum is modified and coupled with a state predictor to compensate for the delay. Several coordinate transformations are processed to transform the estimated partial linearized system into an upper-triangular form. Second, nested saturation and backstepping techniques are combined to derive the control law of the transformed system that would complete the design of the whole control input. The effectiveness of the proposed technique is illustrated by numerical simulations. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Periodic solutions of a spring-pendulum system.

NASA Technical Reports Server (NTRS)

Broucke, R.; Baxa, P. A.

1973-01-01

A study has been made of a dynamical system composed of a pendulum and a harmonic oscillator, in order to show the remarkable resemblance with many classical celestial mechanics problems, in particular, the restricted three-body problem. It is shown that the well-known investigations of periodic orbits can be applied to the present dynamics problem.

Using a Modified Simple Pendulum to Find the Variations in the Value of “g”

NASA Astrophysics Data System (ADS)

Arnold, Jonathan P.; Efthimiou, C.

2007-05-01

The simple pendulum is one of the most known and studied system of Newtonian Mechanics. It also provides one of the most elegant and simple devices to measure the acceleration of gravity at any location. In this presentation we will revisit the problem of measuring the acceleration of gravity using a simple pendulum and will present a modification to the standard technique that increases the accuracy of the measurement.

A swing driven by liquid crystals

NASA Astrophysics Data System (ADS)

Cheng, Cheng

Angular momentum in liquid crystals exists as flow, director reorientation, etc. However, it is hard to observe and measure angular momentum in liquid crystals by a direct mechanical approach. Torsion pendulum is a general tool to measure angular momentum by torque balance. Our torsion pendulum can harvest the angular momentum in liquid crystals to make it observable. The oscillation of the pendulum keeps increasing by constructively adding a small angular momentum of liquid crystals each period at the resonant frequency of the pendulum. Its similar to a swing driven by a force at its resonant frequency. For the torsion pendulum, a cage made of two aluminum discs, in which a liquid crystal cell is placed, is suspended between two thin tungsten wires. A gold mirror, which is a part of the optical lever system, is attached on one tungsten wire. As first demonstration, we fabricate a circular hybrid liquid crystal cell, which can induce concentric backflows to generate angular momentum. The alignment on the planar substrate is concentric and tangential. Due to the coupling between director rotation and flow, the induced backflow goes around the cell when we add electrical pulses between top and bottom substrates. The oscillation is observed by a position sensitive detector and analyzed on the basis of Eriksen-Leslie theory. With vacuum condition and synchronous driving system, the oscillation signal is improved. We demonstrate that this torsion pendulum can sensitively detect the angular momentum in liquid crystals.

Demonstration of a switchable damping system to allow low-noise operation of high-Q low-mass suspension systems

NASA Astrophysics Data System (ADS)

Hennig, Jan-Simon; Barr, Bryan W.; Bell, Angus S.; Cunningham, William; Danilishin, Stefan L.; Dupej, Peter; Gräf, Christian; Hough, James; Huttner, Sabina H.; Jones, Russell; Leavey, Sean S.; Pascucci, Daniela; Sinclair, Martin; Sorazu, Borja; Spencer, Andrew; Steinlechner, Sebastian; Strain, Kenneth A.; Wright, Jennifer; Zhang, Teng; Hild, Stefan

2017-12-01

Low-mass suspension systems with high-Q pendulum stages are used to enable quantum radiation pressure noise limited experiments. Utilizing multiple pendulum stages with vertical blade springs and materials with high-quality factors provides attenuation of seismic and thermal noise; however, damping of these high-Q pendulum systems in multiple degrees of freedom is essential for practical implementation. Viscous damping such as eddy-current damping can be employed, but it introduces displacement noise from force noise due to thermal fluctuations in the damping system. In this paper we demonstrate a passive damping system with adjustable damping strength as a solution for this problem that can be used for low-mass suspension systems without adding additional displacement noise in science mode. We show a reduction of the damping factor by a factor of 8 on a test suspension and provide a general optimization for this system.

Development of a two-dimensional dual pendulum thrust stand for Hall thrusters

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

Nagao, N.; Yokota, S.; Komurasaki, K.

A two-dimensional dual pendulum thrust stand was developed to measure thrust vectors (axial and horizontal (transverse) direction thrusts) of a Hall thruster. A thruster with a steering mechanism is mounted on the inner pendulum, and thrust is measured from the displacement between inner and outer pendulums, by which a thermal drift effect is canceled out. Two crossover knife-edges support each pendulum arm: one is set on the other at a right angle. They enable the pendulums to swing in two directions. Thrust calibration using a pulley and weight system showed that the measurement errors were less than 0.25 mN (1.4%)more » in the main thrust direction and 0.09 mN (1.4%) in its transverse direction. The thrust angle of the thrust vector was measured with the stand using the thruster. Consequently, a vector deviation from the main thrust direction of {+-}2.3 deg. was measured with the error of {+-}0.2 deg. under the typical operating conditions for the thruster.« less

A classification of large amplitude oscillations of a spring-pendulum system

NASA Technical Reports Server (NTRS)

Broucke, R.

1977-01-01

We present a detailed classification of large amplitude oscillations of a non-integrable autonomous system with two degrees of freedom: the spring pendulum system. The classification is made with the method of invariant curves. The results show the importance of three types of motion: periodic, quasi-periodic and semi-ergodic. The numerical results are given for nine different values of the energy constant.

Automatic design optimization tool for passive structural control systems

NASA Astrophysics Data System (ADS)

Mojolic, Cristian; Hulea, Radu; Parv, Bianca Roxana

2017-07-01

The present paper proposes an automatic dynamic process in order to find the parameters of the seismic isolation systems applied to large span structures. Three seismic isolation solutions are proposed for the model of the new Slatina Sport Hall. The first case uses friction pendulum system (FP), the second one uses High Damping Rubber Bearing (HDRB) and Lead Rubber Bearings, while (LRB) are used for the last case of isolation. The placement of the isolation level is at the top end of the roof supporting columns. The aim is to calculate the parameters of each isolation system so that the whole's structure first vibration periods is the one desired by the user. The model is computed with the use of SAP2000 software. In order to find the best solution for the optimization problem, an optimization process based on Genetic Algorithms (GA) has been developed in Matlab. With the use of the API (Application Programming Interface) libraries a two way link is created between the two programs in order to exchange results and link parameters. The main goal is to find the best seismic isolation method for each desired modal period so that the bending moment on the supporting columns should be minimum.

Simulation and Visualization of Chaos in a Driven Nonlinear Pendulum -- An Aid to Introducing Chaotic Systems in Physics

NASA Astrophysics Data System (ADS)

Akpojotor, Godfrey; Ehwerhemuepha, Louis; Amromanoh, Ogheneriobororue

2013-03-01

The presence of physical systems whose characteristics change in a seemingly erratic manner gives rise to the study of chaotic systems. The characteristics of these systems are due to their hypersensitivity to changes in initial conditions. In order to understand chaotic systems, some sort of simulation and visualization is pertinent. Consequently, in this work, we have simulated and graphically visualized chaos in a driven nonlinear pendulum as a means of introducing chaotic systems. The results obtained which highlight the hypersensitivity of the pendulum are used to discuss the effectiveness of teaching and learning the physics of chaotic system using Python. This study is one of the many studies under the African Computational Science and Engineering Tour Project (PASET) which is using Python to model, simulate and visualize concepts, laws and phenomena in Science and Engineering to compliment the teaching/learning of theory and experiment.

Stability of controlled inverted pendulum under permanent horizontal perturbations of the supporting point

NASA Astrophysics Data System (ADS)

Aleksandrov, V. V.; Reyes-Romero, M.; Sidorenko, G. Yu.; Temoltzi-Auila, R.

2010-04-01

We consider the problem of choosing a test perturbation of a movable foundation of a single-link inverted pendulum so as to test a vestibular prosthesis prototype located at the top of this pendulum in an extreme situation. The obtained results permit concluding that the information transmitted from otolithic organs of the human vestibular system to muscles of the locomotor apparatus is very important and improves the quality of stabilization of the human vertical posture preventing the possible fall.

[Isolation and preparation of an imidazole alkaloid from radix radix of Aconitum pendulum Busch by semi-preparative high-speed counter-current chromatography].

PubMed

Liu, Yongling; Chen, Tao; Chen, Chen; Zou, Denglang; Li, Yulin

2014-05-01

Aconitum pendulum Busch is rich C19 diterpenoid alkaloids, but there is no report of imidazole alkaloid in Aconitum pendulum Busch. In this study, an imidazole alkaloid named 1H-imidazole-2-carboxylic acid, butyl ester (ICABE) was successfully separated from Aconitum pendulum Busch with semi-preparative high-speed counter-current chromatography (HSCCC). The partition coefficient was measured by HPLC to select the solvent systems for ICABE separation by HSCCC. The separation was performed with a two-phase solvent system composed of n-hexane-chloroform-ethanol-water (10:1 : 13:2, v/v/v/v). The upper phase was used as the stationary phase and the lower phase as the mobile phase. It was operated at a flow rate of 1.8 mL/min. The apparatus was rotated at 850 r/min, and the detection wavelength was set at 230 nm. Under the selected conditions, a high efficiency separation of HSCCC was achieved, and 7.5 mg of ICABE was obtained from 100 mg of the crude sample of Aconitum pendulum in one-step separation within 350 min. The HPLC analysis showed that the purity of the compound was over 98%. The chemical structure was confirmed by UV, 1H-NMR and 13C-NMR. The established method is simple, highly efficient and suitable for large scale separation of ICABE from radix of Aconitum pendulum Busch.

Control of the constrained planar simple inverted pendulum

NASA Technical Reports Server (NTRS)

Bavarian, B.; Wyman, B. F.; Hemami, H.

1983-01-01

Control of a constrained planar inverted pendulum by eigenstructure assignment is considered. Linear feedback is used to stabilize and decouple the system in such a way that specified subspaces of the state space are invariant for the closed-loop system. The effectiveness of the feedback law is tested by digital computer simulation. Pre-compensation by an inverse plant is used to improve performance.

Investigation of UH-60A Rotor Structural Loads from Flight and Wind Tunnel Tests

DTIC Science & Technology

2016-05-19

and main rotor blades. A bifilar pendulum -type vibration absorber system was mounted on top of the hub to reduce 3/rev rotating in-plane loads. Main... pendulum weights were not attached (no 3/rev in-plane load absorption). The rotor assembly was mounted on a large test stand with its own fixed system

Shock-operated valve would automatically protect fluid systems

NASA Technical Reports Server (NTRS)

Branum, L. W.; Wells, G. H.

1966-01-01

Glandless valve shuts down high-pressure fluid systems when severe shock from an explosion or earthquake occurs. The valve uses a pendulum to support the valve closure plug in the open position. When jarred, the valve body is moved relative to the pendulum and the plug support is displaced, allowing the plug to seat and be held by spring pressure.

Dynamic Modeling and Simulation of a Rotational Inverted Pendulum

NASA Astrophysics Data System (ADS)

Duart, J. L.; Montero, B.; Ospina, P. A.; González, E.

2017-01-01

This paper presents an alternative way to the dynamic modeling of a rotational inverted pendulum using the classic mechanics known as Euler-Lagrange allows to find motion equations that describe our model. It also has a design of the basic model of the system in SolidWorks software, which based on the material and dimensions of the model provides some physical variables necessary for modeling. In order to verify the theoretical results, It was made a contrast between the solutions obtained by simulation SimMechanics-Matlab and the system of equations Euler-Lagrange, solved through ODE23tb method included in Matlab bookstores for solving equations systems of the type and order obtained. This article comprises a pendulum trajectory analysis by a phase space diagram that allows the identification of stable and unstable regions of the system.

Linear active disturbance rejection control of underactuated systems: the case of the Furuta pendulum.

PubMed

Ramírez-Neria, M; Sira-Ramírez, H; Garrido-Moctezuma, R; Luviano-Juárez, A

2014-07-01

An Active Disturbance Rejection Control (ADRC) scheme is proposed for a trajectory tracking problem defined on a nonfeedback linearizable Furuta Pendulum example. A desired rest to rest angular position reference trajectory is to be tracked by the horizontal arm while the unactuated vertical pendulum arm stays around its unstable vertical position without falling down during the entire maneuver and long after it concludes. A linear observer-based linear controller of the ADRC type is designed on the basis of the flat tangent linearization of the system around an arbitrary equilibrium. The advantageous combination of flatness and the ADRC method makes it possible to on-line estimate and cancels the undesirable effects of the higher order nonlinearities disregarded by the linearization. These effects are triggered by fast horizontal arm tracking maneuvers driving the pendulum substantially away from the initial equilibrium point. Convincing experimental results, including a comparative test with a sliding mode controller, are presented. © 2013 ISA. Published by ISA. All rights reserved.

Pendulum Motion in Main Parachute Clusters

NASA Technical Reports Server (NTRS)

Ray, Eric S.; Machin, Ricardo A.

2015-01-01

The coupled dynamics of a cluster of parachutes to a payload are notoriously difficult to predict. Often the payload is designed to be insensitive to the range of attitude and rates that might occur, but spacecraft generally do not have the mass and volume budgeted for this robust of a design. The National Aeronautics and Space Administration (NASA) Orion Capsule Parachute Assembly System (CPAS) implements a cluster of three mains for landing. During testing of the Engineering Development Unit (EDU) design, it was discovered that with a cluster of two mains (a fault tolerance required for human rating) the capsule coupled to the parachute cluster could get into a limit cycle pendulum motion which would exceed the spacecraft landing capability. This pendulum phenomenon could not be predicted with the existing models and simulations. A three phased effort has been undertaken to understand the consequence of the pendulum motion observed, and explore potential design changes that would mitigate this phenomenon. This paper will review the early analysis that was performed of the pendulum motion observed during EDU testing, summarize the analysis ongoing to understand the root cause of the pendulum phenomenon, and discuss the modeling and testing that is being pursued to identify design changes that would mitigate the risk.

Simultaneous measurement of friction and wear in hip simulators.

PubMed

Haider, Hani; Weisenburger, Joel N; Garvin, Kevin L

2016-05-01

We propose and have evaluated a method to measure hip friction during wear testing on a popular multi-station hip simulator. A 6-degree-of-freedom load cell underneath the specimen sensed forces and torques during implant wear testing of simulated walking. This included internal-external and adduction-abduction rotations which are often neglected during friction testing on pendulum-type machines. Robust mathematical analysis and data processing provided friction estimates in three simultaneous orthogonal rotations, over extended multi-million cycle wear tests. We tested various bearing couples including metal-on-plastic, ceramic-on-plastic, and metal-on-metal material couples. In one test series, new and intentionally scratched CoCrMo 40-mm-diameter femoral heads were tested against conventional ultrahigh-molecular-weight polyethylene, highly cross-linked, and highly cross-linked with vitamin E versions. The scratching significantly increased friction and doubled the wear of all groups. Before scratching, friction levels for the aforementioned plastic groups were 0.056 ± 0.0060, 0.062 ± 0.0080, and 0.070 ± 0.0045, respectively, but after scratching increased to 0.088 ± 0.018, 0.076 ± 0.0066, and 0.082 ± 0.0049, respectively, all statistically significant increases (p = 0.00059, 0.00005, 0.0115, respectively). In another test series of 44-mm femoral head diameter hips, metal-on-plastic hips with conventional ultrahigh-molecular-weight polyethylene showed the lowest friction at 0.045 ± 0.0085, followed by highly cross-linked with 0.046 ± 0.0035 (not significantly different). In a ceramic-on-plastic design with conventional ultrahigh-molecular-weight polyethylene, higher friction 0.079 ± 0.0070 was measured likely due to that ceramic surface being rougher than usual. Metal-on-metal hips were compared without and with a TiN coating, resulting in 0.049 ± 0.014 and 0.097 ± 0.020 friction factors, respectively (statistically significant, p < 0.001), and the coating wore away on all coated hips eventually. Higher friction mostly correlated with higher wear or damage to femoral heads or implant coatings, except for the highly cross-linked wear resistant ultrahigh-molecular-weight polyethylene which had slightly higher friction, confirming the same finding in other independent studies. This type of friction measurements can help screen for clamping and elevated wear of metal-on-metal and resurfacing total hip replacements, surgical malpositioning, and abraded and otherwise damaged surfaces. © IMechE 2016.

An energy-optimal solution for transportation control of cranes with double pendulum dynamics: Design and experiments

NASA Astrophysics Data System (ADS)

Sun, Ning; Wu, Yiming; Chen, He; Fang, Yongchun

2018-03-01

Underactuated cranes play an important role in modern industry. Specifically, in most situations of practical applications, crane systems exhibit significant double pendulum characteristics, which makes the control problem quite challenging. Moreover, most existing planners/controllers obtained with standard methods/techniques for double pendulum cranes cannot minimize the energy consumption when fulfilling the transportation tasks. Therefore, from a practical perspective, this paper proposes an energy-optimal solution for transportation control of double pendulum cranes. By applying the presented approach, the transportation objective, including fast trolley positioning and swing elimination, is achieved with minimized energy consumption, and the residual oscillations are suppressed effectively with all the state constrains being satisfied during the entire transportation process. As far as we know, this is the first energy-optimal solution for transportation control of underactuated double pendulum cranes with various state and control constraints. Hardware experimental results are included to verify the effectiveness of the proposed approach, whose superior performance is reflected by being experimentally compared with some comparative controllers.

Proposal of a new electromechanical total artificial heart: the TAH Serpentina.

PubMed

Sauer, I M; Frank, J; Bücherl, E S

1999-03-01

A new type of energy converter for an electro-mechanical total artificial heart (TAH) based on the principle of a unidirectional moving motor is described. Named the TAH Serpentina, the concept consists of 2 major parts, a pendulum shaped movable element fixed on one side using a joint bearing and a special shaped drum cam. Pusher plates are mounted flexibly to the crossbar of the pendulum. A motor drives the special shaped drum cam linked to the pendulum through a ball bearing. The circular motion of the unidirectional moving brushless DC motor is transferred into the linear motion of the pendulum to drive the pusher plates. Using a crossbar with a variable length, the stroke of the pendulum and therefore the displaced blood volume is alterable. To achieve a variable length, an electric driven screw thread or a hydraulic system is possible. Comparable to the natural heart, cardiac output would be determined by frequency and stroke volume.

Cervical total disc replacement exhibits similar stiffness to intact cervical functional spinal units tested on a dynamic pendulum testing system.

PubMed

Esmende, Sean M; Daniels, Alan H; Paller, David J; Koruprolu, Sarath; Palumbo, Mark A; Crisco, Joseph J

2015-01-01

The pendulum testing system is capable of applying physiologic compressive loads without constraining the motion of functional spinal units (FSUs). The number of cycles to equilibrium observed under pendulum testing is a measure of the energy absorbed by the FSU. To examine the dynamic bending stiffness and energy absorption of the cervical spine, with and without implanted cervical total disc replacement (TDR) under simulated physiologic motion. A biomechanical cadaver investigation. Nine unembalmed, frozen human cervical FSUs from levels C3-C4 and C5-C6 were tested on the pendulum system with axial compressive loads of 25, 50, and 100 N before and after TDR implantation. Testing in flexion, extension, and lateral bending began by rotating the pendulum to 5°, resulting in unconstrained oscillatory motion. The number of rotations to equilibrium was recorded and the bending stiffness (Newton-meter/°) was calculated and compared for each testing mode. In flexion/extension, with increasing compressive loading from 25 to 100 N, the average number of cycles to equilibrium for the intact FSUs increased from 6.6 to 19.1, compared with 4.1 to 12.7 after TDR implantation (p<.05 for loads of 50 and 100 N). In flexion, with increasing compressive loading from 25 to 100 N, the bending stiffness of the intact FSUs increased from 0.27 to 0.59 Nm/°, compared with 0.21 to 0.57 Nm/° after TDR implantation. No significant differences were found in stiffness between the intact FSU and the TDR in flexion/extension and lateral bending at any load (p<.05). Cervical FSUs with implanted TDR were found to have similar stiffness, but had greater energy absorption than intact FSUs during cyclic loading with an unconstrained pendulum system. These results provide further insight into the biomechanical behavior of cervical TDR under approximated physiologic loading conditions. Copyright © 2015 Elsevier Inc. All rights reserved.

Dynamic biomechanical examination of the lumbar spine with implanted total disc replacement using a pendulum testing system.

PubMed

Daniels, Alan H; Paller, David J; Koruprolu, Sarath; McDonnell, Matthew; Palumbo, Mark A; Crisco, Joseph J

2012-11-01

Biomechanical cadaver investigation. To examine dynamic bending stiffness and energy absorption of the lumbar spine with and without implanted total disc replacement (TDR) under simulated physiological motion. The pendulum testing system is capable of applying physiological compressive loads without constraining motion of functional spinal units (FSUs). The number of cycles to equilibrium observed under pendulum testing is a measure of the energy absorbed by the FSU. Five unembalmed, frozen human lumbar FSUs were tested on the pendulum system with axial compressive loads of 181 N, 282 N, 385 N, and 488 N before and after Synthes ProDisc-L TDR implantation. Testing in flexion, extension, and lateral bending began by rotating the pendulum to 5º resulting in unconstrained oscillatory motion. The number of rotations to equilibrium was recorded and bending stiffness (N·m/º) was calculated and compared for each testing mode. In flexion/extension, the TDR constructs reached equilibrium with significantly (P < 0.05) fewer cycles than the intact FSU with compressive loads of 282 N, 385 N, and 488 N. Mean dynamic bending stiffness in flexion, extension, and lateral bending increased significantly with increasing load for both the intact FSU and TDR constructs (P < 0.001). In flexion, with increasing compressive loading from 181 N to 488 N, the bending stiffness of the intact FSUs increased from 4.0 N·m/º to 5.5 N·m/º, compared with 2.1 N·m/º to 3.6 N·m/º after TDR implantation. At each compressive load, the intact FSU was significantly stiffer than the TDR (P < 0.05). Lumbar FSUs with implanted TDR were found to be less stiff, but absorbed more energy during cyclic loading with an unconstrained pendulum system. Although the effects on clinical performance of motion-preserving devices are not fully known, these results provide further insight into the biomechanical behavior of these devices under approximated physiological loading conditions.

Orion Multi-Purpose Crew Vehicle Solving and Mitigating the Two Main Cluster Pendulum Problem

NASA Technical Reports Server (NTRS)

Ali, Yasmin; Sommer, Bruce; Troung, Tuan; Anderson, Brian; Madsen, Christopher

2017-01-01

The Orion Multi-purpose Crew Vehicle (MPCV) Orion spacecraft will return humans from beyond earth's orbit, including Mars and will be required to land 20,000 pounds of mass safely in the ocean. The parachute system nominally lands under 3 main parachutes, but the system is designed to be fault tolerant and land under 2 main parachutes. During several of the parachute development tests, it was observed that a pendulum, or swinging, motion could develop while the Crew Module (CM) was descending under two parachutes. This pendulum effect had not been previously predicted by modeling. Landing impact analysis showed that the landing loads would double in some places across the spacecraft. The CM structural design limits would be exceeded upon landing if this pendulum motion were to occur. The Orion descent and landing team was faced with potentially millions of dollars in structural modifications and a severe mass increase. A multidisciplinary team was formed to determine root cause, model the pendulum motion, study alternate canopy planforms and assess alternate operational vehicle controls & operations providing mitigation options resulting in a reliability level deemed safe for human spaceflight. The problem and solution is a balance of risk to a known solution versus a chance to improve the landing performance for the next human-rated spacecraft.

Intermittent Feedback-Control Strategy for Stabilizing Inverted Pendulum on Manually Controlled Cart as Analogy to Human Stick Balancing

PubMed Central

Yoshikawa, Naoya; Suzuki, Yasuyuki; Kiyono, Ken; Nomura, Taishin

2016-01-01

The stabilization of an inverted pendulum on a manually controlled cart (cart-inverted-pendulum; CIP) in an upright position, which is analogous to balancing a stick on a fingertip, is considered in order to investigate how the human central nervous system (CNS) stabilizes unstable dynamics due to mechanical instability and time delays in neural feedback control. We explore the possibility that a type of intermittent time-delayed feedback control, which has been proposed for human postural control during quiet standing, is also a promising strategy for the CIP task and stick balancing on a fingertip. Such a strategy hypothesizes that the CNS exploits transient contracting dynamics along a stable manifold of a saddle-type unstable upright equilibrium of the inverted pendulum in the absence of control by inactivating neural feedback control intermittently for compensating delay-induced instability. To this end, the motions of a CIP stabilized by human subjects were experimentally acquired, and computational models of the system were employed to characterize the experimental behaviors. We first confirmed fat-tailed non-Gaussian temporal fluctuation in the acceleration distribution of the pendulum, as well as the power-law distributions of corrective cart movements for skilled subjects, which was previously reported for stick balancing. We then showed that the experimental behaviors could be better described by the models with an intermittent delayed feedback controller than by those with the conventional continuous delayed feedback controller, suggesting that the human CNS stabilizes the upright posture of the pendulum by utilizing the intermittent delayed feedback-control strategy. PMID:27148031

The frequency of human, manual adjustments in balancing an inverted pendulum is constrained by intrinsic physiological factors

PubMed Central

Loram, Ian D; Gawthrop, Peter J; Lakie, Martin

2006-01-01

While standing naturally and when manually or pedally balancing an equivalent inverted pendulum, the load sways slowly (characteristic unidirectional duration ∼1 s) and the controller, calf muscles or hand, makes more frequent adjustments (characteristic unidirectional duration 400 ms). Here we test the hypothesis that these durations reflect load properties rather than some intrinsic property of the human neuromuscular system. Using a specialized set-up mechanically analogous to real standing, subjects manually balanced inverted pendulums with different moments of inertia through a compliant spring representing the Achilles tendon. The spring bias was controlled by a sensitive joystick via a servo motor and accurate visual feedback was provided on an oscilloscope. As moment of inertia decreased, inverted pendulum sway size increased and it became difficult to sustain successful balance. The mean duration of unidirectional balance adjustments did not change. Moreover, the mean duration of unidirectional inverted pendulum sway reduced only slightly, remaining around 1 s. The simplest explanation is that balance was maintained by a process of manual adjustments intrinsically limited to a mean frequency of two to three unidirectional adjustments per second corresponding to intermittent control observed in manual tracking experiments. Consequently the inverted pendulum sway duration, mechanically related to the bias duration, reflects an intrinsic constraint of the neuromuscular control system. Given the similar durations of sway and muscle adjustments observed in real standing, we postulate that the characteristic duration of unidirectional standing sway reflects intrinsic intermittent control rather than the inertial properties of the body. PMID:16973712

Intermittent Feedback-Control Strategy for Stabilizing Inverted Pendulum on Manually Controlled Cart as Analogy to Human Stick Balancing.

PubMed

Yoshikawa, Naoya; Suzuki, Yasuyuki; Kiyono, Ken; Nomura, Taishin

2016-01-01

The stabilization of an inverted pendulum on a manually controlled cart (cart-inverted-pendulum; CIP) in an upright position, which is analogous to balancing a stick on a fingertip, is considered in order to investigate how the human central nervous system (CNS) stabilizes unstable dynamics due to mechanical instability and time delays in neural feedback control. We explore the possibility that a type of intermittent time-delayed feedback control, which has been proposed for human postural control during quiet standing, is also a promising strategy for the CIP task and stick balancing on a fingertip. Such a strategy hypothesizes that the CNS exploits transient contracting dynamics along a stable manifold of a saddle-type unstable upright equilibrium of the inverted pendulum in the absence of control by inactivating neural feedback control intermittently for compensating delay-induced instability. To this end, the motions of a CIP stabilized by human subjects were experimentally acquired, and computational models of the system were employed to characterize the experimental behaviors. We first confirmed fat-tailed non-Gaussian temporal fluctuation in the acceleration distribution of the pendulum, as well as the power-law distributions of corrective cart movements for skilled subjects, which was previously reported for stick balancing. We then showed that the experimental behaviors could be better described by the models with an intermittent delayed feedback controller than by those with the conventional continuous delayed feedback controller, suggesting that the human CNS stabilizes the upright posture of the pendulum by utilizing the intermittent delayed feedback-control strategy.

CORRECTION OF THE INERTIAL EFFECT RESULTING FROM A PLATE MOVING UNDER LOW FRICTION CONDITIONS

PubMed Central

Yang, Feng; Pai, Yi-Chung

2007-01-01

The purpose of the present study was to develop a set of equations that can be employed to remove the inertial effect introduced by the movable platform upon which a person stands during a slip induced in gait; this allows the real ground reaction force (GRF) and its center of pressure (COP) to be determined. Analyses were also performed to determine how sensitive the COP offsets were to the changes of the parameters in the equation that affected the correction of the inertial effect. In addition, the results were verified empirically using a low friction movable platform together with a stationary object, a pendulum, and human subjects during a slip induced during gait. Our analyses revealed that the amount of correction required for the inertial effect due to the movable component is affected by its mass and its center of mass (COM) position, acceleration, the friction coefficient, and the landing position of the foot relative to the COM. The maximum error in the horizontal component of the GRF was close to 0.09 body weight during the recovery from a slip in walking. When uncorrected, the maximum error in the COP measurement could reach as much as 4 cm. Finally, these errors were magnified in the joint moment computation and propagated proximally, ranging from 0.2 to 1.0 Nm/body mass from the ankle to the hip. PMID:17306274

Polyurethane as a potential knee hemiarthroplasty biomaterial: an in-vitro simulation of its tribological performance.

PubMed

Luo, Y; McCann, L; Ingham, E; Jin, Z-M; Ge, S; Fisher, J

2010-01-01

Hemiarthroplasty is an attractive alternative to total joint replacement for the young active patient, when only one side of the synovial joint is damaged. In the development of a hemiarthroplasty prosthesis, a comprehensive understanding of the tribology of both the natural joint and the hemireplaced joint is necessary. The objectives of this study were to investigate the tribological response of polyurethane (PU) as a potential hemiarthroplasty material. Bovine medial compartmental knees were tested in a Prosim pendulum friction simulator, which applied physiologically relevant loading and motion. The healthy medial compartment was investigated as a negative control; a stainless steel hemiarthroplasty was investigated as a positive control; and three PU hemiarthroplasty plates of different moduli (1.4 MPa, 6.5 MPa, and 22 MPa) were also investigated. Using the lower-modulus PU caused reduced levels of contact stress and friction shear stress, which resulted in reduced levels of opposing cartilage wear. The two PU bearings with the lowest moduli demonstrated a similar tribological performance to the negative control. The higher-modulus PU (22 MPa) did demonstrate higher levels of friction shear stress, and wear resulted on the opposing cartilage, although not as severe as the wear from the stainless steel group. This study supports the use of compliant PU designs in future tribological experiments and hemiarthroplasty design applications.

Extending the Range for Force Calibration in Magnetic Tweezers

PubMed Central

Daldrop, Peter; Brutzer, Hergen; Huhle, Alexander; Kauert, Dominik J.; Seidel, Ralf

2015-01-01

Magnetic tweezers are a wide-spread tool used to study the mechanics and the function of a large variety of biomolecules and biomolecular machines. This tool uses a magnetic particle and a strong magnetic field gradient to apply defined forces to the molecule of interest. Forces are typically quantified by analyzing the lateral fluctuations of the biomolecule-tethered particle in the direction perpendicular to the applied force. Since the magnetic field pins the anisotropy axis of the particle, the lateral fluctuations follow the geometry of a pendulum with a short pendulum length along and a long pendulum length perpendicular to the field lines. Typically, the short pendulum geometry is used for force calibration by power-spectral-density (PSD) analysis, because the movement of the bead in this direction can be approximated by a simple translational motion. Here, we provide a detailed analysis of the fluctuations according to the long pendulum geometry and show that for this direction, both the translational and the rotational motions of the particle have to be considered. We provide analytical formulas for the PSD of this coupled system that agree well with PSDs obtained in experiments and simulations and that finally allow a faithful quantification of the magnetic force for the long pendulum geometry. We furthermore demonstrate that this methodology allows the calibration of much larger forces than the short pendulum geometry in a tether-length-dependent manner. In addition, the accuracy of determination of the absolute force is improved. Our force calibration based on the long pendulum geometry will facilitate high-resolution magnetic-tweezers experiments that rely on short molecules and large forces, as well as highly parallelized measurements that use low frame rates. PMID:25992733

Foucault pendulum with eddy-current damping of the elliptical motion

NASA Astrophysics Data System (ADS)

Mastner, G.; Vokurka, V.; Maschek, M.; Vogt, E.; Kaufmann, H. P.

1984-10-01

A newly designed Foucault pendulum is described in which the mechanical Charron ring, used throughout in previous designs for damping of the elliptical motion of the pendulum, is replaced by an electromagnetic eddy-current brake, consisting of a permanent magnet attached to the bottom of the bob and a metallic ring. This damping device is very efficient, as it is self-aligning, symmetrical in the damping effect, and never wears out. The permanent magnet is also used, together with a coil assembly and an electronic circuitry, for the dipole-torque drive of the pendulum as well as for accurate stabilization of the amplitude of the swing. A latched time display, controlled by Hall probes activated by the magnet, is used to visualize the Foucault rotation. The pendulum system and its associated electronic circuitry are described in detail. The optimizing of the drive mode is discussed. Measurements of deviations from theoretical value of the Foucault rotation velocity made automatically in a continuous run show a reproducible accuracy of ±1% or better in individual 360° rotations during the summer months. The quality factor of the pendulum as mechanical resonator was measured as a function of the amplitude in the presence of the eddy-current damping ring.

Pendulum Therapy of Molar Distalization in Mixed Dentition.

PubMed

Patil, Raju Umaji; Prakash, Amit; Agarwal, Anshu

2016-01-01

Early and timely pedo-orthodontic treatment is aimed at eliminating the disturbances of skeletal or dentoalveolar development, to harmonize the stomatognathic system before the full eruption of all permanent teeth. The advantages of pendulum appliance are its minimal dependence on patient's compliance (child cooperation), ease of fabrication, onetime activation and adjustment of the springs if necessary to correct minor transverse and vertical molar positions. This article reports a successful treatment method of class II malocclusion with pendulum appliance in mixed dentition phase. Distalization of maxillary molar was done, followed by guidance of canine impaction orthodontically and other dental correction using 0.022 MBT appliances. Posttreatment results were stable and remarkable. How to cite this article: Patil RU, Prakash A, Agarwal A. Pendulum Therapy of Molar Distalization in Mixed Dentition. Int J Clin Pediatr Dent 2016;9(1):67-73.

Pendulum Therapy of Molar Distalization in Mixed Dentition

PubMed Central

Prakash, Amit; Agarwal, Anshu

2016-01-01

ABSTRACT Early and timely pedo-orthodontic treatment is aimed at eliminating the disturbances of skeletal or dentoalveolar development, to harmonize the stomatognathic system before the full eruption of all permanent teeth. The advantages of pendulum appliance are its minimal dependence on patient’s compliance (child cooperation), ease of fabrication, onetime activation and adjustment of the springs if necessary to correct minor transverse and vertical molar positions. This article reports a successful treatment method of class II malocclusion with pendulum appliance in mixed dentition phase. Distalization of maxillary molar was done, followed by guidance of canine impaction orthodontically and other dental correction using 0.022 MBT appliances. Posttreatment results were stable and remarkable. How to cite this article: Patil RU, Prakash A, Agarwal A. Pendulum Therapy of Molar Distalization in Mixed Dentition. Int J Clin Pediatr Dent 2016;9(1):67-73. PMID:27274159

Determination of the Optimal Position of Pendulums of an Active Self-balancing Device

NASA Astrophysics Data System (ADS)

Ziyakaev, G. R.; Kazakova, O. A.; Yankov, V. V.; Ivkina, O. P.

2017-04-01

The demand of the modern manufacturing industry for machines with high motion speed leads to increased load and vibration activity of the main elements of rotor systems. Vibration reduces operating life of bearings, has adversary effects on human organism, and can cause accidents. One way to compensate for a rotating rotor's imbalance is the use of active self-balancing devices. The aim of this work is to determine the position of their pendulums, in which the imbalance is minimized. As a result of the study, a formula for determining the angle of the pendulums was obtained.

Robust sliding mode control applied to double Inverted pendulum system

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

Mahjoub, Sonia; Derbel, Nabil; Mnif, Faical

A three hierarchical sliding mode control is presented for a class of an underactuated system which can overcome the mismatched perturbations. The considered underactuated system is a double inverted pendulum (DIP), can be modeled by three subsystems. Such structure allows the construction of several designs of hierarchies for the controller. For all hierarchical designs, the asymptotic stability of every layer sliding mode surface and the sliding mode surface of subsystems are proved theoretically by Barbalat's lemma. Simulation results show the validity of these methods.

Dynamics and Thermodynamics of Many Particle Cold Atom Systems

DTIC Science & Technology

2016-05-05

Dynamical Stability of a Many-body Kapitza Pendulum , R. Citro, E. G. Dalla Torre, L. DÁlessio, A. Polkovnikov, M. Babadi, T. Oka, E. Demler, Annals...Kapitza Pendulum , R. Citro, E. G. Dalla Torre, L. DÁlessio, A. Polkovnikov, M. Babadi, T. Oka, E. Demler, Annals of Physics 360, 694-710 (2015). 17

Attitude Stability of a Spacecraft with Slosh Mass Subject to Parametric Excitation

NASA Astrophysics Data System (ADS)

Kang, Ja-Young

2003-09-01

The attitude motion of a spin-stabilized, upper-stage spacecraft is investigated based on a two-body model, consisting of a symmetric body, representing the spacecraft, and a spherical pendulum, representing the liquid slag pool entrapped in the aft section of the rocket motor. Exact time-varying nonlinear equations are derived and used to eliminate the drawbacks of conventional linear models. To study the stability of the spacecraft's attitude motion, both the spacecraft and pendulum are assumed to be in states of steady spin about the symmetry axis of the spacecraft and the coupled time-varying nonlinear equation of the pendulum is simplified. A quasi-stationary solution to that equation and approximate resonance conditions are determined in terms of the system parameters. The analysis shows that the pendulum is subject to a combination of parametric and external-type excitation by the main body and that energy from the excited pendulum is fed into the main body to develop the coning instability. In this paper, numerical examples are presented to explain the mechanism of the coning angle growth and how angular momenta and disturbance moments are generated.

Helicopter vibration suppression using simple pendulum absorbers on the rotor blade

NASA Technical Reports Server (NTRS)

Pierce, G. A.; Hanouva, M. N. H.

1982-01-01

A comprehensive anaytical design procedure for the installation of simple pendulums on the blades of a helicopter rotor to suppress the root reactions is presented. A frequency response anaysis is conducted of typical rotor blades excited by a harmonic variation of spanwise airload distributions as well as a concentrated load at the tip. The results presented included the effect of pendulum tuning on the minimization of the hub reactions. It is found that a properly designed flapping pendulum attenuates the root out-of-plane force and moment whereas the optimum designed lead-lag pendulum attenuates the root in-plane reactions. For optimum pendulum tuning the parameters to be determined are the pendulum uncoupled natural frequency, the pendulum spanwise location and its mass. It is found that the optimum pendulum frequency is in the vicinity of the excitation frequency. For the optimum pendulum a parametric study is conducted. The parameters varied include prepitch, pretwist, precone and pendulum hinge offset.

The Global Positioning System for Military Users: Current Modernization Plans and Alternatives

DTIC Science & Technology

2011-10-01

stronger signal would not be available. That drawback might be mitigated, however, by the widespread availability on the commercial market of small...development efforts needed to achieve such reductions would have associated costs. An additional drawback of Option 2 is that operation of iGPS...the Foucault pendulum but uses a vibrating element, known as a Micro Electro-Mechanical System, instead of an actual pendulum . iGPS Module. The

A novel approach to periodic event-triggered control: Design and application to the inverted pendulum.

PubMed

Aranda-Escolástico, Ernesto; Guinaldo, María; Gordillo, Francisco; Dormido, Sebastián

2016-11-01

In this paper, periodic event-triggered controllers are proposed for the rotary inverted pendulum. The control strategy is divided in two steps: swing-up and stabilization. In both cases, the system is sampled periodically but the control actions are only computed at certain instances of time (based on events), which are a subset of the sampling times. For the stabilization control, the asymptotic stability is guaranteed applying the Lyapunov-Razumikhin theorem for systems with delays. This result is applicable to general linear systems and not only to the inverted pendulum. For the swing-up control, a trigger function is provided from the derivative of the Lyapunov function for the swing-up control law. Experimental results show a significant improvement with respect to periodic control in the number of control actions. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Dynamic characteristics of rotor blades with pendulum absorbers

NASA Technical Reports Server (NTRS)

Murthy, V. R.; Goglia, G. L.

1977-01-01

The point transmission matrix for a vertical plane pendulum on a rotating blade undergoing combined flapwise bending, and chordwise bending and torsion is derived. The equilibrium equation of the pendulum is linearized for small oscillations about the steady state. A FORTRAN program was written for the case of a vertical plane pendulum attached to a uniform blade with flapwise bending degree of freedom for cantilever boundary conditions. The frequency has a singular value right at the uncoupled pendulum natural frequency and thus introduces two frequencies corresponding to the nearest natural frequency of the blade without pendulum. In both of these modes it was observed that the pendulum deflection is large. One frequency can be thought of as a coupled pendulum frequency and the other as a coupled bending and pendulum frequency.

Helicopter vibration suppression using simple pendulum absorbers on the rotor blade

NASA Technical Reports Server (NTRS)

Hamouda, M.-N. H.; Pierce, G. A.

1981-01-01

A design procedure is presented for the installation of simple pendulums on the blades of a helicopter rotor to suppress the root reactions. The procedure consists of a frequency response analysis for a hingeless rotor blade excited by a harmonic variation of spanwise airload distributions during forward flight, as well as a concentrated load at the tip. The structural modeling of the blade provides for elastic degrees of freedom in flap and lead-lag bending plus torsion. Simple flap and lead-lag pendulums are considered individually. Using a rational order scheme, the general nonlinear equations of motion are linearized. A quasi-steady aerodynamic representation is used in the formation of the airloads. The solution of the system equations derives from their representation as a transfer matrix. The results include the effect of pendulum tuning on the minimization of the hub reactions.

Pendulum Underwater - An Approach for Quantifying Viscosity

NASA Astrophysics Data System (ADS)

Leme, José Costa; Oliveira, Agostinho

2017-12-01

The purpose of the experiment presented in this paper is to quantify the viscosity of a liquid. Viscous effects are important in the flow of fluids in pipes, in the bloodstream, in the lubrication of engine parts, and in many other situations. In the present paper, the authors explore the oscillations of a physical pendulum in the form of a long and lightweight wire that carries a ball at its lower end, which is totally immersed in water, so as to determine the water viscosity. The system used represents a viscous damped pendulum and we tried different theoretical models to describe it. The experimental part of the present paper is based on a very simple and low-cost image capturing apparatus that can easily be replicated in a physics classroom. Data on the pendulum's amplitude as a function of time were acquired using digital video analysis with the open source software Tracker.

Hybrid Residual Flexibility/Mass-Additive Method for Structural Dynamic Testing

NASA Technical Reports Server (NTRS)

Tinker, M. L.

2003-01-01

A large fixture was designed and constructed for modal vibration testing of International Space Station elements. This fixed-base test fixture, which weighs thousands of pounds and is anchored to a massive concrete floor, initially utilized spherical bearings and pendulum mechanisms to simulate Shuttle orbiter boundary constraints for launch of the hardware. Many difficulties were encountered during a checkout test of the common module prototype structure, mainly due to undesirable friction and excessive clearances in the test-article-to-fixture interface bearings. Measured mode shapes and frequencies were not representative of orbiter-constrained modes due to the friction and clearance effects in the bearings. As a result, a major redesign effort for the interface mechanisms was undertaken. The total cost of the fixture design, construction and checkout, and redesign was over $2 million. Because of the problems experienced with fixed-base testing, alternative free-suspension methods were studied, including the residual flexibility and mass-additive approaches. Free-suspension structural dynamics test methods utilize soft elastic bungee cords and overhead frame suspension systems that are less complex and much less expensive than fixed-base systems. The cost of free-suspension fixturing is on the order of tens of thousands of dollars as opposed to millions, for large fixed-base fixturing. In addition, free-suspension test configurations are portable, allowing modal tests to be done at sites without modal test facilities. For example, a mass-additive modal test of the ASTRO-1 Shuttle payload was done at the Kennedy Space Center launch site. In this Technical Memorandum, the mass-additive and residual flexibility test methods are described in detail. A discussion of a hybrid approach that combines the best characteristics of each method follows and is the focus of the study.

On the motion of one-dimensional double pendulum

NASA Astrophysics Data System (ADS)

Burian, S. N.; Kalnitsky, V. S.

2018-05-01

A two-dimensional dynamic Lagrangian system of a double mathematical pendulum with one special constraint is considered. Configuration spaces for a given constraints (ellipses) are studied. The diagrams of paths and reactions in the course of motion along them are shown. The calculations of the transversal intersection case and in the case of tangency are given.

Power Series Solution to the Pendulum Equation

ERIC Educational Resources Information Center

Benacka, Jan

2009-01-01

This note gives a power series solution to the pendulum equation that enables to investigate the system in an analytical way only, i.e. to avoid numeric methods. A method of determining the number of the terms for getting a required relative error is presented that uses bigger and lesser geometric series. The solution is suitable for modelling the…

Generating Random Numbers by Means of Nonlinear Dynamic Systems

ERIC Educational Resources Information Center

Zang, Jiaqi; Hu, Haojie; Zhong, Juhua; Luo, Duanbin; Fang, Yi

2018-01-01

To introduce the randomness of a physical process to students, a chaotic pendulum experiment was opened in East China University of Science and Technology (ECUST) on the undergraduate level in the physics department. It was shown chaotic motion could be initiated through adjusting the operation of a chaotic pendulum. By using the data of the…

Dynamic Biomechanical Examination of the Lumbar Spine with Implanted Total Disc Replacement (TDR) Utilizing a Pendulum Testing System

PubMed Central

Daniels, Alan H; Paller, David J; Koruprolu, Sarath; McDonnell, Matthew; Palumbo, Mark A; Crisco, Joseph J

2013-01-01

Study Design Biomechanical cadaver investigation Objective To examine dynamic bending stiffness and energy absorption of the lumbar spine with and without implanted Total Disc Replacement (TDR) under simulated physiologic motion. Summary of background data The pendulum testing system is capable of applying physiologic compressive loads without constraining motion of functional spinal units (FSUs). The number of cycles to equilibrium observed under pendulum testing is a measure of the energy absorbed by the FSU. Methods Five unembalmed, frozen human lumbar FSUs were tested on the pendulum system with axial compressive loads of 181N, 282N, 385N, and 488N before and after Synthes ProDisc-L TDR implantation. Testing in flexion, extension, and lateral bending began by rotating the pendulum to 5° resulting in unconstrained oscillatory motion. The number of rotations to equilibrium was recorded and bending stiffness (N-m/°) was calculated and compared for each testing mode. Results In flexion/extension, the TDR constructs reached equilibrium with significantly (p<0.05) fewer cycles than the intact FSU with compressive loads of 282N, 385N and 488N. Mean dynamic bending stiffness in flexion, extension, and lateral bending increased significantly with increasing load for both the intact FSU and TDR constructs (p<0.001). In flexion, with increasing compressive loading from 181N to 488N, the bending stiffness of the intact FSUs increased from 4.0N-m/° to 5.5N-m/°, compared to 2.1N-m/° to 3.6N-m/° after TDR implantation. At each compressive load, the intact FSU was significantly more stiff than the TDR (p<0.05). Conclusion Lumbar FSUs with implanted TDR were found to be less stiff, but also absorbed more energy during cyclic loading with an unconstrained pendulum system. Although the effects on clinical performance of motion preserving devices are not fully known, these results provide further insight into the biomechanical behavior of this device under approximated physiologic loading conditions. PMID:22869057

A New Fuzzy-Evidential Controller for Stabilization of the Planar Inverted Pendulum System

PubMed Central

Tang, Yongchuan; Zhou, Deyun

2016-01-01

In order to realize the stability control of the planar inverted pendulum system, which is a typical multi-variable and strong coupling system, a new fuzzy-evidential controller based on fuzzy inference and evidential reasoning is proposed. Firstly, for each axis, a fuzzy nine-point controller for the rod and a fuzzy nine-point controller for the cart are designed. Then, in order to coordinate these two controllers of each axis, a fuzzy-evidential coordinator is proposed. In this new fuzzy-evidential controller, the empirical knowledge for stabilization of the planar inverted pendulum system is expressed by fuzzy rules, while the coordinator of different control variables in each axis is built incorporated with the dynamic basic probability assignment (BPA) in the frame of fuzzy inference. The fuzzy-evidential coordinator makes the output of the control variable smoother, and the control effect of the new controller is better compared with some other work. The experiment in MATLAB shows the effectiveness and merit of the proposed method. PMID:27482707

A New Fuzzy-Evidential Controller for Stabilization of the Planar Inverted Pendulum System.

PubMed

Tang, Yongchuan; Zhou, Deyun; Jiang, Wen

2016-01-01

In order to realize the stability control of the planar inverted pendulum system, which is a typical multi-variable and strong coupling system, a new fuzzy-evidential controller based on fuzzy inference and evidential reasoning is proposed. Firstly, for each axis, a fuzzy nine-point controller for the rod and a fuzzy nine-point controller for the cart are designed. Then, in order to coordinate these two controllers of each axis, a fuzzy-evidential coordinator is proposed. In this new fuzzy-evidential controller, the empirical knowledge for stabilization of the planar inverted pendulum system is expressed by fuzzy rules, while the coordinator of different control variables in each axis is built incorporated with the dynamic basic probability assignment (BPA) in the frame of fuzzy inference. The fuzzy-evidential coordinator makes the output of the control variable smoother, and the control effect of the new controller is better compared with some other work. The experiment in MATLAB shows the effectiveness and merit of the proposed method.

An automated digital data collection and analysis system for the Charpy Impact Tester

NASA Technical Reports Server (NTRS)

Kohne, Glenn S.; Spiegel, F. Xavier

1994-01-01

The standard Charpy Impact Tester has been modified by the addition of a system of hardware and software to improve the accuracy and consistency of measurements made during specimen fracturing experiments. An optical disc, light source, and detector generate signals that indicate the pendulum position as a function of time. These signals are used by a computer to calculate the velocity and kinetic energy of the pendulum as a function of its position.

Stick balancing with reflex delay in case of parametric forcing

NASA Astrophysics Data System (ADS)

Insperger, Tamas

2011-04-01

The effect of parametric forcing on a PD control of an inverted pendulum is analyzed in the presence of feedback delay. The stability of the time-periodic and time-delayed system is determined numerically using the first-order semi-discretization method in the 5-dimensional parameter space of the pendulum's length, the forcing frequency, the forcing amplitude, the proportional and the differential gains. It is shown that the critical length of the pendulum (that can just be balanced against the time-delay) can significantly be decreased by parametric forcing even if the maximum forcing acceleration is limited. The numerical analysis showed that the critical stick length about 30 cm corresponding to the unforced system with reflex delay 0.1 s can be decreased to 18 cm with keeping maximum acceleration below the gravitational acceleration.

Evaluation of dynamic electromagnetic tracking deviation

NASA Astrophysics Data System (ADS)

Hummel, Johann; Figl, Michael; Bax, Michael; Shahidi, Ramin; Bergmann, Helmar; Birkfellner, Wolfgang

2009-02-01

Electromagnetic tracking systems (EMTS's) are widely used in clinical applications. Many reports have evaluated their static behavior and errors caused by metallic objects were examined. Although there exist some publications concerning the dynamic behavior of EMTS's the measurement protocols are either difficult to reproduce with respect of the movement path or only accomplished at high technical effort. Because dynamic behavior is of major interest with respect to clinical applications we established a simple but effective modal measurement easy to repeat at other laboratories. We built a simple pendulum where the sensor of our EMTS (Aurora, NDI, CA) could be mounted. The pendulum was mounted on a special bearing to guarantee that the pendulum path is planar. This assumption was tested before starting the measurements. All relevant parameters defining the pendulum motion such as rotation center and length are determined by static measurement at satisfactory accuracy. Then position and orientation data were gathered over a time period of 8 seconds and timestamps were recorded. Data analysis provided a positioning error and an overall error combining both position and orientation. All errors were calculated by means of the well know equations concerning pendulum movement. Additionally, latency - the elapsed time from input motion until the immediate consequences of that input are available - was calculated using well-known equations for mechanical pendulums for different velocities. We repeated the measurements with different metal objects (rods made of stainless steel type 303 and 416) between field generator and pendulum. We found a root mean square error (eRMS) of 1.02mm with respect to the distance of the sensor position to the fit plane (maximum error emax = 2.31mm, minimum error emin = -2.36mm). The eRMS for positional error amounted to 1.32mm while the overall error was 3.24 mm. The latency at a pendulum angle of 0° (vertical) was 7.8ms.

Measuring g with a classroom pendulum using changes in the pendulum string length

NASA Astrophysics Data System (ADS)

Oliveira, V.

2016-11-01

This frontline presents a simple apparatus for measuring the acceleration of gravity using a classroom pendulum. Instead of the traditional method where the pendulum period is measured as a function of its length, here the period is measured as a function of changes in the pendulum string length. The major advantage of this method is that students can measure these changes with a greater accuracy than measuring the total pendulum length.

Real-Time Demonstration of the Main Characteristics of Chaos in the Motion of a Real Double Pendulum

ERIC Educational Resources Information Center

Vadai, Gergely; Gingl, Zoltan; Mellar, Janos

2012-01-01

Several studies came to the conclusion that chaotic phenomena are worth including in high school and undergraduate education. The double pendulum is one of the simplest systems that is chaotic; therefore, numerical simulations and theoretical studies of it have been given large publicity, and thanks to its spectacular motion, it has become one of…

Effective equations for the quantum pendulum from momentous quantum mechanics

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

Hernandez, Hector H.; Chacon-Acosta, Guillermo; Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120

In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.

Investigation of a Chaotic Double Pendulum in the Basic Level Physics Teaching Laboratory

ERIC Educational Resources Information Center

Vanko, Peter

2007-01-01

First-year physics students at the Technical University of Budapest carry out a wide range of measurements in the Basic Level Physics Teaching Laboratory. One of the most exciting experiments is the investigation of a chaotic double pendulum by a V-scope, a powerful three-dimensional motion tracking system. After a brief introduction to the…

In plane oscillation of a bifilar pendulum

NASA Astrophysics Data System (ADS)

Hinrichsen, Peter F.

2016-11-01

The line tensions, the horizontal and vertical accelerations as well as the period of large angle oscillations parallel to the plane of a bifilar suspension are presented and have been experimentally investigated using strain gauges and a smart phone. This system has a number of advantages over the simple pendulum for studying large angle oscillations, and for measuring the acceleration due to gravity.

Effect of intermittent feedback control on robustness of human-like postural control system

NASA Astrophysics Data System (ADS)

Tanabe, Hiroko; Fujii, Keisuke; Suzuki, Yasuyuki; Kouzaki, Motoki

2016-03-01

Humans have to acquire postural robustness to maintain stability against internal and external perturbations. Human standing has been recently modelled using an intermittent feedback control. However, the causality inside of the closed-loop postural control system associated with the neural control strategy is still unknown. Here, we examined the effect of intermittent feedback control on postural robustness and of changes in active/passive components on joint coordinative structure. We implemented computer simulation of a quadruple inverted pendulum that is mechanically close to human tiptoe standing. We simulated three pairs of joint viscoelasticity and three choices of neural control strategies for each joint: intermittent, continuous, or passive control. We examined postural robustness for each parameter set by analysing the region of active feedback gain. We found intermittent control at the hip joint was necessary for model stabilisation and model parameters affected the robustness of the pendulum. Joint sways of the pendulum model were partially smaller than or similar to those of experimental data. In conclusion, intermittent feedback control was necessary for the stabilisation of the quadruple inverted pendulum. Also, postural robustness of human-like multi-link standing would be achieved by both passive joint viscoelasticity and neural joint control strategies.

Effect of intermittent feedback control on robustness of human-like postural control system.

PubMed

Tanabe, Hiroko; Fujii, Keisuke; Suzuki, Yasuyuki; Kouzaki, Motoki

2016-03-02

Humans have to acquire postural robustness to maintain stability against internal and external perturbations. Human standing has been recently modelled using an intermittent feedback control. However, the causality inside of the closed-loop postural control system associated with the neural control strategy is still unknown. Here, we examined the effect of intermittent feedback control on postural robustness and of changes in active/passive components on joint coordinative structure. We implemented computer simulation of a quadruple inverted pendulum that is mechanically close to human tiptoe standing. We simulated three pairs of joint viscoelasticity and three choices of neural control strategies for each joint: intermittent, continuous, or passive control. We examined postural robustness for each parameter set by analysing the region of active feedback gain. We found intermittent control at the hip joint was necessary for model stabilisation and model parameters affected the robustness of the pendulum. Joint sways of the pendulum model were partially smaller than or similar to those of experimental data. In conclusion, intermittent feedback control was necessary for the stabilisation of the quadruple inverted pendulum. Also, postural robustness of human-like multi-link standing would be achieved by both passive joint viscoelasticity and neural joint control strategies.

Orion GN&C Detection and Mitigation of Parachute Pendulosity

NASA Technical Reports Server (NTRS)

Kane, Mark A.; Wacker, Roger

2016-01-01

New techniques being employed by Orion guidance, navigation, and control (GN&C) using a reaction control system (RCS) under parachutes are described. Pendulosity refers to a pendulum-oscillatory mode that can occur during descent under main parachutes and that has been observed during Orion parachute drop tests. The pendulum mode reduces the ability of GN&C to maneuver the suspended vehicle resulting in undesirable increases to structural loads at touch-down. Parachute redesign efforts have been unsuccessful in reducing the pendulous behavior necessitating GN&C mitigation options. An observer has been developed to estimate the pendulum motion as well as the underlying wind velocity vector. Using this knowledge the control system maneuvers the vehicle using two separate strategies determined by a wind velocity magnitude threshold; at high wind velocities the vehicle is aligned with the wind direction and for cases with lower wind velocities the vehicle is aligned such that it is perpendicular to the swing plane. Pendulum damping techniques using RCS thrusters are discussed but have not been selected for use onboard the Orion spacecraft. The techniques discussed in this paper will be flown on Exploration Mission 1 (EM-1).

Effect of intermittent feedback control on robustness of human-like postural control system

PubMed Central

Tanabe, Hiroko; Fujii, Keisuke; Suzuki, Yasuyuki; Kouzaki, Motoki

2016-01-01

Humans have to acquire postural robustness to maintain stability against internal and external perturbations. Human standing has been recently modelled using an intermittent feedback control. However, the causality inside of the closed-loop postural control system associated with the neural control strategy is still unknown. Here, we examined the effect of intermittent feedback control on postural robustness and of changes in active/passive components on joint coordinative structure. We implemented computer simulation of a quadruple inverted pendulum that is mechanically close to human tiptoe standing. We simulated three pairs of joint viscoelasticity and three choices of neural control strategies for each joint: intermittent, continuous, or passive control. We examined postural robustness for each parameter set by analysing the region of active feedback gain. We found intermittent control at the hip joint was necessary for model stabilisation and model parameters affected the robustness of the pendulum. Joint sways of the pendulum model were partially smaller than or similar to those of experimental data. In conclusion, intermittent feedback control was necessary for the stabilisation of the quadruple inverted pendulum. Also, postural robustness of human-like multi-link standing would be achieved by both passive joint viscoelasticity and neural joint control strategies. PMID:26931281

A nearly-linear computational-cost scheme for the forward dynamics of an N-body pendulum

NASA Technical Reports Server (NTRS)

Chou, Jack C. K.

1989-01-01

The dynamic equations of motion of an n-body pendulum with spherical joints are derived to be a mixed system of differential and algebraic equations (DAE's). The DAE's are kept in implicit form to save arithmetic and preserve the sparsity of the system and are solved by the robust implicit integration method. At each solution point, the predicted solution is corrected to its exact solution within given tolerance using Newton's iterative method. For each iteration, a linear system of the form J delta X = E has to be solved. The computational cost for solving this linear system directly by LU factorization is O(n exp 3), and it can be reduced significantly by exploring the structure of J. It is shown that by recognizing the recursive patterns and exploiting the sparsity of the system the multiplicative and additive computational costs for solving J delta X = E are O(n) and O(n exp 2), respectively. The formulation and solution method for an n-body pendulum is presented. The computational cost is shown to be nearly linearly proportional to the number of bodies.

Friction-Induced Mitochondrial Dysregulation Contributes to Joint Deterioration in Prg4 Knockout Mice

PubMed Central

Waller, Kimberly A.; Zhang, Ling X.; Jay, Gregory D.

2017-01-01

Deficiency of PRG4 (lubricin), the boundary lubricant in mammalian joints, contributes to increased joint friction accompanied by superficial and upper intermediate zone chondrocyte caspase-3 activation, as shown in lubricin-null (Prg4−/−) mice. Caspase-3 activity appears to be reversible upon the restitution of Prg4 either endogenously in vivo, in a gene trap mouse, or as an applied lubricant in vitro. In this study we show that intra-articular injection of human PRG4 in vivo in Prg4−/− mice prevented caspase-3 activation in superficial zone chondrocytes and was associated with a modest decrease in whole joint friction measured ex vivo using a joint pendulum method. Non-lubricated Prg4−/− mouse cartilage shows caspase cascade activation caused by mitochondrial dysregulation, and significantly higher levels of peroxynitrite (ONOO− and −OH) and superoxide (O−2) compared to Prg4+/+ and Prg4+/− cartilage. Enzymatic activity levels of caspase 8 across Prg4 mutant mice were not significantly different, indicating no extrinsic apoptosis pathway activation. Western blots showed caspase-3 and 9 activation in Prg4−/− tissue extracts, and the appearance of nitrosylated Cys163 in the active cleft of caspase-3 which inhibits its enzymatic activity. These findings are relevant to patients at risk for arthrosis, from camptodactyl-arthropathy-coxa vara-pericarditis (CACP) syndrome and transient lubricin insufficiency due to trauma and inflammation. PMID:28604608

Experiment with Conical Pendulum

ERIC Educational Resources Information Center

Tongaonkar, S. S.; Khadse, V. R.

2011-01-01

Conical pendulum is similar to simple pendulum with the difference that the bob, instead of moving back and forth, swings around in a horizontal circle. Thus, in a conical pendulum the bob moves at a constant speed in a circle with the string tracing out a cone. This paper describes an experiment with conical pendulum, with determination of g from…

Diagrammatic theory of transition of pendulum like systems. [orbit-orbit and spin-orbit gravitational resonance interactions

NASA Technical Reports Server (NTRS)

Yoder, C. F.

1979-01-01

Orbit-orbit and spin-orbit gravitational resonances are analyzed using the model of a rigid pendulum subject to both a time-dependent periodic torque and a constant applied torque. First, a descriptive model of passage through resonance is developed from an examination of the polynomial equation that determines the extremes of the momentum variable. From this study, a probability estimate for capture into libration is derived. Second, a lowest order solution is constructed and compared with the solution obtained from numerical integration. The steps necessary to systematically improve this solution are also discussed. Finally, the effect of a dissipative term in the pendulum equation is analyzed.

High-power, null-type, inverted pendulum thrust stand.

PubMed

Xu, Kunning G; Walker, Mitchell L R

2009-05-01

This article presents the theory and operation of a null-type, inverted pendulum thrust stand. The thrust stand design supports thrusters having a total mass up to 250 kg and measures thrust over a range of 1 mN to 5 N. The design uses a conventional inverted pendulum to increase sensitivity, coupled with a null-type feature to eliminate thrust alignment error due to deflection of thrust. The thrust stand position serves as the input to the null-circuit feedback control system and the output is the current to an electromagnetic actuator. Mechanical oscillations are actively damped with an electromagnetic damper. A closed-loop inclination system levels the stand while an active cooling system minimizes thermal effects. The thrust stand incorporates an in situ calibration rig. The thrust of a 3.4 kW Hall thruster is measured for thrust levels up to 230 mN. The uncertainty of the thrust measurements in this experiment is +/-0.6%, determined by examination of the hysteresis, drift of the zero offset and calibration slope variation.

Responding to Mechanical Antigravity

NASA Technical Reports Server (NTRS)

Millis, Marc G.; Thomas, Nicholas E.

2006-01-01

Based on the experiences of the NASA Breakthrough Propulsion Physics Project, suggestions are offered for constructively responding to proposals that purport breakthrough propulsion using mechanical devices. Because of the relatively large number of unsolicited submissions received (about 1 per workday) and because many of these involve similar concepts, this report is offered to help the would-be submitters make genuine progress as well as to help reviewers respond to such submissions. Devices that use oscillating masses or gyroscope falsely appear to create net thrust through differential friction or by misinterpreting torques as linear forces. To cover both the possibility of an errant claim and a genuine discovery, reviews should require that submitters meet minimal thresholds of proof before engaging in further correspondence; such as achieving sustained deflection of a level-platform pendulum in the case of mechanical thrusters.

Dynamics of quiet human stance: computer simulations of a triple inverted pendulum model.

PubMed

Günther, Michael; Wagner, Heiko

2016-01-01

For decades, the biomechanical description of quiet human stance has been dominated by the single inverted pendulum (SIP) paradigm. However, in the past few years, the SIP model family has been falsified as an explanatory approach. Double inverted pendulum models have recently proven to be inappropriate. Human topology with three major leg joints suggests in a natural way to examine triple inverted pendulum (TIP) models as an appropriate approach. In this study, we focused on formulating a TIP model that can synthesise stable balancing attractors based on minimalistic sensor information and actuation complexity. The simulated TIP oscillation amplitudes are realistic in vertical direction. Along with the horizontal ankle, knee and hip positions, though, all simulated joint angle amplitudes still exceed the measured ones about threefold. It is likely that they could be eventually brought down to the physiological range by using more sensor information. The TIP systems' eigenfrequency spectra come out as another major result. The eigenfrequencies spread across about 0.1 Hz...20 Hz. Our main result is that joint stiffnesses can be reduced even below statically required values by using an active hip torque balancing strategy. When reducing mono- and bi-articular stiffnesses further down to levels threatening dynamic stability, the spectra indicate a change from torus-like (stable) to strange (chaotic) attractors. Spectra of measured ground reaction forces appear to be strange-attractor-like. We would conclude that TIP models are a suitable starting point to examine more deeply the dynamic character of and the essential structural properties behind quiet human stance. Abbreviations and technical terms Inverted pendulum body exposed to gravity and pivoting in a joint around position of unstable equilibrium (operating point) SIP single inverted pendulum: one rigid body pivoting around fixation to the ground (external joint) DIP double inverted pendulum: two bodies; external and internal joint operate around instability TIP triple inverted pendulum: three bodies; external and both internal joints operate around instability QIP quadruple inverted pendulum: four bodies, foot replaces external joint; all three internal joints operate around instability Eigenfrequency characteristic frequency that a physical system is oscillating at when externally excited at a limited energy level DOF degree of freedom; in mechanics: linear displacement or angle or combination thereof Mono-articular stiffness: coefficient of proportionality between mechanical displacement of a DOF and restoring force/torque component in the respective DOF Bi-articular stiffness coefficient of proportionality between mechanical displacement of a DOF and restoring force/torque component in another DOF GRF ground reaction force HAT segment including head, arms and trunk COM centre of mass COP centre of pressure in the plane of the force platform surface.

Estimating and Comparing Dam Deformation Using Classical and GNSS Techniques.

PubMed

Barzaghi, Riccardo; Cazzaniga, Noemi Emanuela; De Gaetani, Carlo Iapige; Pinto, Livio; Tornatore, Vincenza

2018-03-02

Global Navigation Satellite Systems (GNSS) receivers are nowadays commonly used in monitoring applications, e.g., in estimating crustal and infrastructure displacements. This is basically due to the recent improvements in GNSS instruments and methodologies that allow high-precision positioning, 24 h availability and semiautomatic data processing. In this paper, GNSS-estimated displacements on a dam structure have been analyzed and compared with pendulum data. This study has been carried out for the Eleonora D'Arborea (Cantoniera) dam, which is in Sardinia. Time series of pendulum and GNSS over a time span of 2.5 years have been aligned so as to be comparable. Analytical models fitting these time series have been estimated and compared. Those models were able to properly fit pendulum data and GNSS data, with standard deviation of residuals smaller than one millimeter. These encouraging results led to the conclusion that GNSS technique can be profitably applied to dam monitoring allowing a denser description, both in space and time, of the dam displacements than the one based on pendulum observations.

Dynamic biomechanical examination of the lumbar spine with implanted total spinal segment replacement (TSSR) utilizing a pendulum testing system.

PubMed

Daniels, Alan H; Paller, David J; Koruprolu, Sarath; Palumbo, Mark A; Crisco, Joseph J

2013-01-01

Biomechanical investigations of spinal motion preserving implants help in the understanding of their in vivo behavior. In this study, we hypothesized that the lumbar spine with implanted total spinal segment replacement (TSSR) would exhibit decreased dynamic stiffness and more rapid energy absorption compared to native functional spinal units under simulated physiologic motion when tested with the pendulum system. Five unembalmed, frozen human lumbar functional spinal units were tested on the pendulum system with axial compressive loads of 181 N, 282 N, 385 N, and 488 N before and after Flexuspine total spinal segment replacement implantation. Testing in flexion, extension, and lateral bending began by rotating the pendulum to 5°; resulting in unconstrained oscillatory motion. The number of rotations to equilibrium was recorded and bending stiffness (N-m/°) was calculated and compared for each testing mode. The total spinal segment replacement reached equilibrium with significantly fewer cycles to equilibrium compared to the intact functional spinal unit at all loads in flexion (p<0.011), and at loads of 385 N and 488 N in lateral bending (p<0.020). Mean bending stiffness in flexion, extension, and lateral bending increased with increasing load for both the intact functional spinal unit and total spinal segment replacement constructs (p<0.001), with no significant differences in stiffness between the intact functional spinal unit and total spinal segment replacement in any of the test modes (p>0.18). Lumbar functional spinal units with implanted total spinal segment replacement were found to have similar dynamic bending stiffness, but absorbed energy at a more rapid rate than intact functional spinal units during cyclic loading with an unconstrained pendulum system. Although the effects on clinical performance of motion preserving devices is not fully known, these results provide further insight into the biomechanical behavior of this device under approximated physiologic loading conditions.

Dynamic Biomechanical Examination of the Lumbar Spine with Implanted Total Spinal Segment Replacement (TSSR) Utilizing a Pendulum Testing System

PubMed Central

Daniels, Alan H.; Paller, David J.; Koruprolu, Sarath; Palumbo, Mark A.; Crisco, Joseph J.

2013-01-01

Background Biomechanical investigations of spinal motion preserving implants help in the understanding of their in vivo behavior. In this study, we hypothesized that the lumbar spine with implanted total spinal segment replacement (TSSR) would exhibit decreased dynamic stiffness and more rapid energy absorption compared to native functional spinal units under simulated physiologic motion when tested with the pendulum system. Methods Five unembalmed, frozen human lumbar functional spinal units were tested on the pendulum system with axial compressive loads of 181 N, 282 N, 385 N, and 488 N before and after Flexuspine total spinal segment replacement implantation. Testing in flexion, extension, and lateral bending began by rotating the pendulum to 5°; resulting in unconstrained oscillatory motion. The number of rotations to equilibrium was recorded and bending stiffness (N-m/°) was calculated and compared for each testing mode. Results The total spinal segment replacement reached equilibrium with significantly fewer cycles to equilibrium compared to the intact functional spinal unit at all loads in flexion (p<0.011), and at loads of 385 N and 488 N in lateral bending (p<0.020). Mean bending stiffness in flexion, extension, and lateral bending increased with increasing load for both the intact functional spinal unit and total spinal segment replacement constructs (p<0.001), with no significant differences in stiffness between the intact functional spinal unit and total spinal segment replacement in any of the test modes (p>0.18). Conclusions Lumbar functional spinal units with implanted total spinal segment replacement were found to have similar dynamic bending stiffness, but absorbed energy at a more rapid rate than intact functional spinal units during cyclic loading with an unconstrained pendulum system. Although the effects on clinical performance of motion preserving devices is not fully known, these results provide further insight into the biomechanical behavior of this device under approximated physiologic loading conditions. PMID:23451222

Swinging into Pendulums with a Background.

ERIC Educational Resources Information Center

Barrow, Lloyd H.; Cook, Julie

1993-01-01

Explains reasons why students have misconceptions concerning pendulum swings. Presents a series of 10 pendulum task cards to provide middle-school students with a solid mental scaffolding upon which to build their knowledge of kinetic energy and pendulums. (PR)

Continuation of periodic orbits in symmetric Hamiltonian and conservative systems

NASA Astrophysics Data System (ADS)

Galan-Vioque, J.; Almaraz, F. J. M.; Macías, E. F.

2014-12-01

We present and review results on the continuation and bifurcation of periodic solutions in conservative, reversible and Hamiltonian systems in the presence of symmetries. In particular we show how two-point boundary value problem continuation software can be used to compute families of periodic solutions of symmetric Hamiltonian systems. The technique is introduced with a very simple model example (the mathematical pendulum), justified with a theoretical continuation result and then applied to two non trivial examples: the non integrable spring pendulum and the continuation of the figure eight solution of the three body problem.

Socio-hydrologic modeling to understand and mediate the competition for water between agriculture development and environmental health: Murrumbidgee River Basin, Australia

NASA Astrophysics Data System (ADS)

van Emmerik, T. H. M.; Li, Z.; Sivapalan, M.; Pande, S.; Kandasamy, J.; Savenije, H. H. G.; Chanan, A.; Vigneswaran, S.

2014-03-01

Competition for water between humans and ecosystems is set to become a flash point in the coming decades in many parts of the world. An entirely new and comprehensive quantitative framework is needed to establish a holistic understanding of that competition, thereby enabling the development of effective mediation strategies. This paper presents a modeling study centered on the Murrumbidgee River Basin (MRB). The MRB has witnessed a unique system dynamics over the last 100 years as a result of interactions between patterns of water management and climate driven hydrological variability. Data analysis has revealed a pendulum swing between agricultural development and restoration of environmental health and ecosystem services over different stages of basin scale water resource development. A parsimonious, stylized, quasi-distributed coupled socio-hydrologic system model that simulates the two-way coupling between human and hydrological systems of the MRB is used to mimic dominant features of the pendulum swing. The model consists of coupled nonlinear ordinary differential equations that describe the interaction between five state variables that govern the co-evolution: reservoir storage, irrigated area, human population, ecosystem health, and a measure of environmental awareness. The model simulations track the propagation of the external climatic and socio-economic drivers through this coupled, complex system to the emergence of the pendulum swing. The model results point to a competition between human "productive" and environmental "restorative" forces that underpin the pendulum swing. Both the forces are endogenous, i.e., generated by the system dynamics in response to external drivers and mediated by humans through technology change and environmental awareness, respectively. We propose this as a generalizable modeling framework for coupled human hydrological systems that is potentially transferable to systems in different climatic and socio-economic settings.

How Short and Light Can a Simple Pendulum Be for Classroom Use?

ERIC Educational Resources Information Center

Oliveira, V.

2014-01-01

We compare the period of oscillation of an ideal simple pendulum with the period of a more "real" pendulum constituted of a rigid sphere and a rigid slender rod. We determine the relative error in the calculation of the local acceleration of gravity if the period of the ideal pendulum is used instead of the period of this real pendulum.

How short and light can a simple pendulum be for classroom use?

NASA Astrophysics Data System (ADS)

Oliveira, V.

2014-07-01

We compare the period of oscillation of an ideal simple pendulum with the period of a more ‘real’ pendulum constituted of a rigid sphere and a rigid slender rod. We determine the relative error in the calculation of the local acceleration of gravity if the period of the ideal pendulum is used instead of the period of this real pendulum.

A contribution to calculation of the mathematical pendulum

NASA Astrophysics Data System (ADS)

Anakhaev, K. N.

2014-11-01

In this work, as a continuation of rigorous solutions of the mathematical pendulum theory, calculated dependences were obtained in elementary functions (with construction of plots) for a complete description of the oscillatory motion of the pendulum with determination of its parameters, such as the oscillation period, deviation angles, time of motion, angular velocity and acceleration, and strains in the pendulum rod (maximum, minimum, zero, and gravitational). The results of calculations according to the proposed dependences closely (≪1%) coincide with the exact tabulated data for individual points. The conditions of ascending at which the angular velocity, angular acceleration, and strains in the pendulum rod reach their limiting values equal to and 5 m 1 g, respectively, are shown. It was revealed that the angular acceleration does not depend on the pendulum oscillation amplitude; the pendulum rod strain equal to the gravitation force of the pendulum R s = m 1 g at the time instant is also independent on the amplitude. The dependences presented in this work can also be invoked for describing oscillations of a physical pendulum, mass on a spring, electric circuit, etc.

The anisosphere as a new tool for interpreting Foucault pendulum experiments. Part I: harmonic oscillators

NASA Astrophysics Data System (ADS)

Verreault, René

2017-08-01

In an attempt to explain the tendency of Foucault pendula to develop elliptical orbits, Kamerlingh Onnes derived equations of motion that suggest the use of great circles on a spherical surface as a graphical illustration for an anisotropic bi-dimensional harmonic oscillator, although he did not himself exploit the idea any further. The concept of anisosphere is introduced in this work as a new means of interpreting pendulum motion. It can be generalized to the case of any two-dimensional (2-D) oscillating system, linear or nonlinear, including the case where coupling between the 2 degrees of freedom is present. Earlier pendulum experiments in the literature are revisited and reanalyzed as a test for the anisosphere approach. While that graphical method can be applied to strongly nonlinear cases with great simplicity, this part I is illustrated through a revisit of Kamerlingh Onnes' dissertation, where a high performance pendulum skillfully emulates a 2-D harmonic oscillator. Anisotropy due to damping is also described. A novel experiment strategy based on the anisosphere approach is proposed. Finally, recent original results with a long pendulum using an electronic recording alidade are presented. A gain in precision over traditional methods by 2-3 orders of magnitude is achieved.

Interpreting lateral dynamic weight shifts using a simple inverted pendulum model.

PubMed

Kennedy, Michael W; Bretl, Timothy; Schmiedeler, James P

2014-01-01

Seventy-five young, healthy adults completed a lateral weight-shifting activity in which each shifted his/her center of pressure (CoP) to visually displayed target locations with the aid of visual CoP feedback. Each subject's CoP data were modeled using a single-link inverted pendulum system with a spring-damper at the joint. This extends the simple inverted pendulum model of static balance in the sagittal plane to lateral weight-shifting balance. The model controlled pendulum angle using PD control and a ramp setpoint trajectory, and weight-shifting was characterized by both shift speed and a non-minimum phase (NMP) behavior metric. This NMP behavior metric examines the force magnitude at shift initiation and provides weight-shifting balance performance information that parallels the examination of peak ground reaction forces in gait analysis. Control parameters were optimized on a subject-by-subject basis to match balance metrics for modeled results to metric values calculated from experimental data. Overall, the model matches experimental data well (average percent error of 0.35% for shifting speed and 0.05% for NMP behavior). These results suggest that the single-link inverted pendulum model can be used effectively to capture lateral weight-shifting balance, as it has been shown to model static balance. Copyright © 2014 Elsevier B.V. All rights reserved.

Pendulum motions of extended lunar space elevator

NASA Astrophysics Data System (ADS)

Burov, A. A.; Kosenko, I. I.

2014-09-01

In the usual everyday life, it is well known that the inverted pendulum is unstable and is ready to fall to "all four sides," to the left and to the right, forward and backward. The theoretical studies and the lunar experience of moon robots and astronauts also confirms this property. The question arises: Is this property preserved if the pendulum is "very, very long"? It turns out that the answer is negative; namely, if the pendulum length significantly exceeds the Moon radius, then the radial equilibria at which the pendulum is located along the straight line connecting the Earth and Moon centers are Lyapunov stable and the pendulum does not fall in any direction at all. Moreover, if the pendulum goes beyond the collinear libration points, then it can be extended and manufactured from cables. This property was noted by F. A. Tsander and underlies the so-called lunar space elevator (e.g., see [1]). In the plane of the Earth and Moon orbits, there are some other equilibria which turn out to be unstable. The question is, Are there equilibria at which the pendulum is located outside the orbital plane? In this paper, we show that the answer is positive, but such equilibria are unstable in the secular sense. We also study necessary conditions for the stability of lunar pendulum oscillations in the plane of the lunar orbit. It was numerically discovered that stable and unstable equilibria alternate depending on the oscillation amplitude and the angular velocity of rotation. The study of the lunar elevator dynamics originates in [2]. The concept of lunar elevator was developed in detail in [3, 4]. Several classes of equilibria with the finiteness of the Moon size taken into account were studied in [5]. The possibility of location of an orbital station fixed to the Moon surface by a pair of tethers was investigated in [6]. The problem of orientation of the terminal station of the lunar space elevator was studied in [7]. The influence of the tether length variations on the motion of the lunar tether system was considered in [8]. The alternation of stable and unstable flat oscillations is well known in the problem of satellite oscillations in a circular orbit [9, 10].

The method of Ritz applied to the equation of Hamilton. [for pendulum systems

NASA Technical Reports Server (NTRS)

Bailey, C. D.

1976-01-01

Without any reference to the theory of differential equations, the initial value problem of the nonlinear, nonconservative double pendulum system is solved by the application of the method of Ritz to the equation of Hamilton. Also shown is an example of the reduction of the traditional eigenvalue problem of linear, homogeneous, differential equations of motion to the solution of a set of nonhomogeneous algebraic equations. No theory of differential equations is used. Solution of the time-space path of the linear oscillator is demonstrated and compared to the exact solution.

Thrust Stand for Electric Propulsion Performance Evaluation

NASA Technical Reports Server (NTRS)

Markusic, T. E.; Jones, J. E.; Cox, M. D.

2004-01-01

An electric propulsion thrust stand capable of supporting thrusters with total mass of up to 125 kg and 1 mN to 1 N thrust levels has been developed and tested. The mechanical design features a conventional hanging pendulum arm attached to a balance mechanism that transforms horizontal motion into amplified vertical motion, with accommodation for variable displacement sensitivity. Unlike conventional hanging pendulum thrust stands, the deflection is independent of the length of the pendulum arm, and no reference structure is required at the end of the pendulum. Displacement is measured using a non-contact, optical linear gap displacement transducer. Mechanical oscillations are attenuated using a passive, eddy current damper. An on-board microprocessor-based level control system, which includes a two axis accelerometer and two linear-displacement stepper motors, continuously maintains the level of the balance mechanism - counteracting mechanical %era drift during thruster testing. A thermal control system, which includes heat exchange panels, thermocouples, and a programmable recirculating water chiller, continuously adjusts to varying thermal loads to maintain the balance mechanism temperature, to counteract thermal drifts. An in-situ calibration rig allows for steady state calibration both prior to and during thruster testing. Thrust measurements were carried out on a well-characterized 1 kW Hall thruster; the thrust stand was shown to produce repeatable results consistent with previously published performance data.

Strange mechanics of the neutrino flavor pendulum

NASA Astrophysics Data System (ADS)

Johns, Lucas; Fuller, George M.

2018-01-01

We identify in the flavor transformation of astrophysical neutrinos a new class of phenomena, a common outcome of which is the suppression of flavor conversion. Appealing to the equivalence between a bipolar neutrino system and a gyroscopic pendulum, we find that these phenomena have rather striking interpretations in the mechanical picture: in one instance, the gyroscopic pendulum initially precesses in one direction, then comes to a halt and begins to precess in the opposite direction—a counterintuitive behavior that we analogize to the motion of a toy known as a rattleback. We analyze these behaviors in the early Universe, wherein a chance connection to sterile neutrino dark matter emerges, and we briefly suggest how they might manifest in compact-object environments.

The influences of load mass changing on inverted pendulum stability based on simulation study

NASA Astrophysics Data System (ADS)

Pangaribuan, Timbang; Nasruddin, M. N.; Marlianto, Eddy; Sigiro, Mula

2017-09-01

An inverted pendulum has nonlinear dynamic, so it is not easy to do in analysis to see its behavior. From many observations which have been made, there are two things that need to be added on the perfection of inverted pendulum. Firstly, when the pendulum has a large mass, and the second when the pendulum is given a load mass much larger than mass of the inverted pendulum. There are some question, first, how big the load mass can be given so that the movement of the inverted pendulum stay stable is. Second, how weight the changes and moves of load mass which can be given. For all the changes, it hopes the inverted pendulum is stay stable. Finally, the final result is still expected to be as stable, it must need conclude what kind of controller is capable of carrying such a mass burden, and how large the mass load limit can be given.

Validation of a robotic balance system for investigations in the control of human standing balance.

PubMed

Luu, Billy L; Huryn, Thomas P; Van der Loos, H F Machiel; Croft, Elizabeth A; Blouin, Jean-Sébastien

2011-08-01

Previous studies have shown that human body sway during standing approximates the mechanics of an inverted pendulum pivoted at the ankle joints. In this study, a robotic balance system incorporating a Stewart platform base was developed to provide a new technique to investigate the neural mechanisms involved in standing balance. The robotic system, programmed with the mechanics of an inverted pendulum, controlled the motion of the body in response to a change in applied ankle torque. The ability of the robotic system to replicate the load properties of standing was validated by comparing the load stiffness generated when subjects balanced their own body to the robot's mechanical load programmed with a low (concentrated-mass model) or high (distributed-mass model) inertia. The results show that static load stiffness was not significantly (p > 0.05) different for standing and the robotic system. Dynamic load stiffness for the robotic system increased with the frequency of sway, as predicted by the mechanics of an inverted pendulum, with the higher inertia being accurately matched to the load properties of the human body. This robotic balance system accurately replicated the physical model of standing and represents a useful tool to simulate the dynamics of a standing person. © 2011 IEEE

Dynamics of low velocity collisions of ice particle, coated with frost

NASA Technical Reports Server (NTRS)

Bridges, F.; Lin, D.; Boone, L.; Darknell, D.

1991-01-01

We continued our investigations of low velocity collisions of ice particles for velocities in range 10(exp -3) - 2 cm/s. The work focused on two effects: (1) the sticking forces for ice particles coated with CO2 frost, and (2) the completion of a 2-D pendulum system for glancing collisions. A new computer software was also developed to control and monitor the position of the 2-D pendulum.

Use of videos for students to see the effect of changing gravity on harmonic oscillators

NASA Astrophysics Data System (ADS)

Benge, Raymond; Young, Charlotte; Worley, Alan; Davis, Shirley; Smith, Linda; Gell, Amber

2010-03-01

In introductory physics classes, students are introduced to harmonic oscillators such as masses on springs and the simple pendulum. In derivation of the equations describing these systems, the term ``g'' for the acceleration due to gravity cancels in the equation for the period of a mass oscillating on a spring, but it remains in the equation for the period of a pendulum. Frequently there is a homework problem asking how the system described would behave on the Moon, Mars, etc. Students have to have faith in the equations. In January, 2009, a team of community college faculty flew an experiment aboard an aircraft in conjunction with NASA's Microgravity University program. The experiment flown was a study in harmonic oscillator and pendulum behavior under various gravity situations. The aircraft simulated zero gravity, Martian, Lunar, and hypergravity conditions. The experiments were video recorded for students to study the behavior of the systems in varying gravity conditions. These videos are now available on the internet for anyone to use in introductory physics classes.

Vibration analysis of rotor blades with pendulum absorbers

NASA Technical Reports Server (NTRS)

Murthy, V. R.; Hammond, C. E.

1979-01-01

A comprehensive vibration analysis of rotor blades with spherical pendulum absorbers is presented. Linearized equations of motion for small oscillations about the steady-state deflection of a spherical pendulum on elastic rotor blades undergoing coupled flapwise bending, chordwise bending, and torsional vibrations are obtained. A transmission matrix formulation is given to determine the natural vibrational characteristics of rotor blades with spherical or simple flapping pendulum absorbers. The natural frequencies and mode shapes of a hingeless rotor blade with a spherical pendulum are computed.

Lyapunov stability analysis for the generalized Kapitza pendulum

NASA Astrophysics Data System (ADS)

Druzhinina, O. V.; Sevastianov, L. A.; Vasilyev, S. A.; Vasilyeva, D. G.

2017-12-01

In this work generalization of Kapitza pendulum whose suspension point moves in the vertical and horizontal planes is made. Lyapunov stability analysis of the motion for this pendulum subjected to excitation of periodic driving forces and stochastic driving forces that act in the vertical and horizontal planes has been studied. The numerical study of the random motion for generalized Kapitza pendulum under stochastic driving forces has made. It is shown the existence of stable quasi-periodic motion for this pendulum.

An instrumented pendulum system for measuring energy absorption during fracture insult to large animal joints in vivo.

PubMed

Diestelmeier, B W; Rudert, M J; Tochigi, Y; Baer, T E; Fredericks, D C; Brown, T D

2014-06-01

For systematic laboratory studies of bone fractures in general and intra-articular fractures in particular, it is often necessary to control for injury severity. Quantitatively, a parameter of primary interest in that regard is the energy absorbed during the injury event. For this purpose, a novel technique has been developed to measure energy absorption in experimental impaction. The specific application is for fracture insult to porcine hock (tibiotalar) joints in vivo, for which illustrative intra-operative data are reported. The instrumentation allowed for the measurement of the delivered kinetic energy and of the energy passed through the specimen during impaction. The energy absorbed by the specimen was calculated as the difference between those two values. A foam specimen validation study was first performed to compare the energy absorption measurements from the pendulum instrumentation versus the work of indentation performed by an MTS machine. Following validation, the pendulum apparatus was used to measure the energy absorbed during intra-articular fractures created in 14 minipig hock joints in vivo. The foam validation study showed close correspondence between the pendulum-measured energy absorption and MTS-performed work of indentation. In the survival animal series, the energy delivered ranged from 31.5 to 48.3 Js (41.3±4.0, mean±s.d.) and the proportion of energy absorbed to energy delivered ranged from 44.2% to 64.7% (53.6%±4.5%). The foam validation results support the reliability of the energy absorption measure provided by the instrumented pendulum system. Given that a very substantial proportion of delivered energy passed--unabsorbed--through the specimens, the energy absorption measure provided by this novel technique arguably provides better characterization of injury severity than is provided simply by energy delivery.

Intermittent control with ankle, hip, and mixed strategies during quiet standing: a theoretical proposal based on a double inverted pendulum model.

PubMed

Suzuki, Yasuyuki; Nomura, Taishin; Casadio, Maura; Morasso, Pietro

2012-10-07

Human upright posture, as a mechanical system, is characterized by an instability of saddle type, involving both stable and unstable dynamic modes. The brain stabilizes such system by generating active joint torques, according to a time-delayed neural feedback control. What is still unsolved is a clear understanding of the control strategies and the control mechanisms that are used by the central nervous system in order to stabilize the unstable posture in a robust way while maintaining flexibility. Most studies in this direction have been limited to the single inverted pendulum model, which is useful for formalizing fundamental mechanical aspects but insufficient for addressing more general issues concerning neural control strategies. Here we consider a double inverted pendulum model in the sagittal plane with small passive viscoelasticity at the ankle and hip joints. Despite difficulties in stabilizing the double pendulum model in the presence of the large feedback delay, we show that robust and flexible stabilization of the upright posture can be established by an intermittent control mechanism that achieves the goal of stabilizing the body posture according to a "divide and conquer strategy", which switches among different controllers in different parts of the state space of the double inverted pendulum. Remarkably, it is shown that a global, robust stability is achieved even if the individual controllers are unstable and the information exploited for switching from one controller to another is severely delayed, as it happens in biological reality. Moreover, the intermittent controller can automatically resolve coordination among multiple active torques associated with the muscle synergy, leading to the emergence of distinct temporally coordinated active torque patterns, referred to as the intermittent ankle, hip, and mixed strategies during quiet standing, depending on the passive elasticity at the hip joint. Copyright © 2012 Elsevier Ltd. All rights reserved.

Stabilization and tracking control of X-Z inverted pendulum with sliding-mode control.

PubMed

Wang, Jia-Jun

2012-11-01

X-Z inverted pendulum is a new kind of inverted pendulum which can move with the combination of the vertical and horizontal forces. Through a new transformation, the X-Z inverted pendulum is decomposed into three simple models. Based on the simple models, sliding-mode control is applied to stabilization and tracking control of the inverted pendulum. The performance of the sliding mode control is compared with that of the PID control. Simulation results show that the design scheme of sliding-mode control is effective for the stabilization and tracking control of the X-Z inverted pendulum. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

Balancing a simulated inverted pendulum through motor imagery: an EEG-based real-time control paradigm.

PubMed

Yue, Jingwei; Zhou, Zongtan; Jiang, Jun; Liu, Yadong; Hu, Dewen

2012-08-30

Most brain-computer interfaces (BCIs) are non-time-restraint systems. However, the method used to design a real-time BCI paradigm for controlling unstable devices is still a challenging problem. This paper presents a real-time feedback BCI paradigm for controlling an inverted pendulum on a cart (IPC). In this paradigm, sensorimotor rhythms (SMRs) were recorded using 15 active electrodes placed on the surface of the subject's scalp. Subsequently, common spatial pattern (CSP) was used as the basic filter to extract spatial patterns. Finally, linear discriminant analysis (LDA) was used to translate the patterns into control commands that could stabilize the simulated inverted pendulum. Offline trainings were employed to teach the subjects to execute corresponding mental tasks, such as left/right hand motor imagery. Five subjects could successfully balance the online inverted pendulum for more than 35s. The results demonstrated that BCIs are able to control nonlinear unstable devices. Furthermore, the demonstration and extension of real-time continuous control might be useful for the real-life application and generalization of BCI. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Mechanical design of the University of Florida Torsion Pendulum for testing the LISA Gravitational Reference Sensor

NASA Astrophysics Data System (ADS)

Shelley, Ryan; Chilton, Andrew; Olatunde, Tawio; Ciani, Giacomo; Mueller, Guido; Conklin, John

2014-03-01

The Laser Interferometer Space Antenna (LISA) requires free falling test masses, whose acceleration must be below 3 fm/s2/rtHz in the lower part of LISA's frequency band ranging from 0.1 to 100 mHz. Gravitational reference sensors (GRS) house the test masses, shield them from external disturbances, control their orientation, and sense their position at the nm/rtHz level. The GRS torsion pendulum is a laboratory test bed for GRS technology. By decoupling the system of test masses from the gravity of the Earth, it is possible to identify and quantify many sources of noise in the sensor. The mechanical design of the pendulum is critical to the study of the noise sources and the development of new technologies that can improve performance and reduce cost. The suspended test mass is a hollow, gold-coated, aluminum cube which rests inside a gold-coated, aluminum housing with electrodes for sensing and actuating all six degrees of freedom. This poster describes the design, analysis, and assembly of the mechanical subsystems of the UF Torsion Pendulum.

Reinforcement learning state estimator.

PubMed

Morimoto, Jun; Doya, Kenji

2007-03-01

In this study, we propose a novel use of reinforcement learning for estimating hidden variables and parameters of nonlinear dynamical systems. A critical issue in hidden-state estimation is that we cannot directly observe estimation errors. However, by defining errors of observable variables as a delayed penalty, we can apply a reinforcement learning frame-work to state estimation problems. Specifically, we derive a method to construct a nonlinear state estimator by finding an appropriate feedback input gain using the policy gradient method. We tested the proposed method on single pendulum dynamics and show that the joint angle variable could be successfully estimated by observing only the angular velocity, and vice versa. In addition, we show that we could acquire a state estimator for the pendulum swing-up task in which a swing-up controller is also acquired by reinforcement learning simultaneously. Furthermore, we demonstrate that it is possible to estimate the dynamics of the pendulum itself while the hidden variables are estimated in the pendulum swing-up task. Application of the proposed method to a two-linked biped model is also presented.

Estimating and Comparing Dam Deformation Using Classical and GNSS Techniques

PubMed Central

Barzaghi, Riccardo; De Gaetani, Carlo Iapige

2018-01-01

Global Navigation Satellite Systems (GNSS) receivers are nowadays commonly used in monitoring applications, e.g., in estimating crustal and infrastructure displacements. This is basically due to the recent improvements in GNSS instruments and methodologies that allow high-precision positioning, 24 h availability and semiautomatic data processing. In this paper, GNSS-estimated displacements on a dam structure have been analyzed and compared with pendulum data. This study has been carried out for the Eleonora D’Arborea (Cantoniera) dam, which is in Sardinia. Time series of pendulum and GNSS over a time span of 2.5 years have been aligned so as to be comparable. Analytical models fitting these time series have been estimated and compared. Those models were able to properly fit pendulum data and GNSS data, with standard deviation of residuals smaller than one millimeter. These encouraging results led to the conclusion that GNSS technique can be profitably applied to dam monitoring allowing a denser description, both in space and time, of the dam displacements than the one based on pendulum observations. PMID:29498650

Physics Teacher Demonstrations for the Classroom

NASA Astrophysics Data System (ADS)

Murfee, Lee

2005-04-01

A sharing of physics and physics teaching demonstrations by Lee Murfee, a teacher of students learning physics and mathematics at Berkeley Preparatory School and the United States Military Academy for 21 years, and active member of the Florida Section of American Association of Physics Teachers (AAPT). Presentation is a fast paced array of physics and physics teaching demonstrations. Topics include who and what we teach, a successful science department philosophy, forces, acceleration, impulse, momentum, observations, pendulums, springs, friction, inclined plane, rotational motion, moment of inertia, teaching description of motion with data, equations and graphing, slope, uniform circular motion, derivatives, integrals, PASCO Data Studio sensor applications, students presenting to students, flashboards, sound, pressure, and sensitivity analysis in determining specific heat. Demonstrations apply to high school and college introductory physics teaching; handouts and some door prizes/gifts will be provided.

Towards the miniaturization of monolithic folded pendulums: a new approach to the implementation of small and light sensors for ground, space, and marine applications

NASA Astrophysics Data System (ADS)

Barone, F.; Giordano, G.

2018-03-01

The UNISA Folded Pendulum technological platform is very promising for the implementation of high sensitive, large band miniaturized mechanical seismometers and accelerometers in different materials. In fact, the symmetry of its mechanical architecture allows to take full advantage of one of the most relevant properties of the folded pendulum, that is the scalability. This property is very useful for the design of folded pendulums of small size and weight, provided with a suitable combination of physical and geometrical parameters. Using a lagrangian simplified model of folded pendulum, we present and discuss this idea, showing different possible approaches that may lead to the miniaturization of a folded pendulum. Finally we present a first prototype of miniaturized folded pendulum, discussing its characteristics and limitations, in connection with scientific ground, marine and space applications.

Pendulums in the Physics Education Literature: A Bibliography

ERIC Educational Resources Information Center

Gauld, Colin

2004-01-01

Articles about the pendulum in four journals devoted to the teaching of physics and one general science teaching journal (along with other miscellaneous articles from other journals) are listed in three broad categories--types of pendulums, the contexts in which these pendulums are used in physics teaching at secondary or tertiary levels and a…

Introduction to the Treatment of Non-Linear Effects Using a Gravitational Pendulum

ERIC Educational Resources Information Center

Weltner, Klaus; Esperidiao, Antonio Sergio C.; Miranda, Paulo

2004-01-01

We show that the treatment of pendulum movement, other than the linear approximation,may be an instructive experimentally based introduction to the physics of non-linear effects. Firstly the natural frequency of a gravitational pendulum is measured as function of its amplitude. Secondly forced oscillations of a gravitational pendulum are…

Adaptive Neural Network Control for the Trajectory Tracking of the Furuta Pendulum.

PubMed

Moreno-Valenzuela, Javier; Aguilar-Avelar, Carlos; Puga-Guzman, Sergio A; Santibanez, Victor

2016-12-01

The purpose of this paper is to introduce a novel adaptive neural network-based control scheme for the Furuta pendulum, which is a two degree-of-freedom underactuated system. Adaptation laws for the input and output weights are also provided. The proposed controller is able to guarantee tracking of a reference signal for the arm while the pendulum remains in the upright position. The key aspect of the derivation of the controller is the definition of an output function that depends on the position and velocity errors. The internal and external dynamics are rigorously analyzed, thereby proving the uniform ultimate boundedness of the error trajectories. By using real-time experiments, the new scheme is compared with other control methodologies, therein demonstrating the improved performance of the proposed adaptive algorithm.

Pendulum and modified pendulum appliances for maxillary molar distalization in Class II malocclusion - a systematic review.

PubMed

Al-Thomali, Yousef; Basha, Sakeenabi; Mohamed, Roshan Noor

2017-08-01

The main purpose of the present systematic review was to evaluate the quantitative effects of the pendulum appliance and modified pendulum appliances for maxillary molar distalization in Class II malocclusion. Our systematic search included MEDLINE, EMBASE, CINAHL, PsychINFO, Scopus and key journals and review articles; the date of the last search was 30 January 2017. We graded the methodological quality of the studies by means of the Quality Assessment Tool for Quantitative Studies, developed for the Effective Public Health Practice Project (EPHPP). In total, 203 studies were identified for screening, and 25 studies were eligible. The quality assessment rated four (16%) of the study as being of strong quality and 21 (84%) of these studies as being of moderate quality. The pendulum appliances showed mean molar distalization of 2-6.4 mm, distal tipping of molars from 6.67° to 14.50° and anchorage loss with mean premolar and incisor mesial movement of 1.63-3.6 mm and 0.9-6.5 mm, respectively. The bone anchored pendulum appliances (BAPAs) showed mean molar distalization of 4.8-6.4 mm, distal tipping of molars from 9° to 11.3° and mean premolar distalization of 2.7-5.4 mm. Pendulum and modified pendulum appliances are effective in molar distalization. Pendulum appliance with K-loop modification, implant supported pendulum appliance and BAPA significantly reduced anchorage loss of the anterior teeth and distal tipping of the molar teeth.

Robust reinforcement learning.

PubMed

Morimoto, Jun; Doya, Kenji

2005-02-01

This letter proposes a new reinforcement learning (RL) paradigm that explicitly takes into account input disturbance as well as modeling errors. The use of environmental models in RL is quite popular for both offline learning using simulations and for online action planning. However, the difference between the model and the real environment can lead to unpredictable, and often unwanted, results. Based on the theory of H(infinity) control, we consider a differential game in which a "disturbing" agent tries to make the worst possible disturbance while a "control" agent tries to make the best control input. The problem is formulated as finding a min-max solution of a value function that takes into account the amount of the reward and the norm of the disturbance. We derive online learning algorithms for estimating the value function and for calculating the worst disturbance and the best control in reference to the value function. We tested the paradigm, which we call robust reinforcement learning (RRL), on the control task of an inverted pendulum. In the linear domain, the policy and the value function learned by online algorithms coincided with those derived analytically by the linear H(infinity) control theory. For a fully nonlinear swing-up task, RRL achieved robust performance with changes in the pendulum weight and friction, while a standard reinforcement learning algorithm could not deal with these changes. We also applied RRL to the cart-pole swing-up task, and a robust swing-up policy was acquired.

A novel tribological study on DLC-coated micro-dimpled orthopedics implant interface.

PubMed

Choudhury, Dipankar; Urban, Filip; Vrbka, Martin; Hartl, Martin; Krupka, Ivan

2015-05-01

This study investigates a tribological performance of diamond like carbon (DLC) coated micro dimpled prosthesis heads against ceramic cups in a novel pendulum hip joint simulator. The simulator enables determining friction coefficient and viscous effects of a concave shaped specimen interface (conformal contact). Two types of DLC such as hydrogenated amorphous carbon (a-C:H) and tetrahedral amorphous carbon (Ta-C) and one set of micro dimple (diameter of 300µm, depth of 70µm, and pitch of 900µm) were fabricated on metallic prosthesis heads. The experiment results reveal a significant friction coefficient reduction to the 'dimpled a-C:H/ceramic' prosthesis compared to a 'Metal (CoCr)/ceramic' prosthesis because of their improved material and surface properties and viscous effect. The post-experiment surface analysis displays that the dimpled a-C:H yielded a minor change in the surface roughness, and generated a larger sizes of wear debris (40-200nm sized, equivalent diameter), a size which could be certainly stored in the dimple, thus likely to reducing their possible third body abrasive wear rate. Thus, dimpled a:C-H can be used as a 'metal on ceramic hip joint interface', whereas the simulator can be utilized as an advanced bio-tribometer. Copyright © 2015 Elsevier Ltd. All rights reserved.

49 CFR 572.193 - Neck assembly.

Code of Federal Regulations, 2014 CFR

2014-10-01

... or V2-B in appendix A to this subpart, to the 49 CFR Part 572 pendulum test fixture (Figure 22, 49... motion of the pendulum longitudinal centerline; (3) Release the pendulum from a height sufficient to achieve a velocity of 5.57 ±0.06 m/s measured at the center of the pendulum accelerometer, as shown in 49...

49 CFR 572.73 - Neck assembly and test procedure.

Code of Federal Regulations, 2011 CFR

2011-10-01

... rotate, while translating in the direction of the pendulum preimpact flight, in reference to the pendulum... displacement at time “T” is defined as the straight line distance between the position relative to the pendulum arm of the head's center of gravity at time “zero;” and the position relative to the pendulum arm of...

49 CFR 572.193 - Neck assembly.

Code of Federal Regulations, 2012 CFR

2012-10-01

... or V2-B in appendix A to this subpart, to the 49 CFR Part 572 pendulum test fixture (Figure 22, 49... motion of the pendulum longitudinal centerline; (3) Release the pendulum from a height sufficient to achieve a velocity of 5.57 ±0.06 m/s measured at the center of the pendulum accelerometer, as shown in 49...

49 CFR 572.73 - Neck assembly and test procedure.

Code of Federal Regulations, 2013 CFR

2013-10-01

... rotate, while translating in the direction of the pendulum preimpact flight, in reference to the pendulum... displacement at time “T” is defined as the straight line distance between the position relative to the pendulum arm of the head's center of gravity at time “zero;” and the position relative to the pendulum arm of...

A Simple Method to Measure the Trajectory of a Spherical Pendulum

ERIC Educational Resources Information Center

Yang, Hujiang; Xiao, Jinghua; Yang, Tianyu; Qiu, Chen

2011-01-01

Compared with a single gravity pendulum, the spherical pendulum behaves more complicatedly in experiments, which makes it difficult to measure. In this paper, we present a method to visualize the trajectories of a spherical pendulum by employing a gravity ball with a lit LED and a digital camera. This new measurement is inexpensive and easy to…

49 CFR 572.193 - Neck assembly.

Code of Federal Regulations, 2013 CFR

2013-10-01

... or V2-B in appendix A to this subpart, to the 49 CFR Part 572 pendulum test fixture (Figure 22, 49... motion of the pendulum longitudinal centerline; (3) Release the pendulum from a height sufficient to achieve a velocity of 5.57 ±0.06 m/s measured at the center of the pendulum accelerometer, as shown in 49...

49 CFR 572.193 - Neck assembly.

Code of Federal Regulations, 2011 CFR

2011-10-01

... or V2-B in appendix A to this subpart, to the 49 CFR Part 572 pendulum test fixture (Figure 22, 49... of motion of the pendulum longitudinal centerline; (3) Release the pendulum from a height sufficient to achieve a velocity of 5.57 ± 0.06 m/s measured at the center of the pendulum accelerometer, as...

49 CFR 572.73 - Neck assembly and test procedure.

Code of Federal Regulations, 2010 CFR

2010-10-01

... rotate, while translating in the direction of the pendulum preimpact flight, in reference to the pendulum... displacement at time “T” is defined as the straight line distance between the position relative to the pendulum arm of the head's center of gravity at time “zero;” and the position relative to the pendulum arm of...

Turning Points of the Spherical Pendulum and the Golden Ratio

ERIC Educational Resources Information Center

Essen, Hanno; Apazidis, Nicholas

2009-01-01

We study the turning point problem of a spherical pendulum. The special cases of the simple pendulum and the conical pendulum are noted. For simple initial conditions the solution to this problem involves the golden ratio, also called the golden section, or the golden number. This number often appears in mathematics where you least expect it. To…

49 CFR 572.73 - Neck assembly and test procedure.

Code of Federal Regulations, 2014 CFR

2014-10-01

... rotate, while translating in the direction of the pendulum preimpact flight, in reference to the pendulum... displacement at time “T” is defined as the straight line distance between the position relative to the pendulum arm of the head's center of gravity at time “zero;” and the position relative to the pendulum arm of...

49 CFR 572.193 - Neck assembly.

Code of Federal Regulations, 2010 CFR

2010-10-01

... or V2-B in appendix A to this subpart, to the 49 CFR Part 572 pendulum test fixture (Figure 22, 49... of motion of the pendulum longitudinal centerline; (3) Release the pendulum from a height sufficient to achieve a velocity of 5.57 ± 0.06 m/s measured at the center of the pendulum accelerometer, as...

49 CFR 572.73 - Neck assembly and test procedure.

Code of Federal Regulations, 2012 CFR

2012-10-01

... rotate, while translating in the direction of the pendulum preimpact flight, in reference to the pendulum... displacement at time “T” is defined as the straight line distance between the position relative to the pendulum arm of the head's center of gravity at time “zero;” and the position relative to the pendulum arm of...

Inverting the Pendulum Using Fuzzy Control (Center Director's Discretionary Fund (Project 93-02)

NASA Technical Reports Server (NTRS)

Kissel, R. R.; Sutherland, W. T.

1997-01-01

A single pendulum was simulated in software and then built on a rotary base. A fuzzy controller was used to show its advantages as a nonlinear controller since bringing the pendulum inverted is extremely nonlinear. The controller was implemented in a Motorola 6811 microcontroller. A double pendulum was simulated and fuzzy control was used to hold it in a vertical position. The double pendulum was not built into hardware for lack of time. This project was for training and to show advantages of fuzzy control.

Tracing the transition of a macro electron shuttle into nonlinear response

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

Kim, Chulki; Prada, Marta; Qin, Hua

We present a study on a macroscopic electron shuttle in the transition from linear to nonlinear response. The shuttle consists of a classical mechanical pendulum situated between two capacitor plates. The metallic pendulum enables mechanical transfer of electrons between the plates, hence allowing to directly trace electron shuttling in the time domain. By applying a high voltage to the plates, we drive the system into a controlled nonlinear response, where we observe period doubling.

The Response of Monterey Bay to the Great Tohoku Earthquake of 2011

DTIC Science & Technology

2011-01-01

in this report come from three sources. First, bottom pressure data were acquired from the Monterey Accelerated Research System (MARS) array...where S is the great circle distance, H, the mean depth along the great circle path, g, the acceleration of gravity, and yjgH represents the shallow...so-called Pendulum day, which depends upon the latitude, with OFC having periods smaller then the Pendulum Day and OSC having periods greater than

Interactive Internet Based Pendulum for Learning Mechatronics

NASA Astrophysics Data System (ADS)

Sethson, Magnus R.

2003-01-01

This paper describes an Internet based remote experimental setup of a double lined pendulum mechanism for students experiments at the M. Sc. Level. Some of the first year experience using this web-based setup in classes is referred. In most of the courses given at the division of mechanical engineering systems at Linkoeping Institute of Technology we provide experimental setups to enhance the teaching Of M.Sc. students. Many of these experimental setups involve mechatronical systems. Disciplines like fluid power, electronics, and mechanics and also software technologies are used in each experiment. As our campus has recently been split into two different cities some new concepts for distance learning have been studied. The one described here tries to implement remotely controlled mechatronic setups for teaching basic programming of real-time operating systems and analysis of the dynamics of mechanical systems. The students control the regulators for the pendulum through a web interface and get measurement results and a movie back through their email. The present setup uses a double linked pendulum that is controlled by a DC-motor and monitored through both camera and angular position sensors. All software needed is hosted on a double-processor PC running the RedHat 7.1. distribution complemented with real-time scheduling using DIAPM-RTAI 1.7. The Internet site is presented to the students using PHP, Apache and MySQL. All of the used software originates from the open source domain. The experience from integrating these technologies and security issues is discussed together with the web-camera interface. One of the important experiences from this project so far is the need for a good visual feedback. This is both in terms of video speed but also in resolution. It has been noticed that when the students makes misstates and wants to search the failure they want clear, large images with high resolution to support their personal believes in the cause of the failure. Even if the student does not need a high resolution image to get the idea of the mechanics and the function of the pendulum, they need such high quality images to get confidence in the hardware. It is important to support this when the ability to direct hand-on contact with the hardware is taken away. Some of the experiences in combining open source software; real-time scheduling and measurement hardware into a cost efficient way is also discussed. The pendulum has been available publicly on the Internet but has now been removed due to security issues.

Roles of Abductive Reasoning and Prior Belief in Children's Generation of Hypotheses about Pendulum Motion

ERIC Educational Resources Information Center

Kwon, Yong-Ju; Jeong, Jin-Su; Park, Yun-Bok

2006-01-01

The purpose of the present study was to test the hypothesis that student's abductive reasoning skills play an important role in the generation of hypotheses on pendulum motion tasks. To test the hypothesis, a hypothesis-generating test on pendulum motion, and a prior-belief test about pendulum motion were developed and administered to a sample of…

Tiltmeter studies in earthquake prediction

USGS Publications Warehouse

Johnston, M.

1978-01-01

tilt measurements give us a means of monitoring vertical displacements or local uplift of the crust. The simplest type of tiltmeter is a stationary pendulum (fig. 1). As the Earth's surface distorts locally, the pendulum housing is tilted while, of course, the pendulum continues to hang vertically (that is, in the direction of the gravity vector). The tilt angle is the angle through which the pendulum housing is tilted. The pendulum is the inertial reference (the force of gravity remains unchanged at the site), and tilting of the instrument housing represents the moving reference frame. We note in passing that the tiltmeter could also be used to measure the force of gravity by using the pendulum in the same way as Henry Kater did in his celebrated measurement of g in 1817. 

A simple pendulum laser interferometer for determining the gravitational constant

PubMed Central

Parks, Harold V.; Faller, James E.

2014-01-01

We present a detailed account of our 2004 experiment to measure the Newtonian constant of gravitation with a suspended laser interferometer. The apparatus consists of two simple pendulums hanging from a common support. Each pendulum has a length of 72 cm and their separation is 34 cm. A mirror is embedded in each pendulum bob, which then in combination form a Fabry–Perot cavity. A laser locked to the cavity measures the change in pendulum separation as the gravitational field is modulated due to the displacement of four 120 kg tungsten masses. PMID:25201994

Pendulum test measure correlates with gait parameters in children with cerebral palsy.

PubMed

Lotfian, M; Mirbagheri, M M; Kharazi, M R; Dadashi, F; Nourian, R; Irani, A; Mirbagheri, A

2016-08-01

Individuals with cerebral palsy (CP) usually suffer from different impairments including gait impairment and spasticity. Spastic hypertonia is a defining feature of spasticity and manifests as a mechanical abnormality. The objective of this study was to determine the relationship between spastic hypertonia and gait impairments in spastic children with CP, addressing an important controversial issue. Spastic hypertonia was quantified using the pendulum test. The gait impairments were evaluated using the motion capture system in a gait laboratory. Our results showed significant correlations among gait parameters; i.e. walking speed, step length, and the pendulum test measures. This indicates that neuromuscular abnormalities are associated with spasticity and may contribute to gait impairments. The clinical implication is that the impaired gait in children with CP may be improved with the treatment of neuromuscular abnormalities.

Coupled pendula chains under parametric PT-symmetric driving force

NASA Astrophysics Data System (ADS)

Destyl, E.; Nuiro, S. P.; Pelinovsky, D. E.; Poullet, P.

2017-12-01

We consider a chain of coupled pendula pairs, where each pendulum is connected to the nearest neighbors in the longitudinal and transverse directions. The common strings in each pair are modulated periodically by an external force. In the limit of small coupling and near the 1 : 2 parametric resonance, we derive a novel system of coupled PT-symmetric discrete nonlinear Schrödinger equations, which has Hamiltonian symmetry but has no phase invariance. By using the conserved energy, we find the parameter range for the linear and nonlinear stability of the zero equilibrium. Numerical experiments illustrate how destabilization of the zero equilibrium takes place when the stability constraints are not satisfied. The central pendulum excites nearest pendula and this process continues until a dynamical equilibrium is reached where each pendulum in the chain oscillates at a finite amplitude.

The Pendulum as a Vehicle for Transitioning from Classical to Quantum Physics: History, Quantum Concepts, and Educational Challenges

ERIC Educational Resources Information Center

Barnes, Marianne B.; Garner, James; Reid, David

2004-01-01

In this article we use the pendulum as the vehicle for discussing the transition from classical to quantum physics. Since student knowledge of the classical pendulum can be generalized to all harmonic oscillators, we propose that a quantum analysis of the pendulum can lead students into the unanticipated consequences of quantum phenomena at the…

Segmented Hoop as a Physical Pendulum

ERIC Educational Resources Information Center

Layton, William; Rodriguez, Nuria

2013-01-01

An interesting demonstration with a surprising result is to suspend a hoop from a point near its edge and set it swinging in a vertical plane as a pendulum. If a simple pendulum of length equal to the diameter of the hoop is set oscillating at the same time, the two will have nearly the same period. However, the real surprise is if the pendulum is…

A Novel Real-Time Data Acquisition Using an Excel Spreadsheet in Pendulum Experiment Tool with Light-Based Timer

ERIC Educational Resources Information Center

Adhitama, Egy; Fauzi, Ahmad

2018-01-01

In this study, a pendulum experimental tool with a light-based timer has been developed to measure the period of a simple pendulum. The obtained data was automatically recorded in an Excel spreadsheet. The intensity of monochromatic light, sensed by a 3DU5C phototransistor, dynamically changes as the pendulum swings. The changed intensity varies…

Ask the pendulum: personality predictors of ideomotor performance.

PubMed

Olson, Jay A; Jeyanesan, Ewalina; Raz, Amir

2017-01-01

For centuries, people have asked questions to hand-held pendulums and interpreted their movements as responses from the divine. These movements occur due to the ideomotor effect, wherein priming or thinking of a motion causes muscle movements that end up swinging the pendulum. By associating particular swinging movements with "yes" and "no" responses, we investigated whether pendulums can aid decision-making and which personality traits correlate with this performance. Participants ( N = 80 ) completed a visual detection task in which they searched for a target letter among rapidly presented characters. In the verbal condition, participants stated whether they saw the target in each trial. In the pendulum condition, participants instead mentally "asked" a hand-held pendulum whether the target was present; particular motions signified "yes" and "no". We measured the accuracy of their responses as well as their sensitivity and bias using signal detection theory. We also assessed four personality measures: locus of control (feelings of control over one's life), transliminality (sensitivity to subtle stimuli), need for cognition (preference for analytical thinking), and faith in intuition (preference for intuitive thinking). Overall, locus of control predicted verbal performance and transliminality predicted pendulum performance. Accuracy was low in both conditions (verbal: 57%, pendulum: 53%), but bias was higher in the verbal condition ( d = 1.10 ). We confirmed this bias difference in a second study ( d = 0.47 , N = 40 ). Our results suggest that people have different decision strategies when using a pendulum compared to conscious guessing. These findings may help explain why some people can answer questions more accurately with pendulums and Ouija boards. More broadly, identifying the differences between ideomotor and verbal responses could lead to practical ways to improve decision-making.

Ask the pendulum: personality predictors of ideomotor performance

PubMed Central

Olson, Jay A; Jeyanesan, Ewalina; Raz, Amir

2017-01-01

Abstract For centuries, people have asked questions to hand-held pendulums and interpreted their movements as responses from the divine. These movements occur due to the ideomotor effect, wherein priming or thinking of a motion causes muscle movements that end up swinging the pendulum. By associating particular swinging movements with “yes” and “no” responses, we investigated whether pendulums can aid decision-making and which personality traits correlate with this performance. Participants (N=80) completed a visual detection task in which they searched for a target letter among rapidly presented characters. In the verbal condition, participants stated whether they saw the target in each trial. In the pendulum condition, participants instead mentally “asked” a hand-held pendulum whether the target was present; particular motions signified “yes” and “no”. We measured the accuracy of their responses as well as their sensitivity and bias using signal detection theory. We also assessed four personality measures: locus of control (feelings of control over one’s life), transliminality (sensitivity to subtle stimuli), need for cognition (preference for analytical thinking), and faith in intuition (preference for intuitive thinking). Overall, locus of control predicted verbal performance and transliminality predicted pendulum performance. Accuracy was low in both conditions (verbal: 57%, pendulum: 53%), but bias was higher in the verbal condition (d=1.10). We confirmed this bias difference in a second study (d=0.47, N=40). Our results suggest that people have different decision strategies when using a pendulum compared to conscious guessing. These findings may help explain why some people can answer questions more accurately with pendulums and Ouija boards. More broadly, identifying the differences between ideomotor and verbal responses could lead to practical ways to improve decision-making. PMID:29877514

A biomechanical model of the craniomandibular complex and cervical spine based on the inverted pendulum.

PubMed

Gillies, G T; Broaddus, W C; Stenger, J M; Taylor, A G

1998-01-01

The head and neck constitute an inverted pendulum that is stabilized during consciousness by neuromuscular restoring forces. An analysis of the dynamics of this inverted pendulum suggests that the mechanics of the mandible and temporomandibular joint might couple into those of the pendulum's stabilization process. In this article, physical principles of the inverted pendulum model as these apply to the head and neck are explored, and the authors describe implications of mandibular mechanics for the forces acting on the head and neck at equilibrium. This novel application of the inverted pendulum model predicts that alteration or pathology of temporomandibular mechanics would lead to perturbations of the normal forces acting in the head and neck. Under certain circumstances, these perturbations could be expected to contribute to symptoms and result in additional or accelerated degenerative effects.

Charge management for gravitational-wave observatories using UV LEDs

NASA Astrophysics Data System (ADS)

Pollack, S. E.; Turner, M. D.; Schlamminger, S.; Hagedorn, C. A.; Gundlach, J. H.

2010-01-01

Accumulation of electrical charge on the end mirrors of gravitational-wave observatories can become a source of noise limiting the sensitivity of such detectors through electronic couplings to nearby surfaces. Torsion balances provide an ideal means for testing gravitational-wave technologies due to their high sensitivity to small forces. Our torsion pendulum apparatus consists of a movable plate brought near a plate pendulum suspended from a nonconducting quartz fiber. A UV LED located near the pendulum photoejects electrons from the surface, and a UV LED driven electron gun directs photoelectrons towards the pendulum surface. We have demonstrated both charging and discharging of the pendulum with equivalent charging rates of ˜105e/s, as well as spectral measurements of the pendulum charge resulting in a white noise level equivalent to 3×105e/Hz.

Parallel Plate System for Collecting Data Used to Determine Viscosity

NASA Technical Reports Server (NTRS)

Ethridge, Edwin C. (Inventor); Kaukler, William (Inventor)

2013-01-01

A parallel-plate system collects data used to determine viscosity. A first plate is coupled to a translator so that the first plate can be moved along a first direction. A second plate has a pendulum device coupled thereto such that the second plate is suspended above and parallel to the first plate. The pendulum device constrains movement of the second plate to a second direction that is aligned with the first direction and is substantially parallel thereto. A force measuring device is coupled to the second plate for measuring force along the second direction caused by movement of the second plate.

Functional Role of the Front and Back Legs During a Track Start with Special Reference to an Inverted Pendulum Model in College Swimmers.

PubMed

Ikeda, Yusuke; Ichikawa, Hiroshi; Nara, Rio; Baba, Yasuhiro; Shimoyama, Yoshimitsu; Kubo, Yasuyuki

2016-10-01

This study investigated factors that determine the velocity of the center of mass (CM) and flight distance from a track start to devise effective technical and physical training methods. Nine male and 5 female competitive swimmers participated in this study. Kinematics and ground reaction forces of the front and back legs were recorded using a video camera and force plates. The track start was modeled as an inverted pendulum system including a compliant leg, connecting the CM and front edge of the starting block. The increase in the horizontal velocity of the CM immediately after the start signal was closely correlated with the rotational component of the inverted pendulum. This rotational component at hands-off was significantly correlated with the average vertical force of the back plate from the start signal to hands-off (r = .967, P < .001). The flight distance / height was significantly correlated with the average vertical force of the front plate from the back foot-off to front foot-off (r = .783, P < .01). The results indicate that the legs on the starting block in the track start play a different role in the behavior of the inverted pendulum.

Effect of reduced gravity on the preferred walk-run transition speed

NASA Technical Reports Server (NTRS)

Kram, R.; Domingo, A.; Ferris, D. P.

1997-01-01

We investigated the effect of reduced gravity on the human walk-run gait transition speed and interpreted the results using an inverted-pendulum mechanical model. We simulated reduced gravity using an apparatus that applied a nearly constant upward force at the center of mass, and the subjects walked and ran on a motorized treadmill. In the inverted pendulum model for walking, gravity provides the centripetal force needed to keep the pendulum in contact with the ground. The ratio of the centripetal and gravitational forces (mv2/L)/(mg) reduces to the dimensionless Froude number (v2/gL). Applying this model to a walking human, m is body mass, v is forward velocity, L is leg length and g is gravity. In normal gravity, humans and other bipeds with different leg lengths all choose to switch from a walk to a run at different absolute speeds but at approximately the same Froude number (0.5). We found that, at lower levels of gravity, the walk-run transition occurred at progressively slower absolute speeds but at approximately the same Froude number. This supports the hypothesis that the walk-run transition is triggered by the dynamics of an inverted-pendulum system.

A simple pendulum laser interferometer for determining the gravitational constant.

PubMed

Parks, Harold V; Faller, James E

2014-10-13

We present a detailed account of our 2004 experiment to measure the Newtonian constant of gravitation with a suspended laser interferometer. The apparatus consists of two simple pendulums hanging from a common support. Each pendulum has a length of 72 cm and their separation is 34 cm. A mirror is embedded in each pendulum bob, which then in combination form a Fabry-Perot cavity. A laser locked to the cavity measures the change in pendulum separation as the gravitational field is modulated due to the displacement of four 120 kg tungsten masses. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Inverted Pendulum Standing Apparatus for Investigating Closed-Loop Control of Ankle Joint Muscle Contractions during Functional Electrical Stimulation.

PubMed

Tan, John F; Masani, Kei; Vette, Albert H; Zariffa, José; Robinson, Mark; Lynch, Cheryl; Popovic, Milos R

2014-01-01

The restoration of arm-free standing in individuals with paraplegia can be facilitated via functional electrical stimulation (FES). In developing adequate control strategies for FES systems, it remains challenging to test the performance of a particular control scheme on human subjects. In this study, we propose a testing platform for developing effective control strategies for a closed-loop FES system for standing. The Inverted Pendulum Standing Apparatus (IPSA) is a mechanical inverted pendulum, whose angular position is determined by the subject's ankle joint angle as controlled by the FES system while having the subject's body fixed in a standing frame. This approach provides a setup that is safe, prevents falling, and enables a research and design team to rigorously test various closed-loop controlled FES systems applied to the ankle joints. To demonstrate the feasibility of using the IPSA, we conducted a case series that employed the device for studying FES closed-loop controllers for regulating ankle joint kinematics during standing. The utilized FES system stimulated, in able-bodied volunteers, the plantarflexors as they prevent toppling during standing. Four different conditions were compared, and we were able to show unique performance of each condition using the IPSA. We concluded that the IPSA is a useful tool for developing and testing closed-loop controlled FES systems for regulating ankle joint position during standing.

Inverted Pendulum Standing Apparatus for Investigating Closed-Loop Control of Ankle Joint Muscle Contractions during Functional Electrical Stimulation

PubMed Central

Tan, John F.; Masani, Kei; Vette, Albert H.; Zariffa, José; Robinson, Mark; Lynch, Cheryl; Popovic, Milos R.

2014-01-01

The restoration of arm-free standing in individuals with paraplegia can be facilitated via functional electrical stimulation (FES). In developing adequate control strategies for FES systems, it remains challenging to test the performance of a particular control scheme on human subjects. In this study, we propose a testing platform for developing effective control strategies for a closed-loop FES system for standing. The Inverted Pendulum Standing Apparatus (IPSA) is a mechanical inverted pendulum, whose angular position is determined by the subject's ankle joint angle as controlled by the FES system while having the subject's body fixed in a standing frame. This approach provides a setup that is safe, prevents falling, and enables a research and design team to rigorously test various closed-loop controlled FES systems applied to the ankle joints. To demonstrate the feasibility of using the IPSA, we conducted a case series that employed the device for studying FES closed-loop controllers for regulating ankle joint kinematics during standing. The utilized FES system stimulated, in able-bodied volunteers, the plantarflexors as they prevent toppling during standing. Four different conditions were compared, and we were able to show unique performance of each condition using the IPSA. We concluded that the IPSA is a useful tool for developing and testing closed-loop controlled FES systems for regulating ankle joint position during standing. PMID:27350992

Shoulder Injuries and Disorders - Multiple Languages

MedlinePlus

... Af-Soomaali (Somali) Bilingual PDF Health Information Translations Pendulum Exercises for Shoulder - Af-Soomaali (Somali) Bilingual PDF ... Exercises - español (Spanish) Bilingual PDF Health Information Translations Pendulum Exercises for Shoulder - English PDF Pendulum Exercises for ...

Plume Characterization of Busek 600W Hall Thruster

DTIC Science & Technology

2012-03-09

probe was used to examine the thruster plume current density while the ion species fractions were determined by the ExB probe. The inverted pendulum ...25 A. Inverted Pendulum ...Diagnostic Equipment .....................................................................................45 A. Inverted Pendulum

Precessional Periods of Long and Short Foucault Pendulums

ERIC Educational Resources Information Center

Soga, Michitoshi

1978-01-01

Derives the precessional period of a Foucault pendulum without using small oscillation amplitudes. Shows that if the path of the pendulum passes through the origin, the periods for differing amplitudes are essentially the same. (GA)

[Study on molecular recognition technology in active constituents extracted and isolated from Aconitum pendulum].

PubMed

Ma, Xue-Qin; Li, Guo-Shan; Fu, Xue-Yan; Ma, Jing-Zu

2011-03-01

To investigate CD molecular recognition technology applied in active constituents extracted and isolated from traditional Chinese medicine--Aconitum pendulum. The inclusion constant and form probability of the inclusion complex of Aconitum pendulum with p-CD was calculated by UV spectra method. The active constituents of Aconitum pendulum were extracted and isolated by molecular recognition technology. The inclusion complex was identified by UV. The chemical constituents of Aconitum pendulum and inclusion complex was determined by HPLC. The analgesic effects of inclusion complex was investigated by experiment of intraperitoneal injection of acetic acid in rats. The inclusion complex was identified and confirmed by UV spectra method, the chemical components of inclusion complex were simple, and the content of active constituents increased significantly, the analgesic effects of inclusion complex was well. The molecular recognition technology can be used for extracting and isolating active constituents of Aconitum pendulum, and the effects are obvious.

Charge management for gravitational-wave observatories using UV LEDs

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

Pollack, S. E.; Turner, M. D.; Schlamminger, S.

Accumulation of electrical charge on the end mirrors of gravitational-wave observatories can become a source of noise limiting the sensitivity of such detectors through electronic couplings to nearby surfaces. Torsion balances provide an ideal means for testing gravitational-wave technologies due to their high sensitivity to small forces. Our torsion pendulum apparatus consists of a movable plate brought near a plate pendulum suspended from a nonconducting quartz fiber. A UV LED located near the pendulum photoejects electrons from the surface, and a UV LED driven electron gun directs photoelectrons towards the pendulum surface. We have demonstrated both charging and discharging ofmore » the pendulum with equivalent charging rates of {approx}10{sup 5}e/s, as well as spectral measurements of the pendulum charge resulting in a white noise level equivalent to 3x10{sup 5}e/{radical}(Hz).« less

The Reproduction of Scientific Understanding about Pendulum Motion in the Public

NASA Astrophysics Data System (ADS)

Manabu, Sumida

This paper describes life-span development of understanding about pendulum motion and effects of school science. The subjects were 2,766 people ranging from kindergartners up to 88 years senior citizens. The conflict and consensus between children and their parent's understanding of pendulum motion were also analyzed. The kindergartner's understanding, mostly non-scientific, made a marked developmental change to another type of non-scientific understanding by the time they reach G 4. Parents with scientific understanding do not presumably nurture scientifically minded children,even though about half of them can apply scientific conceptions that shorter pendulums swing faster, and the amplitude and speed of pendulum motion do not depend on its weight. There seems to be another type of developmental change from scientific understanding to non-scientific understanding around their fifties. Itis suggested that the scientific understanding in the public about pendulum motion become predominant due to the educational intervention through school science.

Dynamics of bow-tie shaped bursting: Forced pendulum with dynamic feedback.

PubMed

Hongray, Thotreithem; Balakrishnan, Janaki

2016-12-01

A detailed study is performed on the parameter space of the mechanical system of a driven pendulum with damping and constant torque under feedback control. We report an interesting bow-tie shaped bursting oscillatory behaviour, which is exhibited for small driving frequencies, in a certain parameter regime, which has not been reported earlier in this forced system with dynamic feedback. We show that the bursting oscillations are caused because of a transition of the quiescent state to the spiking state by a saddle-focus bifurcation, and because of another saddle-focus bifurcation, which leads to cessation of spiking, bringing the system back to the quiescent state. The resting period between two successive bursts (T rest ) is estimated analytically.

A Wave Power Device with Pendulum Based on Ocean Monitoring Buoy

NASA Astrophysics Data System (ADS)

Chai, Hui; Guan, Wanchun; Wan, Xiaozheng; Li, Xuanqun; Zhao, Qiang; Liu, Shixuan

2018-01-01

The ocean monitoring buoy usually exploits solar energy for power supply. In order to improve power supply capacity, this paper proposes a wave power device according to the structure and moving character of buoy. The wave power device composes of pendulum mechanism that converts wave energy into mechanical energy and energy storage mechanism where the mechanical energy is transferred quantitatively to generator. The hydrodynamic equation for the motion of buoy system with generator devise is established based on the potential flow theory, and then the characteristics of pendulum motion and energy conversion properties are analysed. The results of this research show that the proposed wave power devise is able to efficiently and periodically convert wave energy into power, and increasing the stiffness of energy storage spring is benefit for enhancing the power supply capacity of the buoy. This study provides a theory reference for the development of technology on wave power generator for ocean monitoring buoy.

Experimental demonstration of active vibration control for flexible structures

NASA Technical Reports Server (NTRS)

Phillips, Douglas J.; Hyland, David C.; Collins, Emmanuel G., Jr.

1990-01-01

Active vibration control of flexible structures for future space missions is addressed. Three experiments that successfully demonstrate control of flexible structures are described. The first is the pendulum experiment. The structure is a 5-m compound pendulum and was designed as an end-to-end test bed for a linear proof mass actuator and its supporting electronics. Experimental results are shown for a maximum-entropy/optimal-projection controller designed to achieve 5 percent damping in the first two pendulum modes. The second experiment was based upon the Harris Multi-Hex prototype experiment (MHPE) apparatus. This is a large optical reflector structure comprising a seven-panel array and supporting truss which typifies a number of generic characteristics of large space systems. The third experiment involved control design and implementation for the ACES structure at NASA Marshall Space Flight Center. The authors conclude with some remarks on the lessons learned from conducting these experiments.

The Pendulum Weaves All Knots and Links

NASA Astrophysics Data System (ADS)

Starrett, John

2003-08-01

From a topological point of view, periodic orbits of three dimensional dynamical systems are knots, that is, circles (S∧1) embedded in the three sphere (S∧3) or in R∧3. The ensemble of periodic orbits comprising the skeleton of a 3-D strange attractor form a link: a collection of (not necessarily linked) knots. Joan Birman and Robert Williams used a topological device known as the template, a branched two-manifold that results when the stable direction is collapsed out of an attractor, to analyze the knot and link types appearing in the geometric Lorenz attractor. More recently, Robert Ghrist has shown the existence of universal templates: templates that support all knot and link types. I show that the template constructed from the geometric attractor of a forced physical pendulum contains a universal template as a subtemplate, and therefore the orbit set of the pendulum contains every knot and link type.

Generating random numbers by means of nonlinear dynamic systems

NASA Astrophysics Data System (ADS)

Zang, Jiaqi; Hu, Haojie; Zhong, Juhua; Luo, Duanbin; Fang, Yi

2018-07-01

To introduce the randomness of a physical process to students, a chaotic pendulum experiment was opened in East China University of Science and Technology (ECUST) on the undergraduate level in the physics department. It was shown chaotic motion could be initiated through adjusting the operation of a chaotic pendulum. By using the data of the angular displacements of chaotic motion, random binary numerical arrays can be generated. To check the randomness of generated numerical arrays, the NIST Special Publication 800-20 method was adopted. As a result, it was found that all the random arrays which were generated by the chaotic motion could pass the validity criteria and some of them were even better than the quality of pseudo-random numbers generated by a computer. Through the experiments, it is demonstrated that chaotic pendulum can be used as an efficient mechanical facility in generating random numbers, and can be applied in teaching random motion to the students.

Motion of a pendulum with damping and vibrating axis of suspension at unconventional values of parameters

NASA Astrophysics Data System (ADS)

Demidov, Ivan; Sorokin, Vladislav

2018-05-01

Motion of a pendulum with damping and vibrating axis of suspension is considered at unconventional values of parameters. Case when the frequency of external loading and the natural frequency of the pendulum in the absence of this loading are of the same order is studied. Vibration intensity is assumed to be relatively low. In this case, the corresponding equation of the pendulum's motions doesn't involve an explicit small parameter. To solve the equation a new modification of the method of direct separation of motions is used. As the result, stability conditions of the pendulum inverted position are determined. Effects of damping on these conditions are discussed.

A novel real-time data acquisition using an Excel spreadsheet in pendulum experiment tool with light-based timer

NASA Astrophysics Data System (ADS)

Adhitama, Egy; Fauzi, Ahmad

2018-05-01

In this study, a pendulum experimental tool with a light-based timer has been developed to measure the period of a simple pendulum. The obtained data was automatically recorded in an Excel spreadsheet. The intensity of monochromatic light, sensed by a 3DU5C phototransistor, dynamically changes as the pendulum swings. The changed intensity varies the resistance value and was processed by the microcontroller, ATMega328, to obtain a signal period as a function of time and brightness when the pendulum crosses the light. Through the experiment, using calculated average periods, the gravitational acceleration value has been accurately and precisely determined.

Maxillary molar distalization: Pendulum and Fast-Back, comparison between two approaches for Class II malocclusion.

PubMed

Caprioglio, Alberto; Beretta, Matteo; Lanteri, Claudio

2011-01-01

To compare the dento-alveolar and skeletal effects produced by two different molar intraoral distalization appliances, Pendulum and Fast-Back, both followed by fixed appliances, in the treatment of Class II malocclusion. 41 patients for Pendulum (18 males and 23 females) and 35 for Fast-Back (14 males and 21 females) were selected, with a mean age at the start of treatment of 12.11 years in the Pendulum group and 13.3 for in the Fast-Back group. The durations of the distalization phase were 8 months in the Pendulum group and 9 months in the Fast-Back group, and the durations of the second phase of treatment with fixed appliances were 19 months in the Pendulum group and 20 months in the Fast-Back group. Lateral cephalograms were analyzed at 3 observation times: before treatment, after distalization and after comprehensive orthodontic treatment. During molar distalization the Pendulum subjects showed greater distal molar movement and less anchorage loss at both the premolars and maxillary incisors than the Fast-Back subjects. Pendulum and Fast-Back produced similar amounts of distal molar movement and overcorrection of molar relationship at the end of distalization though the Fast-Back induced a more bodily movement. Very little change occurred in the inclination of the mandibular plane at the end of the 2-phase treatment in both groups. At the end of treatment the maxillary first molars were on average 1mm more distal in the Pendulum group compared to the Fast-Back group, while the total molar correction was 3.2mm with 3.9° of distal inclination for the Pendulum and 2mm with 1.1° of mesial inclination for the Fast-Back. Both appliance were equally effective in inducing a satisfactory Class I relationship in 97.2% of the cases. The Pendulum and the Fast-Back induce similar dentoskeletal effects. The use of the two distalization devices, therefore, can be considered clinically equivalent. Copyright © 2011 Società Italiana di Ortodonzia SIDO. Published by Elsevier Srl. All rights reserved.

Square-Wave Model for a Pendulum with Oscillating Suspension

ERIC Educational Resources Information Center

Yorke, Ellen D.

1978-01-01

Demonstrates that if a sinusoidal oscillation of the point of support of a pendulum is approximated by a square wave, a matrix method may be used to discuss parametric resonance and the stability of the inverted pendulum. (Author/SL)

Examining Functions in Mathematics and Science Using Computer Interfacing.

ERIC Educational Resources Information Center

Walton, Karen Doyle

1988-01-01

Introduces microcomputer interfacing as a method for explaining and demonstrating various aspects of the concept of function. Provides three experiments with illustrations and typical computer graphic displays: pendulum motion, pendulum study using two pendulums, and heat absorption and radiation. (YP)

Development of a Ground Test Concept Based on Multi-Rotors for In-Flight RVD Experimentation

DTIC Science & Technology

2015-08-01

approach was tried by [2, 23]. The drawback of this second approach is that to perform the flight experiments to acquire identification data, the...the idea is to use the rules of compound pendulum [27] for evaluating the moments of inertia of the body. It is also a prototypical system for...Lagrangian dynamics L = K − V where K is the kinetic energy and V is the potential energy of the pendulum . We assume that the total energy at the zero

Measurement properties of a new wireless electrogoniometer for quantifying spasticity during the pendulum test in ARSACS patients.

PubMed

Bui, Hung Tien; Gagnon, Cynthia; Audet, Olivier; Mathieu, Jean; Leone, Mario

2017-04-15

Autosomal recessive spastic ataxia of Charlevoix/Saguenay (ARSACS) is a neuromuscular disorder that induces spasticity in lower limbs. The Wartenberg pendulum test is a classical method of assessing lower limb spasticity based on the dynamics of the pendular leg motion. However, in its original form, this test only provides subjective results and do not allow accurate assessment of spasticity. Thirteen ARSACS patients were assessed using a new wireless electrogoniometer to measure spasticity by quantifying oscillation amplitudes and relaxation indices during the Wartenburg pendulum test. The validity of the instrument was evaluated by comparing its measurements to a known precise goniometer whereas discriminant validity was evaluated by comparing healthy participants and ARSACS patients. Reliability was measured using intraclass correlation (ICC) between pendulum test scores obtained at different moments in time. Data from different tests show that the proposed device is accurate (standard error of measurement of 0.0005°), discriminates healthy and ARSACS patients (most variables have p=0.00) and provides repeatable results (significant ICC usually higher than 0.64 and p<0.05). The proposed tool allows the clinician to analyze pendulum oscillation amplitudes and ratios and thus, provide an index of spasticity for the patients affected by ARSACS. This is important as the original procedure is only evaluated visually and the progression cannot be detected until the condition changes drastically. Thus, the system proposed meets the requirements of being useful, precise and user-friendly in the evaluation of patients in a research as well as a clinical environment. Copyright © 2017 Elsevier B.V. All rights reserved.

Quadriceps femoris spasticity in children with cerebral palsy: measurement with the pendulum test and relationship with gait abnormalities.

PubMed

Szopa, Andrzej; Domagalska-Szopa, Małgorzata; Kidoń, Zenon; Syczewska, Małgorzata

2014-12-16

Development of a reliable and objective test of spasticity is important for assessment and treatment of children with cerebral palsy. The pendulum test has been reported to yield reliable measurements of spasticity and to be sensitive to variations in spasticity in these children. However, the relationship between the pendulum test scores and other objective measures of spasticity has not been studied. The present study aimed to assess the effectiveness of an accelerometer-based pendulum test as a measurement of spasticity in CP, and to explore the correlation between the measurements of this test and the global index of deviation from normal gait in in children with cerebral palsy. We studied thirty-six children with cerebral palsy, including 18 with spastic hemiplegia and 18 with spastic diplegia, and a group of 18 typically-developing children. Knee extensor spasticity was assessed bilaterally using the accelerometer-based pendulum test and three-dimensional gait analysis. The Gillette Gait Index was calculated from the results of the gait analysis. The data from the accelerometer-based pendulum test could be used to distinguish between able-bodied children and children with cerebral palsy. Additionally, two of the measurements, first swing excursion and relaxation index, could be used to differentiate the degree of knee extensor spasticity in the children with cerebral palsy. Only a few moderate correlations were found between the Gillette Gait Index and the pendulum test data. This study demonstrates that the pendulum test can be used to discriminate between typically developing children and children with CP, as well as between various degrees of spasticity, such as spastic hemiplegia and spastic diplegia, in the knee extensor muscle of children with CP. Deviations from normal gait in children with CP were not correlated with the results of the pendulum test.

Comparison of the effects produced by headgear and pendulum appliances followed by fixed orthodontic treatment.

PubMed

Angelieri, Fernanda; de Almeida, Renato Rodrigues; Janson, Guilherme; Castanha Henriques, José Fernando; Pinzan, Arnaldo

2008-12-01

This study compared the effects produced by two different molar distalizers, namely cervical headgear (CHG) and the intraoral pendulum appliance, associated with fixed orthodontic appliances. The headgear group comprised 30 patients (19 females, 11 males), with an initial age of 13.07 years [standard deviation (SD) = 1.3], treated with CHG and fixed orthodontic appliances for a mean period of 3.28 years, and the pendulum group 22 patients (15 females, 7 males), with initial age of 13.75 years (SD = 1.86), treated with the pendulum appliance followed by fixed orthodontic appliances for a mean period of 4.12 years. Lateral cephalograms were taken at the start (T1) and on completion (T2) of orthodontic treatment. The pendulum and CHG groups were similar as to initial age, severity of the Class II malocclusion, gender distribution, initial cephalometric characteristics, and initial and final treatment priority index (TPI). Only treatment time was not similar between the groups, with a need for annualization for data for the pendulum group. The data were compared with independent t-tests. There was significantly greater restriction of maxillary forward growth and improvement of the skeletal maxillomandibular relationship in the CHG group (P < 0.05). The maxillary molars were more mesially tipped and extruded and the mandibular molars more uprighted in the CHG group compared with the pendulum group (P < 0.05). There was more labial tipping of the mandibular incisors and greater overbite reduction in the pendulum group. The pendulum appliance produced only dentoalveolar effects, different from the CHG appliance, which restricted maxillary forward displacement, thus improving the skeletal maxillomandibular relationship.

Analyzing spring pendulum phenomena with a smart-phone acceleration sensor

NASA Astrophysics Data System (ADS)

Kuhn, Jochen; Vogt, Patrik

2012-11-01

This paper describes two further pendulum experiments using the acceleration sensor of a smartphone in this column (for earlier contributions concerning this topic, including the description of the operation and use of the acceleration sensor, see Refs. 1 and 2). In this paper we focus on analyzing spring pendulum phenomena. Therefore two spring pendulum experiments will be described in which a smartphone is used as a pendulum body and SPARKvue3 software is used in conjunction with an iPhone or an iPod touch, or the Accelogger4 app for an Android device.1,2 As described in Ref. 1, the values measured by the smartphone are subsequently exported to a spreadsheet application (e.g., MS Excel) for analysis.

Magnetic effect in the test of the weak equivalence principle using a rotating torsion pendulum

NASA Astrophysics Data System (ADS)

Zhu, Lin; Liu, Qi; Zhao, Hui-Hui; Yang, Shan-Qing; Luo, Pengshun; Shao, Cheng-Gang; Luo, Jun

2018-04-01

The high precision test of the weak equivalence principle (WEP) using a rotating torsion pendulum requires thorough analysis of systematic effects. Here we investigate one of the main systematic effects, the coupling of the ambient magnetic field to the pendulum. It is shown that the dominant term, the interaction between the average magnetic field and the magnetic dipole of the pendulum, is decreased by a factor of 1.1 × 104 with multi-layer magnetic shield shells. The shield shells reduce the magnetic field to 1.9 × 10-9 T in the transverse direction so that the dipole-interaction limited WEP test is expected at η ≲ 10-14 for a pendulum dipole less than 10-9 A m2. The high-order effect, the coupling of the magnetic field gradient to the magnetic quadrupole of the pendulum, would also contribute to the systematic errors for a test precision down to η ˜ 10-14.

Magnetic effect in the test of the weak equivalence principle using a rotating torsion pendulum.

PubMed

Zhu, Lin; Liu, Qi; Zhao, Hui-Hui; Yang, Shan-Qing; Luo, Pengshun; Shao, Cheng-Gang; Luo, Jun

2018-04-01

The high precision test of the weak equivalence principle (WEP) using a rotating torsion pendulum requires thorough analysis of systematic effects. Here we investigate one of the main systematic effects, the coupling of the ambient magnetic field to the pendulum. It is shown that the dominant term, the interaction between the average magnetic field and the magnetic dipole of the pendulum, is decreased by a factor of 1.1 × 10 4 with multi-layer magnetic shield shells. The shield shells reduce the magnetic field to 1.9 × 10 -9 T in the transverse direction so that the dipole-interaction limited WEP test is expected at η ≲ 10 -14 for a pendulum dipole less than 10 -9 A m 2 . The high-order effect, the coupling of the magnetic field gradient to the magnetic quadrupole of the pendulum, would also contribute to the systematic errors for a test precision down to η ∼ 10 -14 .

Instability dynamics and breather formation in a horizontally shaken pendulum chain.

PubMed

Xu, Y; Alexander, T J; Sidhu, H; Kevrekidis, P G

2014-10-01

Inspired by the experimental results of Cuevas et al. [Phys. Rev. Lett. 102, 224101 (2009)], we consider theoretically the behavior of a chain of planar rigid pendulums suspended in a uniform gravitational field and subjected to a horizontal periodic driving force applied to the pendulum pivots. We characterize the motion of a single pendulum, finding bistability near the fundamental resonance and near the period-3 subharmonic resonance. We examine the development of modulational instability in a driven pendulum chain and find both a critical chain length and a critical frequency for the appearance of the instability. We study the breather solutions and show their connection to the single-pendulum dynamics and extend our analysis to consider multifrequency breathers connected to the period-3 periodic solution, showing also the possibility of stability in these breather states. Finally we examine the problem of breather generation and demonstrate a robust scheme for generation of on-site and off-site breathers.

Mathematic study of the rotor motion with a pendulum selfbalancing device

NASA Astrophysics Data System (ADS)

Ivkina, O. P.; Ziyakaev, G. R.; Pashkov, E. N.

2016-09-01

The rotary machines used in manufacturing may become unbalanced leading to vibration. In some cases, the problem may be solved by installing self-balancing devices (SBDs). Certain factors, however, exhibit a pronounced effect on the efficiency of these devices. The objective of the research comprised of establishing the most beneficial spatial position of pendulums to minimize the necessary time to repair the rotor unbalance. The mathematical research of the motion of a rotor with pendulum SBDs in the situation of their misalignment was undertaken. This objective was achieved by using the Lagrange equations of the second type. The analysis identified limiting cases of location of the rotor unbalance vector and the vector of housing's unbalance relative to each other, as well as the minimum capacity of the pendulum. When determining pendulums ’ parameters during the SBD design process, it is necessary to take into account the rotor unbalance and the unbalance of the machine body, which is caused by the misalignment of rotor axis and pendulum's axis of rotation.

A new torsion pendulum for gravitational reference sensor technology development.

PubMed

Ciani, Giacomo; Chilton, Andrew; Apple, Stephen; Olatunde, Taiwo; Aitken, Michael; Mueller, Guido; Conklin, John W

2017-06-01

We report on the design and sensitivity of a new torsion pendulum for measuring the performance of ultra-precise inertial sensors and for the development of associated technologies for space-based gravitational wave observatories and geodesy missions. The apparatus comprises a 1 m-long, 50 μm-diameter tungsten fiber that supports an inertial member inside a vacuum system. The inertial member is an aluminum crossbar with four hollow cubic test masses at each end. This structure converts the rotation of the torsion pendulum into translation of the test masses. Two test masses are enclosed in capacitive sensors which provide readout and actuation. These test masses are electrically insulated from the rest of the crossbar and their electrical charge is controlled by photoemission using fiber-coupled ultraviolet light emitting diodes. The capacitive readout measures the test mass displacement with a broadband sensitivity of 30 nm∕Hz and is complemented by a laser interferometer with a sensitivity of about 0.5 nm∕Hz. The performance of the pendulum, as determined by the measured residual torque noise and expressed in terms of equivalent force acting on a single test mass, is roughly 200 fN∕Hz around 2 mHz, which is about a factor of 20 above the thermal noise limit of the fiber.

Methodology and Politics in Science: The Fate of Huygens' 1673 Proposal of the Seconds Pendulum as an International Standard of Length and Some Educational Suggestions

NASA Astrophysics Data System (ADS)

Matthews, Michael R.

This paper is part of a larger work on the history, philosophy and utilisation of pendulum motion studies (Matthews 2000). The paper deals with the fate of Christiaan Huygens 1673 proposal to use the length of a seconds pendulum (effectively one metre) as a universal, natural and objective standard of length. This is something which, if it had been adopted, would have been of inestimable scientific, commercial and cultural benefit. Why it was not originally adopted in the late seventeenth century, and why it was again rejected in the late eighteenth century (1795) when the Revolutionary Assembly in France adopted the metric system with the metre being defined as one ten-millionth of the quarter meridan distance - raise interesting questions about the methodology and politics of science. Given that pendulum motion is a standard component of all science courses throughout the world, and given that most science education reforms, including the US National Science Education Standards and recent Australian state reforms, require that something of the big picture of science be conveyed to students (the relationship of science to culture, commerce, history and philosophy) - it is suggested that these educational goals can be advanced by teaching about the fate of Huygens' proposal.

Development of a software-hardware complex for studying the process of grinding by a pendulum deformer

NASA Astrophysics Data System (ADS)

Borisov, A. P.

2018-01-01

The article is devoted to the development of a software and hardware complex for investigating the grinding process on a pendulum deformer. The hardware part of this complex is the Raspberry Pi model 2B platform, to which a contactless angle sensor is connected, which allows to obtain data on the angle of deviation of the pendulum surface, usb-cameras, which allow to obtain grain images before and after grinding, and stepping motors allowing lifting of the pendulum surface and adjust the clearance between the pendulum and the supporting surfaces. The program part of the complex is written in C # and allows receiving data from the sensor and usb-cameras, processing the received data, and also controlling the synchronous-step motors in manual and automatic mode. The conducted studies show that the rational mode is the deviation of the pendulum surface by an angle of 400, and the location of the grain in the central zone of the support surface, regardless of the orientation of the grain in space. Also, due to the non-contact angle sensor, energy consumption for grinding, speed and acceleration of the pendulum surface, as well as vitreousness of grain and the energy consumption are calculated. With the help of photographs obtained from usb cameras, the work of a pendulum deformer based on the Rebinder formula and calculation of the grain area before and after grinding is determined.

Socio-hydrologic modeling to understand and mediate the competition for water between agriculture development and environmental health: Murrumbidgee River basin, Australia

NASA Astrophysics Data System (ADS)

van Emmerik, T. H. M.; Li, Z.; Sivapalan, M.; Pande, S.; Kandasamy, J.; Savenije, H. H. G.; Chanan, A.; Vigneswaran, S.

2014-10-01

Competition for water between humans and ecosystems is set to become a flash point in the coming decades in many parts of the world. An entirely new and comprehensive quantitative framework is needed to establish a holistic understanding of that competition, thereby enabling the development of effective mediation strategies. This paper presents a modeling study centered on the Murrumbidgee River basin (MRB). The MRB has witnessed a unique system dynamics over the last 100 years as a result of interactions between patterns of water management and climate driven hydrological variability. Data analysis has revealed a pendulum swing between agricultural development and restoration of environmental health and ecosystem services over different stages of basin-scale water resource development. A parsimonious, stylized, quasi-distributed coupled socio-hydrologic system model that simulates the two-way coupling between human and hydrological systems of the MRB is used to mimic and explain dominant features of the pendulum swing. The model consists of coupled nonlinear ordinary differential equations that describe the interaction between five state variables that govern the co-evolution: reservoir storage, irrigated area, human population, ecosystem health, and environmental awareness. The model simulations track the propagation of the external climatic and socio-economic drivers through this coupled, complex system to the emergence of the pendulum swing. The model results point to a competition between human "productive" and environmental "restorative" forces that underpin the pendulum swing. Both the forces are endogenous, i.e., generated by the system dynamics in response to external drivers and mediated by humans through technology change and environmental awareness, respectively. Sensitivity analysis carried out with the model further reveals that socio-hydrologic modeling can be used as a tool to explain or gain insight into observed co-evolutionary dynamics of diverse human-water coupled systems. This paper therefore contributes to the ultimate development of a generic modeling framework that can be applied to human-water coupled systems in different climatic and socio-economic settings.

Integral backstepping sliding mode control for underactuated systems: swing-up and stabilization of the Cart-Pendulum System.

PubMed

Adhikary, Nabanita; Mahanta, Chitralekha

2013-11-01

In this paper an integral backstepping sliding mode controller is proposed for controlling underactuated systems. A feedback control law is designed based on backstepping algorithm and a sliding surface is introduced in the final stage of the algorithm. The backstepping algorithm makes the controller immune to matched and mismatched uncertainties and the sliding mode control provides robustness. The proposed controller ensures asymptotic stability. The effectiveness of the proposed controller is compared against a coupled sliding mode controller for swing-up and stabilization of the Cart-Pendulum System. Simulation results show that the proposed integral backstepping sliding mode controller is able to reject both matched and mismatched uncertainties with a chattering free control law, while utilizing less control effort than the sliding mode controller. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Stabilization of an inverted pendulum-cart system by fractional PI-state feedback.

PubMed

Bettayeb, M; Boussalem, C; Mansouri, R; Al-Saggaf, U M

2014-03-01

This paper deals with pole placement PI-state feedback controller design to control an integer order system. The fractional aspect of the control law is introduced by a dynamic state feedback as u(t)=K(p)x(t)+K(I)I(α)(x(t)). The closed loop characteristic polynomial is thus fractional for which the roots are complex to calculate. The proposed method allows us to decompose this polynomial into a first order fractional polynomial and an integer order polynomial of order n-1 (n being the order of the integer system). This new stabilization control algorithm is applied for an inverted pendulum-cart test-bed, and the effectiveness and robustness of the proposed control are examined by experiments. Crown Copyright © 2013. Published by Elsevier Ltd. All rights reserved.

49 CFR 572.123 - Neck assembly and test procedure.

Code of Federal Regulations, 2012 CFR

2012-10-01

... with respect to the pendulum's longitudinal centerline between 74 degrees and 92 degrees. Within this... direction of preimpact flight with respect to the pendulum's longitudinal centerline between 85 degrees and... contact between the pendulum striker plate and the honeycomb material. (c) Test procedure. The test...

49 CFR 572.123 - Neck assembly and test procedure.

Code of Federal Regulations, 2013 CFR

2013-10-01

... with respect to the pendulum's longitudinal centerline between 74 degrees and 92 degrees. Within this... direction of preimpact flight with respect to the pendulum's longitudinal centerline between 85 degrees and... contact between the pendulum striker plate and the honeycomb material. (c) Test procedure. The test...

49 CFR 572.123 - Neck assembly and test procedure.

Code of Federal Regulations, 2010 CFR

2010-10-01

... with respect to the pendulum's longitudinal centerline between 74 degrees and 92 degrees. Within this... direction of preimpact flight with respect to the pendulum's longitudinal centerline between 85 degrees and... contact between the pendulum striker plate and the honeycomb material. (c) Test procedure. The test...

49 CFR 572.123 - Neck assembly and test procedure.

Code of Federal Regulations, 2014 CFR

2014-10-01

... with respect to the pendulum's longitudinal centerline between 74 degrees and 92 degrees. Within this... direction of preimpact flight with respect to the pendulum's longitudinal centerline between 85 degrees and... contact between the pendulum striker plate and the honeycomb material. (c) Test procedure. The test...

49 CFR 572.123 - Neck assembly and test procedure.

Code of Federal Regulations, 2011 CFR

2011-10-01

... with respect to the pendulum's longitudinal centerline between 74 degrees and 92 degrees. Within this... direction of preimpact flight with respect to the pendulum's longitudinal centerline between 85 degrees and... contact between the pendulum striker plate and the honeycomb material. (c) Test procedure. The test...

Pendulum Phenomena and the Assessment of Scientific Inquiry Capabilities

ERIC Educational Resources Information Center

Zachos, Paul

2004-01-01

Phenomena associated with the "pendulum" present numerous opportunities for assessing higher order human capabilities related to "scientific inquiry" and the "discovery" of natural law. This paper illustrates how systematic "assessment of scientific inquiry capabilities", using "pendulum" phenomena, can provide a useful tool for classroom teachers…

Observation of the Topological Change Associated with the Dynamical Monodromy

NASA Astrophysics Data System (ADS)

Salmon, Daniel; Nerem, Matthew; Aubin, Seth; Delos, John

2017-04-01

Classical mechanics is an old theory and new phenomena do not often appear. A recently predicted phenomenon is called ``Dynamical Monodromy.'' Monodromy is the study of the behavior of a system as it evolves ``once around a closed circuit''. Systems that do not return to their original state after forming a closed circuit in some space are said to exhibit ``nontrivial monodromy.'' One such system is a collection of non-interacting particles moving in a ``champagne bottle'' potential. A loop of trajectories of this system exhibits a topological change when each of the particles traverse a monodromy circuit in Energy-Angular Momentum space (any closed path that encloses the singular point at the origin). This system has been realized using a rigid spherical pendulum, with a permanent magnet at its end. Magnetic fields generated by coils are used to create the champagne-bottle potential, as well as drive the pendulum through the monodromy circuit.

Robustness of delayed multistable systems with application to droop-controlled inverter-based microgrids

NASA Astrophysics Data System (ADS)

Efimov, Denis; Schiffer, Johannes; Ortega, Romeo

2016-05-01

Motivated by the problem of phase-locking in droop-controlled inverter-based microgrids with delays, the recently developed theory of input-to-state stability (ISS) for multistable systems is extended to the case of multistable systems with delayed dynamics. Sufficient conditions for ISS of delayed systems are presented using Lyapunov-Razumikhin functions. It is shown that ISS multistable systems are robust with respect to delays in a feedback. The derived theory is applied to two examples. First, the ISS property is established for the model of a nonlinear pendulum and delay-dependent robustness conditions are derived. Second, it is shown that, under certain assumptions, the problem of phase-locking analysis in droop-controlled inverter-based microgrids with delays can be reduced to the stability investigation of the nonlinear pendulum. For this case, corresponding delay-dependent conditions for asymptotic phase-locking are given.

Dynamic Modeling and Simulation of an Underactuated System

NASA Astrophysics Data System (ADS)

Libardo Duarte Madrid, Juan; Ospina Henao, P. A.; González Querubín, E.

2017-06-01

In this paper, is used the Lagrangian classical mechanics for modeling the dynamics of an underactuated system, specifically a rotary inverted pendulum that will have two equations of motion. A basic design of the system is proposed in SOLIDWORKS 3D CAD software, which based on the material and dimensions of the model provides some physical variables necessary for modeling. In order to verify the results obtained, a comparison the CAD model simulated in the environment SimMechanics of MATLAB software with the mathematical model who was consisting of Euler-Lagrange’s equations implemented in Simulink MATLAB, solved with the ODE23tb method, included in the MATLAB libraries for the solution of systems of equations of the type and order obtained. This article also has a topological analysis of pendulum trajectories through a phase space diagram, which allows the identification of stable and unstable regions of the system.

Effects of conventional anchorage on premolar root development during treatment with a pendulum appliance.

PubMed

Kinzinger, Gero; Pantel, Cora; Ludwig, Björn; Gülden, Norbert; Glasl, Bettina; Lisson, Jörg

2010-07-01

By metrically analyzing orthopantomograms, we aimed in this study to retrospectively investigate whether maxillary premolars used as anchoring teeth during molar distalization with pendulum appliances would reveal inhibited root development. The upper molars were distalized with a modified pendulum appliance (Pendulum K) in 36 adolescents (14 males, 22 females, mean age 12.3 years). Mean treatment period was 19.5 weeks. Orthopantomograms of each patient were taken at the start (time point T1) and after completion of molar distalization (time point T2). The enlargement of the posterior region was ascertained individually quadrant by quadrant for each radiograph, followed by measurement of the vestibular tooth lengths of the premolars whose root development was for the most part not yet complete. To assess further root development in the premolar region, the differences were calculated between tooth lengths at the start and end of treatment. During treatment with the pendulum appliance a general increase in tooth lengths in the anchorage region was observed (1.37 +/- 1.70 mm, p<0.0001). Differentiated by dental age, we noted increases in tooth lengths of patients with second molars in the budding stage (patient group PG 1: 0.93 +/- 1.37 mm, p<0.0001) as well as of patients with fully-erupted second molars (patient group PG 2: 1.81 +/- 1.88 mm, p<0.0001). Both groups demonstrated greater increases in the second premolars than the first premolars; the increases group-wise were larger in PG 2 than PG 1. However, both the group comparison (PG 1 versus PG 2) and the side comparison (right versus left) (differentiated into first and second molars) showed no statistically relevant differences. Visual assessment of the radiographs revealed no evidence of treatment-related root deviations. A highly complex system of forces acts on the anchoring teeth during molar distalization with the conventionally-anchored Pendulum K. However, the Pendulum K appliance's specific biomechanics make it possible to transfer the reactive forces and moments to the anchorage unit so that they remain within the physiological range, allowing uninhibited premolar root development. This also applies after completed eruption of the second molars, when the treatment period and hence duration of exposure to the active and reactive forces and moments arising during molar distalization are comparatively increased.

The Pendulum Equation

ERIC Educational Resources Information Center

Fay, Temple H.

2002-01-01

We investigate the pendulum equation [theta] + [lambda][squared] sin [theta] = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series approximations for sin [theta] do not yield very good differential equations to approximate the solution of the pendulum equation unless the initial conditions are…

Equilibrium and Stability of a Pendulum in an Orbiting Spaceship.

ERIC Educational Resources Information Center

Blitzer, Leon

1979-01-01

Investigates the behavior of a simple pendulum attached to a fixed point inside a satellite moving in a circular orbit about the earth. It is found that the number of equilibrium positions depends on the length of the pendulum and the location of the point of attachment. (HM)

49 CFR 581.6 - Conditions.

Code of Federal Regulations, 2011 CFR

2011-10-01

... the vehicle if they are optional equipment. (b) Pendulum test conditions. The following conditions apply to the pendulum test procedures of § 581.7 (a) and (b). (1) The test device consists of a block... 1963. From the point of release of the device until the onset of rebound, the pendulum suspension...

49 CFR 572.17 - Neck.

Code of Federal Regulations, 2012 CFR

2012-10-01

... (c) of this section, the head shall rotate in reference to the pendulum's longitudinal centerline a... distance between (1) the position relative to the pendulum arm of the head center of gravity at time zero, and (2) the position relative to the pendulum arm of the head center of gravity at time T as...

49 CFR 572.113 - Neck assembly.

Code of Federal Regulations, 2012 CFR

2012-10-01

...) Using neck brackets 78051-303 and -307, mount the head/neck assembly to the part 572 pendulum test... to the plane of motion of the pendulum's longitudinal centerline (see § 572.33, Figure 20, except... (horizontal surface at the base of the skull) rotation with respect to the pendulum's longitudinal centerline...

49 CFR 572.7 - Neck.

Code of Federal Regulations, 2014 CFR

2014-10-01

... paragraph (c) of this section, the head shall rotate in reference to the pendulum's longitudinal centerline... the straight line distance between (1) the position relative to the pendulum arm of the head center of gravity at time zero, and (2) the position relative to the pendulum arm of the head center of gravity at...

49 CFR 581.6 - Conditions.

Code of Federal Regulations, 2013 CFR

2013-10-01

... the vehicle if they are optional equipment. (b) Pendulum test conditions. The following conditions apply to the pendulum test procedures of § 581.7 (a) and (b). (1) The test device consists of a block... 1963. From the point of release of the device until the onset of rebound, the pendulum suspension...

49 CFR 572.143 - Neck-headform assembly and test procedure.

Code of Federal Regulations, 2013 CFR

2013-10-01

... subpart, shall rotate in the direction of preimpact flight with respect to the pendulum's longitudinal... rotation data channels are defined to be zero when the longitudinal centerline of the neck and pendulum are... of preimpact flight with respect to the pendulum's longitudinal centerline between 83 degrees and 93...

49 CFR 572.36 - Test conditions and instrumentation.

Code of Federal Regulations, 2013 CFR

2013-10-01

... be mounted with its sensitive axis colinear with the pendulum's longitudinal centerline. (h) The... acceleration—Class 1000 (2) Neck forces—Class 1000 (3) Neck moments—Class 600 (4) Neck pendulum acceleration—Class 60 (5) Thorax and thorax pendulum acceleration—Class 180 (6) Thorax deflection—Class 180 (7) Knee...

49 CFR 572.17 - Neck.

Code of Federal Regulations, 2014 CFR

2014-10-01

... (c) of this section, the head shall rotate in reference to the pendulum's longitudinal centerline a... distance between (1) the position relative to the pendulum arm of the head center of gravity at time zero, and (2) the position relative to the pendulum arm of the head center of gravity at time T as...

49 CFR 572.133 - Neck assembly and test procedure.

Code of Federal Regulations, 2012 CFR

2012-10-01

... pendulum's longitudinal centerline between 77 degrees and 91 degrees. During the time interval while the... respect to the pendulum's longitudinal centerline between 99 degrees and 114 degrees. During the time... force to occipital condyle. (3) Time-zero is defined as the time of initial contact between the pendulum...

49 CFR 572.17 - Neck.

Code of Federal Regulations, 2013 CFR

2013-10-01

... (c) of this section, the head shall rotate in reference to the pendulum's longitudinal centerline a... distance between (1) the position relative to the pendulum arm of the head center of gravity at time zero, and (2) the position relative to the pendulum arm of the head center of gravity at time T as...

49 CFR 572.113 - Neck assembly.

Code of Federal Regulations, 2011 CFR

2011-10-01

...) Using neck brackets 78051-303 and -307, mount the head/neck assembly to the part 572 pendulum test... to the plane of motion of the pendulum's longitudinal centerline (see § 572.33, Figure 20, except... (horizontal surface at the base of the skull) rotation with respect to the pendulum's longitudinal centerline...

49 CFR 572.17 - Neck.

Code of Federal Regulations, 2010 CFR

2010-10-01

... (c) of this section, the head shall rotate in reference to the pendulum's longitudinal centerline a... distance between (1) the position relative to the pendulum arm of the head center of gravity at time zero, and (2) the position relative to the pendulum arm of the head center of gravity at time T as...

49 CFR 572.133 - Neck assembly and test procedure.

Code of Federal Regulations, 2010 CFR

2010-10-01

... pendulum's longitudinal centerline between 77 degrees and 91 degrees. During the time interval while the... respect to the pendulum's longitudinal centerline between 99 degrees and 114 degrees. During the time... force to occipital condyle. (3) Time-zero is defined as the time of initial contact between the pendulum...

49 CFR 581.6 - Conditions.

Code of Federal Regulations, 2012 CFR

2012-10-01

... the vehicle if they are optional equipment. (b) Pendulum test conditions. The following conditions apply to the pendulum test procedures of § 581.7 (a) and (b). (1) The test device consists of a block... 1963. From the point of release of the device until the onset of rebound, the pendulum suspension...

49 CFR 572.153 - Neck-headform assembly and test procedure.

Code of Federal Regulations, 2014 CFR

2014-10-01

... subpart shall rotate in the direction of pre-impact flight with respect to the pendulum's longitudinal... shall rotate in the direction of preimpact flight with respect to the pendulum's longitudinal centerline... section, on the pendulum so the midsagittal plane of the headform is vertical and coincides with the plane...

49 CFR 572.143 - Neck-headform assembly and test procedure.

Code of Federal Regulations, 2012 CFR

2012-10-01

... subpart, shall rotate in the direction of preimpact flight with respect to the pendulum's longitudinal... rotation data channels are defined to be zero when the longitudinal centerline of the neck and pendulum are... of preimpact flight with respect to the pendulum's longitudinal centerline between 83 degrees and 93...

49 CFR 572.133 - Neck assembly and test procedure.

Code of Federal Regulations, 2013 CFR

2013-10-01

... pendulum's longitudinal centerline between 77 degrees and 91 degrees. During the time interval while the... respect to the pendulum's longitudinal centerline between 99 degrees and 114 degrees. During the time... force to occipital condyle. (3) Time-zero is defined as the time of initial contact between the pendulum...

49 CFR 572.173 - Neck assembly and test procedure.

Code of Federal Regulations, 2012 CFR

2012-10-01

... respect to the pendulum's longitudinal centerline between 76 degrees and 90 degrees. During the time..., referenced in Figure T3, shall rotate in the direction of preimpact flight with respect to the pendulum's... occipital condyle. (3) Time zero is defined as the time of initial contact between the pendulum striker...

49 CFR 581.6 - Conditions.

Code of Federal Regulations, 2010 CFR

2010-10-01

... the vehicle if they are optional equipment. (b) Pendulum test conditions. The following conditions apply to the pendulum test procedures of § 581.7 (a) and (b). (1) The test device consists of a block... 1963. From the point of release of the device until the onset of rebound, the pendulum suspension...

49 CFR 581.6 - Conditions.

Code of Federal Regulations, 2014 CFR

2014-10-01

... the vehicle if they are optional equipment. (b) Pendulum test conditions. The following conditions apply to the pendulum test procedures of § 581.7 (a) and (b). (1) The test device consists of a block... 1963. From the point of release of the device until the onset of rebound, the pendulum suspension...

49 CFR 572.173 - Neck assembly and test procedure.

Code of Federal Regulations, 2014 CFR

2014-10-01

... respect to the pendulum's longitudinal centerline between 76 degrees and 90 degrees. During the time..., referenced in Figure T3, shall rotate in the direction of preimpact flight with respect to the pendulum's... occipital condyle. (3) Time zero is defined as the time of initial contact between the pendulum striker...

49 CFR 572.153 - Neck-headform assembly and test procedure.

Code of Federal Regulations, 2012 CFR

2012-10-01

... subpart shall rotate in the direction of pre-impact flight with respect to the pendulum's longitudinal... shall rotate in the direction of preimpact flight with respect to the pendulum's longitudinal centerline... section, on the pendulum so the midsagittal plane of the headform is vertical and coincides with the plane...

Conical Pendulum--Linearization Analyses

ERIC Educational Resources Information Center

Dean, Kevin; Mathew, Jyothi

2016-01-01

A theoretical analysis is presented, showing the derivations of seven different linearization equations for the conical pendulum period "T", as a function of radial and angular parameters. Experimental data obtained over a large range of fixed conical pendulum lengths (0.435 m-2.130 m) are plotted with the theoretical lines and…

49 CFR 572.17 - Neck.

Code of Federal Regulations, 2011 CFR

2011-10-01

... (c) of this section, the head shall rotate in reference to the pendulum's longitudinal centerline a... distance between (1) the position relative to the pendulum arm of the head center of gravity at time zero, and (2) the position relative to the pendulum arm of the head center of gravity at time T as...

49 CFR 572.113 - Neck assembly.

Code of Federal Regulations, 2013 CFR

2013-10-01

...) Using neck brackets 78051-303 and -307, mount the head/neck assembly to the part 572 pendulum test... to the plane of motion of the pendulum's longitudinal centerline (see § 572.33, Figure 20, except... (horizontal surface at the base of the skull) rotation with respect to the pendulum's longitudinal centerline...

49 CFR 572.7 - Neck.

Code of Federal Regulations, 2012 CFR

2012-10-01

... paragraph (c) of this section, the head shall rotate in reference to the pendulum's longitudinal centerline... the straight line distance between (1) the position relative to the pendulum arm of the head center of gravity at time zero, and (2) the position relative to the pendulum arm of the head center of gravity at...

49 CFR 572.143 - Neck-headform assembly and test procedure.

Code of Federal Regulations, 2010 CFR

2010-10-01

... subpart, shall rotate in the direction of preimpact flight with respect to the pendulum's longitudinal... rotation data channels are defined to be zero when the longitudinal centerline of the neck and pendulum are... of preimpact flight with respect to the pendulum's longitudinal centerline between 83 degrees and 93...

49 CFR 572.173 - Neck assembly and test procedure.

Code of Federal Regulations, 2013 CFR

2013-10-01

... respect to the pendulum's longitudinal centerline between 76 degrees and 90 degrees. During the time..., referenced in Figure T3, shall rotate in the direction of preimpact flight with respect to the pendulum's... occipital condyle. (3) Time zero is defined as the time of initial contact between the pendulum striker...

49 CFR 572.133 - Neck assembly and test procedure.

Code of Federal Regulations, 2014 CFR

2014-10-01

... pendulum's longitudinal centerline between 77 degrees and 91 degrees. During the time interval while the... respect to the pendulum's longitudinal centerline between 99 degrees and 114 degrees. During the time... force to occipital condyle. (3) Time-zero is defined as the time of initial contact between the pendulum...

49 CFR 572.153 - Neck-headform assembly and test procedure.

Code of Federal Regulations, 2013 CFR

2013-10-01

... subpart shall rotate in the direction of pre-impact flight with respect to the pendulum's longitudinal... shall rotate in the direction of preimpact flight with respect to the pendulum's longitudinal centerline... section, on the pendulum so the midsagittal plane of the headform is vertical and coincides with the plane...

49 CFR 572.133 - Neck assembly and test procedure.

Code of Federal Regulations, 2011 CFR

2011-10-01

... pendulum's longitudinal centerline between 77 degrees and 91 degrees. During the time interval while the... respect to the pendulum's longitudinal centerline between 99 degrees and 114 degrees. During the time... force to occipital condyle. (3) Time-zero is defined as the time of initial contact between the pendulum...

49 CFR 572.113 - Neck assembly.

Code of Federal Regulations, 2010 CFR

2010-10-01

...) Using neck brackets 78051-303 and -307, mount the head/neck assembly to the part 572 pendulum test... to the plane of motion of the pendulum's longitudinal centerline (see § 572.33, Figure 20, except... (horizontal surface at the base of the skull) rotation with respect to the pendulum's longitudinal centerline...

49 CFR 572.7 - Neck.

Code of Federal Regulations, 2013 CFR

2013-10-01

... paragraph (c) of this section, the head shall rotate in reference to the pendulum's longitudinal centerline... the straight line distance between (1) the position relative to the pendulum arm of the head center of gravity at time zero, and (2) the position relative to the pendulum arm of the head center of gravity at...

49 CFR 572.153 - Neck-headform assembly and test procedure.

Code of Federal Regulations, 2011 CFR

2011-10-01

... subpart shall rotate in the direction of pre-impact flight with respect to the pendulum's longitudinal... shall rotate in the direction of preimpact flight with respect to the pendulum's longitudinal centerline... section, on the pendulum so the midsagittal plane of the headform is vertical and coincides with the plane...

49 CFR 572.36 - Test conditions and instrumentation.

Code of Federal Regulations, 2014 CFR

2014-10-01

... be mounted with its sensitive axis colinear with the pendulum's longitudinal centerline. (h) The... acceleration—Class 1000 (2) Neck forces—Class 1000 (3) Neck moments—Class 600 (4) Neck pendulum acceleration—Class 60 (5) Thorax and thorax pendulum acceleration—Class 180 (6) Thorax deflection—Class 180 (7) Knee...

49 CFR 572.7 - Neck.

Code of Federal Regulations, 2010 CFR

2010-10-01

... paragraph (c) of this section, the head shall rotate in reference to the pendulum's longitudinal centerline... the straight line distance between (1) the position relative to the pendulum arm of the head center of gravity at time zero, and (2) the position relative to the pendulum arm of the head center of gravity at...

49 CFR 572.153 - Neck-headform assembly and test procedure.

Code of Federal Regulations, 2010 CFR

2010-10-01

... subpart shall rotate in the direction of pre-impact flight with respect to the pendulum's longitudinal... shall rotate in the direction of preimpact flight with respect to the pendulum's longitudinal centerline... section, on the pendulum so the midsagittal plane of the headform is vertical and coincides with the plane...

49 CFR 572.113 - Neck assembly.

Code of Federal Regulations, 2014 CFR

2014-10-01

...) Using neck brackets 78051-303 and -307, mount the head/neck assembly to the part 572 pendulum test... to the plane of motion of the pendulum's longitudinal centerline (see § 572.33, Figure 20, except... (horizontal surface at the base of the skull) rotation with respect to the pendulum's longitudinal centerline...

49 CFR 572.7 - Neck.

Code of Federal Regulations, 2011 CFR

2011-10-01

... paragraph (c) of this section, the head shall rotate in reference to the pendulum's longitudinal centerline... the straight line distance between (1) the position relative to the pendulum arm of the head center of gravity at time zero, and (2) the position relative to the pendulum arm of the head center of gravity at...

49 CFR 572.36 - Test conditions and instrumentation.

Code of Federal Regulations, 2011 CFR

2011-10-01

... be mounted with its sensitive axis colinear with the pendulum's longitudinal centerline. (h) The... acceleration—Class 1000 (2) Neck forces—Class 1000 (3) Neck moments—Class 600 (4) Neck pendulum acceleration—Class 60 (5) Thorax and thorax pendulum acceleration—Class 180 (6) Thorax deflection—Class 180 (7) Knee...

49 CFR 572.36 - Test conditions and instrumentation.

Code of Federal Regulations, 2012 CFR

2012-10-01

... be mounted with its sensitive axis colinear with the pendulum's longitudinal centerline. (h) The... acceleration—Class 1000 (2) Neck forces—Class 1000 (3) Neck moments—Class 600 (4) Neck pendulum acceleration—Class 60 (5) Thorax and thorax pendulum acceleration—Class 180 (6) Thorax deflection—Class 180 (7) Knee...

49 CFR 572.143 - Neck-headform assembly and test procedure.

Code of Federal Regulations, 2011 CFR

2011-10-01

... subpart, shall rotate in the direction of preimpact flight with respect to the pendulum's longitudinal... rotation data channels are defined to be zero when the longitudinal centerline of the neck and pendulum are... of preimpact flight with respect to the pendulum's longitudinal centerline between 83 degrees and 93...

49 CFR 572.36 - Test conditions and instrumentation.

Code of Federal Regulations, 2010 CFR

2010-10-01

... be mounted with its sensitive axis colinear with the pendulum's longitudinal centerline. (h) The... acceleration—Class 1000 (2) Neck forces—Class 1000 (3) Neck moments—Class 600 (4) Neck pendulum acceleration—Class 60 (5) Thorax and thorax pendulum acceleration—Class 180 (6) Thorax deflection—Class 180 (7) Knee...

49 CFR 572.143 - Neck-headform assembly and test procedure.

Code of Federal Regulations, 2014 CFR

2014-10-01

... subpart, shall rotate in the direction of preimpact flight with respect to the pendulum's longitudinal... rotation data channels are defined to be zero when the longitudinal centerline of the neck and pendulum are... of preimpact flight with respect to the pendulum's longitudinal centerline between 83 degrees and 93...

"Time: What Is It that It Can Be Measured?"

ERIC Educational Resources Information Center

Raju, C. K.

2006-01-01

Experiments with the simple pendulum are easy, but its motion is nevertheless confounded with simple harmonic motion. However, refined theoretical models of the pendulum can, today, be easily taught using software like CALCODE. Similarly, the cycloidal pendulum is isochronous only in simplified theory. But what "are" theoretically equal intervals…

The Pendulum and the Calculus.

ERIC Educational Resources Information Center

Sworder, Steven C.

A pair of experiments, appropriate for the lower division fourth semester calculus or differential equations course, are presented. The second order differential equation representing the equation of motion of a simple pendulum is derived. The period of oscillation for a particular pendulum can be predicted from the solution to this equation. As a…

Multi-directional energy harvesting by piezoelectric cantilever-pendulum with internal resonance

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

Xu, J.; Tang, J., E-mail: jtang@engr.uconn.edu

This letter reports a piezoelectric cantilever-pendulum design for multi-directional energy harvesting. A pendulum is attached to the tip of a piezoelectric cantilever-type energy harvester. This design aims at taking advantage of the nonlinear coupling between the pendulum motion in 3-dimensional space and the beam bending vibration at resonances. Experimental studies indicate that, under properly chosen parameters, 1:2 internal resonance can be induced, which enables the multi-directional energy harvesting with a single cantilever. The advantages of the design with respect to traditional piezoelectric cantilever are examined.

Mood regulation in bipolar disorders viewed through the pendulum dynamics concept.

PubMed

Koutsoukos, Elias; Angelopoulos, Elias

2014-12-01

Bipolar disorders have been characterized by powerful fluctuations of energy, mood, and thinking patterns. Mood episodes (manic or depressive) could be considered as deviations of a psycho-physiological index above or below a conventionally defined value called 'normothymia'. In the present study, we analyzed the feedback techniques used to suppress the oscillatory activity exhibited on an inverted pendulum device. Subsequently, we examine the degree that this multimodal feedback design could be considered on a hypothetical pendulum where the mood plays the role of the suspended mass, and the force balance compensation circuitry is substituted by drug-specific therapeutic interventions. The study does not concern a model of bipolar illness that could simulate numerically various phases of mood episodes but focuses on the functional similarities regarding the correction treatments applied on the two different oscillating systems giving a potential perspective of how techniques of feedback control may enhance the conceptualization of the treatment schemes followed in recent guidelines for biological treatment of bipolar disorders. Our theoretical consideration, along with observations on clinical level, gives support to the concept that the compensation of the mood oscillations should be adaptive with selective therapeutic interventions that compensate the excited system in different time scales.

What Makes the Foucault Pendulum Move among the Stars?

ERIC Educational Resources Information Center

Phillips, Norman

2004-01-01

Foucault's pendulum exhibition in 1851 occurred in an era now known by development of the theorems of Coriolis and the formulation of dynamical meteorology by Ferrel. Yet today the behavior of the pendulum is often misunderstood. The existence of a horizontal component of Newtonian gravitation is essential for understanding the behavior with…

49 CFR 572.189 - Instrumentation and test conditions.

Code of Federal Regulations, 2014 CFR

2014-10-01

.... The sum mass of the attachments and 1/3 cable mass must not exceed 5 percent of the total pendulum... filtered CFC 180; (3)Neck and lumbar spine pendulum accelerations—Digitally filtered CFC 60; (4) Pelvis... 180. (j)(1) Filter the pendulum acceleration data using a SAE J211 CFC 60 filter. (2) Determine the...

49 CFR 572.189 - Instrumentation and test conditions.

Code of Federal Regulations, 2011 CFR

2011-10-01

... mass of the attachments and 1/3 cable mass must not exceed 5 percent of the total pendulum mass. No... lumbar spine pendulum accelerations—Digitally filtered CFC 60; (4) Pelvis, shoulder, thorax without arm...—Digitally filtered at CFC 600; (6) Thorax deflection—Digitally filtered CFC 180. (j)(1) Filter the pendulum...

49 CFR 572.33 - Neck.

Code of Federal Regulations, 2013 CFR

2013-10-01

... (b) of this section, on a rigid pendulum as shown in Figure 22 so that the head's midsagittal plane is vertical and coincides with the plane of motion of the pendulum's longitudinal axis. ER02JN11.011 (4) Release the pendulum and allow it to fall freely from a height such that the tangential velocity...

49 CFR 572.189 - Instrumentation and test conditions.

Code of Federal Regulations, 2013 CFR

2013-10-01

.... The sum mass of the attachments and 1/3 cable mass must not exceed 5 percent of the total pendulum... filtered CFC 180; (3)Neck and lumbar spine pendulum accelerations—Digitally filtered CFC 60; (4) Pelvis... 180. (j)(1) Filter the pendulum acceleration data using a SAE J211 CFC 60 filter. (2) Determine the...

49 CFR 572.35 - Limbs.

Code of Federal Regulations, 2014 CFR

2014-10-01

... in accordance with paragraph (b)(2) of this section, at 6.9 ft/sec ±0.10 ft/sec by the pendulum defined in § 572.36(b), the peak knee impact force, which is a product of pendulum mass and acceleration... the femur load cell simulator. (v) Guide the pendulum so that there is no significant lateral...

49 CFR 572.33 - Neck.

Code of Federal Regulations, 2011 CFR

2011-10-01

... (b) of this section, on a rigid pendulum as shown in Figure 22 so that the head's midsagittal plane is vertical and coincides with the plane of motion of the pendulum's longitudinal axis. EC01AU91.165 (4) Release the pendulum and allow it to fall freely from a height such that the tangential velocity...

49 CFR 572.35 - Limbs.

Code of Federal Regulations, 2013 CFR

2013-10-01

... in accordance with paragraph (b)(2) of this section, at 6.9 ft/sec ±0.10 ft/sec by the pendulum defined in § 572.36(b), the peak knee impact force, which is a product of pendulum mass and acceleration... the femur load cell simulator. (v) Guide the pendulum so that there is no significant lateral...

49 CFR 572.189 - Instrumentation and test conditions.

Code of Federal Regulations, 2010 CFR

2010-10-01

... mass of the attachments and 1/3 cable mass must not exceed 5 percent of the total pendulum mass. No... lumbar spine pendulum accelerations—Digitally filtered CFC 60; (4) Pelvis, shoulder, thorax without arm...—Digitally filtered at CFC 600; (6) Thorax deflection—Digitally filtered CFC 180. (j)(1) Filter the pendulum...

49 CFR 572.33 - Neck.

Code of Federal Regulations, 2012 CFR

2012-10-01

... (b) of this section, on a rigid pendulum as shown in Figure 22 so that the head's midsagittal plane is vertical and coincides with the plane of motion of the pendulum's longitudinal axis. ER02JN11.011 (4) Release the pendulum and allow it to fall freely from a height such that the tangential velocity...

49 CFR 572.35 - Limbs.

Code of Federal Regulations, 2012 CFR

2012-10-01

... in accordance with paragraph (b)(2) of this section, at 6.9 ft/sec ±0.10 ft/sec by the pendulum defined in § 572.36(b), the peak knee impact force, which is a product of pendulum mass and acceleration... the femur load cell simulator. (v) Guide the pendulum so that there is no significant lateral...

49 CFR 572.33 - Neck.

Code of Federal Regulations, 2010 CFR

2010-10-01

... (b) of this section, on a rigid pendulum as shown in Figure 22 so that the head's midsagittal plane is vertical and coincides with the plane of motion of the pendulum's longitudinal axis. EC01AU91.165 (4) Release the pendulum and allow it to fall freely from a height such that the tangential velocity...

49 CFR 572.183 - Neck assembly.

Code of Federal Regulations, 2013 CFR

2013-10-01

... subpart E pendulum test fixture as shown in Figure U2-A in appendix A to this subpart, so that the... pendulum longitudinal centerline shown in Figure U2-A. Torque the half-spherical screws (175-2004) located... equivalent; (3) Release the pendulum from a height sufficient to allow it to fall freely to achieve an impact...

49 CFR 572.183 - Neck assembly.

Code of Federal Regulations, 2012 CFR

2012-10-01

... subpart E pendulum test fixture as shown in Figure U2-A in appendix A to this subpart, so that the... pendulum longitudinal centerline shown in Figure U2-A. Torque the half-spherical screws (175-2004) located... equivalent; (3) Release the pendulum from a height sufficient to allow it to fall freely to achieve an impact...

49 CFR 572.189 - Instrumentation and test conditions.

Code of Federal Regulations, 2012 CFR

2012-10-01

... mass of the attachments and 1/3 cable mass must not exceed 5 percent of the total pendulum mass. No... lumbar spine pendulum accelerations—Digitally filtered CFC 60; (4) Pelvis, shoulder, thorax without arm...—Digitally filtered at CFC 600; (6) Thorax deflection—Digitally filtered CFC 180. (j)(1) Filter the pendulum...

Analysis of the Pendular and Pitch Motions of a Driven Three-Dimensional Pendulum

ERIC Educational Resources Information Center

Findley, T.; Yoshida, S.; Norwood, D. P.

2007-01-01

A three-dimensional pendulum, modelled after the Laser Interferometer Gravitational-Wave Observatory's suspended optics, was constructed to investigate the pendulum's dynamics due to suspension point motion. In particular, we were interested in studying the pendular-pitch energy coupling. Determination of the pendular's Q value (the quality factor…

49 CFR 572.183 - Neck assembly.

Code of Federal Regulations, 2010 CFR

2010-10-01

... subpart E pendulum test fixture as shown in Figure U2-A in appendix A to this subpart, so that the... pendulum longitudinal centerline shown in Figure U2-A. Torque the half-spherical screws (175-2004) located... equivalent; (3) Release the pendulum from a height sufficient to allow it to fall freely to achieve an impact...

49 CFR 572.35 - Limbs.

Code of Federal Regulations, 2011 CFR

2011-10-01

... in accordance with paragraph (b)(2) of this section, at 6.9 ft/sec ±0.10 ft/sec by the pendulum defined in § 572.36(b), the peak knee impact force, which is a product of pendulum mass and acceleration... the femur load cell simulator. (v) Guide the pendulum so that there is no significant lateral...

The Doppler Pendulum Experiment

ERIC Educational Resources Information Center

Lee, C. K.; Wong, H. K.

2011-01-01

An experiment to verify the Doppler effect of sound waves is described. An ultrasonic source is mounted at the end of a simple pendulum. As the pendulum swings, the rapid change of frequency can be recorded by a stationary receiver using a simple frequency-to-voltage converter. The experimental results are in close agreement with the Doppler…

49 CFR 572.183 - Neck assembly.

Code of Federal Regulations, 2011 CFR

2011-10-01

... subpart E pendulum test fixture as shown in Figure U2-A in appendix A to this subpart, so that the... pendulum longitudinal centerline shown in Figure U2-A. Torque the half-spherical screws (175-2004) located... equivalent; (3) Release the pendulum from a height sufficient to allow it to fall freely to achieve an impact...

Steady States of the Parametric Rotator and Pendulum

ERIC Educational Resources Information Center

Bouzas, Antonio O.

2010-01-01

We discuss several steady-state rotation and oscillation modes of the planar parametric rotator and pendulum with damping. We consider a general elliptic trajectory of the suspension point for both rotator and pendulum, for the latter at an arbitrary angle with gravity, with linear and circular trajectories as particular cases. We treat the…

49 CFR 572.35 - Limbs.

Code of Federal Regulations, 2010 CFR

2010-10-01

... in accordance with paragraph (b)(2) of this section, at 6.9 ft/sec ±0.10 ft/sec by the pendulum defined in § 572.36(b), the peak knee impact force, which is a product of pendulum mass and acceleration... the femur load cell simulator. (v) Guide the pendulum so that there is no significant lateral...

49 CFR 572.33 - Neck.

Code of Federal Regulations, 2014 CFR

2014-10-01

... (b) of this section, on a rigid pendulum as shown in Figure 22 so that the head's midsagittal plane is vertical and coincides with the plane of motion of the pendulum's longitudinal axis. ER02JN11.011 (4) Release the pendulum and allow it to fall freely from a height such that the tangential velocity...

49 CFR 572.183 - Neck assembly.

Code of Federal Regulations, 2014 CFR

2014-10-01

... subpart E pendulum test fixture as shown in Figure U2-A in appendix A to this subpart, so that the... pendulum longitudinal centerline shown in Figure U2-A. Torque the half-spherical screws (175-2004) located... equivalent; (3) Release the pendulum from a height sufficient to allow it to fall freely to achieve an impact...

A Simple, Low-Cost, Data-Logging Pendulum Built from a Computer Mouse

ERIC Educational Resources Information Center

Gintautas, Vadas; Hubler, Alfred

2009-01-01

Lessons and homework problems involving a pendulum are often a big part of introductory physics classes and laboratory courses from high school to undergraduate levels. Although laboratory equipment for pendulum experiments is commercially available, it is often expensive and may not be affordable for teachers on fixed budgets, particularly in…

The Reproduction of Scientific Understanding about Pendulum Motion in the Public

ERIC Educational Resources Information Center

Manabu, Sumida

2004-01-01

This paper describes life-span development of understanding about pendulum motion and effects of school science. The subjects were 2,766 people ranging from kindergartners up to 88 years senior citizens. The conflict and consensus between children and their parent's understanding of pendulum motion were also analyzed. The kindergartner's…

Idealisation and Galileo's Pendulum Discoveries: Historical, Philosophical and Pedagogical Considerations

ERIC Educational Resources Information Center

Matthews, Michael R.

2004-01-01

Galileo's discovery of the properties of pendulum motion depended on his adoption of the novel methodology of idealisation. Galileo's laws of pendulum motion could not be accepted until the empiricist methodological constraints placed on science by Aristotle, and by common sense, were overturned. As long as scientific claims were judged by how the…

Linear control of the flywheel inverted pendulum.

PubMed

Olivares, Manuel; Albertos, Pedro

2014-09-01

The flywheel inverted pendulum is an underactuated mechanical system with a nonlinear model but admitting a linear approximation around the unstable equilibrium point in the upper position. Although underactuated systems usually require nonlinear controllers, the easy tuning and understanding of linear controllers make them more attractive for designers and final users. In a recent paper, a simple PID controller was proposed by the authors, leading to an internally unstable controlled plant. To achieve global stability, two options are developed here: first by introducing an internal stabilizing controller and second by replacing the PID controller by an observer-based state feedback control. Simulation and experimental results show the effectiveness of the design. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Human Subject Effects on Torsion Pendulum Oscillations: Further Evidence of Mediation by Convection Currents.

PubMed

Hammerschlag, Richard; Linda Baldwin, Ann; Schwartz, Gary E

When a human subject sits beneath a wire mesh, hemispheric torsion pendulum (TP) a rapid-onset series of oscillations at frequencies both higher and lower than the fundamental frequency of the TP have been consistently observed. This study was designed to replicate and extend prior findings that suggest the human subject effect on TP behavior is due to subject-generated, heat-induced convection currents. Effects on pendulum behavior were tested after draping an aluminized "space blanket" over the subject and by replacing the subject with a thermal mattress pad shaped to approximate the human form. Experiments were performed in a basic science university research laboratory. Real-time recordings and Fast Fourier Transform frequency spectra of pendulum oscillatory movement. The space blanket blocked, while the mattress pad mimicked, the human subject induced complex array of pendulum oscillations. Our findings support and strengthen previous results that suggest the effects of human subjects on behavior of a torsion pendulum are mediated by body-heat-induced air convection rather than an unknown type of biofield. Copyright © 2016 Elsevier Inc. All rights reserved.

Analytical study of the critical behavior of the nonlinear pendulum

NASA Astrophysics Data System (ADS)

Lima, F. M. S.

2010-11-01

The dynamics of a simple pendulum consisting of a small bob and a massless rigid rod has three possible regimes depending on its total energy E: Oscillatory (when E is not enough for the pendulum to reach the top position), "perpetual ascent" when E is exactly the energy needed to reach the top, and nonoscillatory for greater energies. In the latter regime, the pendulum rotates periodically without velocity inversions. In contrast to the oscillatory regime, for which an exact analytic solution is known, the other two regimes are usually studied by solving the equation of motion numerically. By applying conservation of energy, I derive exact analytical solutions to both the perpetual ascent and nonoscillatory regimes and an exact expression for the pendulum period in the nonoscillatory regime. Based on Cromer's approximation for the large-angle pendulum period, I find a simple approximate expression for the decrease of the period with the initial velocity in the nonoscillatory regime, valid near the critical velocity. This expression is used to study the critical slowing down, which is observed near the transition between the oscillatory and nonoscillatory regimes.

U(1)-invariant membranes: The geometric formulation, Abel, and pendulum differential equations

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

Zheltukhin, A. A.; Fysikum, AlbaNova, Stockholm University, 106 91 Stockholm; NORDITA, Roslagstullsbacken 23, 106 91 Stockholm

The geometric approach to study the dynamics of U(1)-invariant membranes is developed. The approach reveals an important role of the Abel nonlinear differential equation of the first type with variable coefficients depending on time and one of the membrane extendedness parameters. The general solution of the Abel equation is constructed. Exact solutions of the whole system of membrane equations in the D=5 Minkowski space-time are found and classified. It is shown that if the radial component of the membrane world vector is only time dependent, then the dynamics is described by the pendulum equation.

Naturally Inspired Firefly Controller For Stabilization Of Double Inverted Pendulum

NASA Astrophysics Data System (ADS)

Srikanth, Kavirayani; Nagesh, Gundavarapu

2015-12-01

A double inverted pendulum plant as an established model that is analyzed as part of this work was tested under the influence of time delay, where the controller was fine tuned using a firefly algorithm taking into considering the fitness function of variation of the cart position and to minimize the cart position displacement and still stabilize it effectively. The naturally inspired algorithm which imitates the fireflies definitely is an energy efficient method owing to the inherent logic of the way the fireflies respond collectively and has shown that critical time delays makes the system healthy.

Reinforcement learning: Solving two case studies

NASA Astrophysics Data System (ADS)

Duarte, Ana Filipa; Silva, Pedro; dos Santos, Cristina Peixoto

2012-09-01

Reinforcement Learning algorithms offer interesting features for the control of autonomous systems, such as the ability to learn from direct interaction with the environment, and the use of a simple reward signalas opposed to the input-outputs pairsused in classic supervised learning. The reward signal indicates the success of failure of the actions executed by the agent in the environment. In this work, are described RL algorithmsapplied to two case studies: the Crawler robot and the widely known inverted pendulum. We explore RL capabilities to autonomously learn a basic locomotion pattern in the Crawler, andapproach the balancing problem of biped locomotion using the inverted pendulum.

Holonomicity analysis of electromechanical systems

NASA Astrophysics Data System (ADS)

Wcislik, Miroslaw; Suchenia, Karol

2017-12-01

Electromechanical systems are described using state variables that contain electrical and mechanical components. The equations of motion, both electrical and mechanical, describe the relationships between these components. These equations are obtained using Lagrange functions. On the basis of the function and Lagrange - d'Alembert equation the methodology of obtaining equations for electromechanical systems was presented, together with a discussion of the nonholonomicity of these systems. The electromechanical system in the form of a single-phase reluctance motor was used to verify the presented method. Mechanical system was built as a system, which can oscillate as the element of physical pendulum. On the base of the pendulum oscillation, parameters of the electromechanical system were defined. The identification of the motor electric parameters as a function of the rotation angle was carried out. In this paper the characteristics and motion equations parameters of the motor are presented. The parameters of the motion equations obtained from the experiment and from the second order Lagrange equations are compared.

Earthquake Resilient Tall Reinforced Concrete Buildings at Near-Fault Sites Using Base Isolation and Rocking Core Walls

NASA Astrophysics Data System (ADS)

Calugaru, Vladimir

This dissertation pursues three main objectives: (1) to investigate the seismic response of tall reinforced concrete core wall buildings, designed following current building codes, subjected to pulse type near-fault ground motion, with special focus on the relation between the characteristics of the ground motion and the higher-modes of response; (2) to determine the characteristics of a base isolation system that results in nominally elastic response of the superstructure of a tall reinforced concrete core wall building at the maximum considered earthquake level of shaking; and (3) to demonstrate that the seismic performance, cost, and constructability of a base-isolated tall reinforced concrete core wall building can be significantly improved by incorporating a rocking core-wall in the design. First, this dissertation investigates the seismic response of tall cantilever wall buildings subjected to pulse type ground motion, with special focus on the relation between the characteristics of ground motion and the higher-modes of response. Buildings 10, 20, and 40 stories high were designed such that inelastic deformation was concentrated at a single flexural plastic hinge at their base. Using nonlinear response history analysis, the buildings were subjected to near-fault seismic ground motions as well as simple close-form pulses, which represented distinct pulses within the ground motions. Euler-Bernoulli beam models with lumped mass and lumped plasticity were used to model the buildings. Next, this dissertation investigates numerically the seismic response of six seismically base-isolated (BI) 20-story reinforced concrete buildings and compares their response to that of a fixed-base (FB) building with a similar structural system above ground. Located in Berkeley, California, 2 km from the Hayward fault, the buildings are designed with a core wall that provides most of the lateral force resistance above ground. For the BI buildings, the following are investigated: two isolation systems (both implemented below a three-story basement), isolation periods equal to 4, 5, and 6 s, and two levels of flexural strength of the wall. The first isolation system combines tension-resistant friction pendulum bearings and nonlinear fluid viscous dampers (NFVDs); the second combines low-friction tension-resistant cross-linear bearings, lead-rubber bearings, and NFVDs. Finally, this dissertation investigates the seismic response of four 20-story buildings hypothetically located in the San Francisco Bay Area, 0.5 km from the San Andreas fault. One of the four studied buildings is fixed-base (FB), two are base-isolated (BI), and one uses a combination of base isolation and a rocking core wall (BIRW). Above the ground level, a reinforced concrete core wall provides the majority of the lateral force resistance in all four buildings. The FB and BI buildings satisfy requirements of ASCE 7-10. The BI and BIRW buildings use the same isolation system, which combines tension-resistant friction pendulum bearings and nonlinear fluid viscous dampers. The rocking core-wall includes post-tensioning steel, buckling-restrained devices, and at its base is encased in a steel shell to maximize confinement of the concrete core. The total amount of longitudinal steel in the wall of the BIRW building is 0.71 to 0.87 times that used in the BI buildings. Response history two-dimensional analysis is performed, including the vertical components of excitation, for a set of ground motions scaled to the design earthquake and to the maximum considered earthquake (MCE). While the FB building at MCE level of shaking develops inelastic deformations and shear stresses in the wall that may correspond to irreparable damage, the BI and the BIRW buildings experience nominally elastic response of the wall, with floor accelerations and shear forces which are 0.36 to 0.55 times those experienced by the FB building. The response of the four buildings to two historical and two simulated near-fault ground motions is also studied, demonstrating that the BIRW building has the largest deformation capacity at the onset of structural damage. (Abstract shortened by UMI.).

Dynamic Mesh CFD Simulations of Orion Parachute Pendulum Motion During Atmospheric Entry

NASA Technical Reports Server (NTRS)

Halstrom, Logan D.; Schwing, Alan M.; Robinson, Stephen K.

2016-01-01

This paper demonstrates the usage of computational fluid dynamics to study the effects of pendulum motion dynamics of the NASAs Orion Multi-Purpose Crew Vehicle parachute system on the stability of the vehicles atmospheric entry and decent. Significant computational fluid dynamics testing has already been performed at NASAs Johnson Space Center, but this study sought to investigate the effect of bulk motion of the parachute, such as pitching, on the induced aerodynamic forces. Simulations were performed with a moving grid geometry oscillating according to the parameters observed in flight tests. As with the previous simulations, OVERFLOW computational fluid dynamics tool is used with the assumption of rigid, non-permeable geometry. Comparison to parachute wind tunnel tests is included for a preliminary validation of the dynamic mesh model. Results show qualitative differences in the flow fields of the static and dynamic simulations and quantitative differences in the induced aerodynamic forces, suggesting that dynamic mesh modeling of the parachute pendulum motion may uncover additional dynamic effects.

Note: A 1-m Foucault pendulum rolling on a ball.

PubMed

Salva, H R; Benavides, R E; Venturino, J A; Cuscueta, D J; Ghilarducci, A A

2013-10-01

We have built a short Foucault pendulum of 1-m length. The aim of this work was to increase the sensitivity to elliptical trajectories from other longer pendula. The design was a semi-rigid pendulum that rolls over a small ball. The measurements of the movements (azimuth and elliptical trajectory) were done by an optical method. The resulting pendulum works in a medium satisfactory way due to problems of the correct choice of the mass of the bob together with the diameter of the supporting ball. It is also important to keep the rolling surface very clean.

Comparison of strain rates of dart impacted plaques and pendulum impacted bumpers

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

Scammell, K.L.

1987-01-01

The difference in strain rates prevailing during pendulum impact of bumpers versus high speed dart impact of plaques was investigated. Uni-axial strain gages were applied to the tension side of the plaques and bumpers directly opposite the point of impact. The plaques were impacted with an instrumented high rate dart impact tester and the bumpers impacted with a full scale bumper pendulum impact tester. Theoretical calculations and actual strain rate data support the conclusion that the strain rate of a plaque during dart impact significantly exceeds that of bumper strain rate during pendulum impact.

Modeling and comparative study of linear and nonlinear controllers for rotary inverted pendulum

NASA Astrophysics Data System (ADS)

Lima, Byron; Cajo, Ricardo; Huilcapi, Víctor; Agila, Wilton

2017-01-01

The rotary inverted pendulum (RIP) is a problem difficult to control, several studies have been conducted where different control techniques have been applied. Literature reports that, although problem is nonlinear, classical PID controllers presents appropriate performances when applied to the system. In this paper, a comparative study of the performances of linear and nonlinear PID structures is carried out. The control algorithms are evaluated in the RIP system, using indices of performance and power consumption, which allow the categorization of control strategies according to their performance. This article also presents the modeling system, which has been estimated some of the parameters involved in the RIP system, using computer-aided design tools (CAD) and experimental methods or techniques proposed by several authors attended. The results indicate a better performance of the nonlinear controller with an increase in the robustness and faster response than the linear controller.

NASA's Preparations for ESA's L3 Gravitational Wave Mission

NASA Technical Reports Server (NTRS)

Stebbins, Robin

2016-01-01

Telescope Subsystem - Jeff Livas (GSFC): Demonstrate pathlength stability, straylight and manufacturability. Phase Measurement System - Bill Klipstein (JPL): Key measurement functions demonstrated. Incorporate full flight functionality. Laser Subsystem - Jordan Camp (GSFC): ECL master oscillator, phase noise of fiber power amplifier, demonstrate end-to-end performance in integrated system, lifetime. Micronewton Thrusters - John Ziemer (JPL): Propellant storage and distribution, system robustness, manufacturing yield, lifetime. Arm-locking Demonstration - Kirk McKenzie (JPL): Studying a demonstration of laser frequency stabilization with GRACE Follow-On. Torsion Pendulum - John Conklin (UF): Develop U.S. capability with GRS and torsion pendulum test bed. Multi-Axis Heterodyne Interferometry - Ira Thorpe (GSFC): Investigate test mass/optical bench interface. UV LEDs - John Conklin+ (UF): Flight qualify UV LEDs to replace mercury lamps in discharging system. Optical Bench - Guido Mueller (UF): Investigate alternate designs and fabrication processes to ease manufacturability. LISA researchers at JPL are leading the Laser Ranging Interferometer instrument on the GRACE Follow-On mission.

A Comprehensive Analytical Solution of the Nonlinear Pendulum

ERIC Educational Resources Information Center

Ochs, Karlheinz

2011-01-01

In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions…

49 CFR 581.5 - Requirements.

Code of Federal Regulations, 2014 CFR

2014-10-01

... the damage criteria of §§ 581.5(c)(1) through 581.5(c)(9) when impacted by a pendulum-type test device... of 1.5 m.p.h., and when impacted by a pendulum-type test device in accordance with the procedures of... original contours 30 minutes after completion of each pendulum and barrier impact, except where such damage...

49 CFR 581.5 - Requirements.

Code of Federal Regulations, 2011 CFR

2011-10-01

... the damage criteria of §§ 581.5(c)(1) through 581.5(c)(9) when impacted by a pendulum-type test device... of 1.5 m.p.h., and when impacted by a pendulum-type test device in accordance with the procedures of... original contours 30 minutes after completion of each pendulum and barrier impact, except where such damage...

Oscillations of a Simple Pendulum with Extremely Large Amplitudes

ERIC Educational Resources Information Center

Butikov, Eugene I.

2012-01-01

Large oscillations of a simple rigid pendulum with amplitudes close to 180[degrees] are treated on the basis of a physically justified approach in which the cycle of oscillation is divided into several stages. The major part of the almost closed circular path of the pendulum is approximated by the limiting motion, while the motion in the vicinity…

49 CFR 581.5 - Requirements.

Code of Federal Regulations, 2012 CFR

2012-10-01

... the damage criteria of §§ 581.5(c)(1) through 581.5(c)(9) when impacted by a pendulum-type test device... of 1.5 m.p.h., and when impacted by a pendulum-type test device in accordance with the procedures of... original contours 30 minutes after completion of each pendulum and barrier impact, except where such damage...

Measurement of Gravitational Acceleration Using a Computer Microphone Port

ERIC Educational Resources Information Center

Khairurrijal; Eko Widiatmoko; Srigutomo, Wahyu; Kurniasih, Neny

2012-01-01

A method has been developed to measure the swing period of a simple pendulum automatically. The pendulum position is converted into a signal frequency by employing a simple electronic circuit that detects the intensity of infrared light reflected by the pendulum. The signal produced by the electronic circuit is sent to the microphone port and…

Einstein versus the Simple Pendulum Formula: Does Gravity Slow All Clocks?

ERIC Educational Resources Information Center

Puri, Avinash

2015-01-01

According to the Newtonian formula for a simple pendulum, the period of a pendulum is inversely proportional to the square root of "g", the gravitational field strength. Einstein's theory of general relativity leads to the result that time slows down where gravity is intense. The two claims look contradictory and can muddle student and…

Maple[R] Version of the "Indian Rope Trick". Classroom Notes

ERIC Educational Resources Information Center

Knight, D. G.

2004-01-01

If the point of suspension of a multiple pendulum is suitably oscillated then the pendulum can remain in motion in an upside-down position. Since such pendulums can model flexible materials, this inverted motion is sometimes referred to as an 'Indian rope trick'. Despite the complexity of the governing differential equations, this rope trick can…

49 CFR 581.5 - Requirements.

Code of Federal Regulations, 2010 CFR

2010-10-01

... the damage criteria of §§ 581.5(c)(1) through 581.5(c)(9) when impacted by a pendulum-type test device... of 1.5 m.p.h., and when impacted by a pendulum-type test device in accordance with the procedures of... original contours 30 minutes after completion of each pendulum and barrier impact, except where such damage...

49 CFR 581.5 - Requirements.

Code of Federal Regulations, 2013 CFR

2013-10-01

... the damage criteria of §§ 581.5(c)(1) through 581.5(c)(9) when impacted by a pendulum-type test device... of 1.5 m.p.h., and when impacted by a pendulum-type test device in accordance with the procedures of... original contours 30 minutes after completion of each pendulum and barrier impact, except where such damage...

An Apparatus to Demonstrate Linear and Nonlinear Oscillations of a Pendulum

ERIC Educational Resources Information Center

Mayer, V. V.; Varaksina, E. I.

2016-01-01

A physical pendulum with a magnetic load is proposed for comparison of linear and nonlinear oscillations. The magnetic load is repelled by permanent magnets which are disposed symmetrically relative to the load. It is established that positions of the pendulum and the magnets determine the dependence of restoring force on displacement of the load.…

Chemistry and the Pendulum--What Have They to Do with Each Other?

ERIC Educational Resources Information Center

De Berg, K. C.

2006-01-01

Physicists have known for some time that pendulum motion is a useful analogy for other physical processes. Chemists have played with the idea from time to time but the strength of the analogy between pendulum motion and chemical processes has only received prominent published recognition since about 1980, although there are details of the analogy…

Robust hopping based on virtual pendulum posture control.

PubMed

Sharbafi, Maziar A; Maufroy, Christophe; Ahmadabadi, Majid Nili; Yazdanpanah, Mohammad J; Seyfarth, Andre

2013-09-01

A new control approach to achieve robust hopping against perturbations in the sagittal plane is presented in this paper. In perturbed hopping, vertical body alignment has a significant role for stability. Our approach is based on the virtual pendulum concept, recently proposed, based on experimental findings in human and animal locomotion. In this concept, the ground reaction forces are pointed to a virtual support point, named virtual pivot point (VPP), during motion. This concept is employed in designing the controller to balance the trunk during the stance phase. New strategies for leg angle and length adjustment besides the virtual pendulum posture control are proposed as a unified controller. This method is investigated by applying it on an extension of the spring loaded inverted pendulum (SLIP) model. Trunk, leg mass and damping are added to the SLIP model in order to make the model more realistic. The stability is analyzed by Poincaré map analysis. With fixed VPP position, stability, disturbance rejection and moderate robustness are achieved, but with a low convergence speed. To improve the performance and attain higher robustness, an event-based control of the VPP position is introduced, using feedback of the system states at apexes. Discrete linear quartic regulator is used to design the feedback controller. Considerable enhancements with respect to stability, convergence speed and robustness against perturbations and parameter changes are achieved.

Oscillators: Old and new perspectives

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

Bhattacharjee, Jayanta K.; Roy, Jyotirmoy

We consider some of the well known oscillators in literature which are known to exhibit interesting effects of nonlinearity. We review the Lindstedt-Poincare technique for dealing with with the nonlinear effects and then go on to introduce the relevance of the renormalization group for the oscillator following the pioneering work of Chen et al. It is pointed out that the traditional Lindstedt-Poincare and the renormalization group techniques have operational connections. We use this to find an unexpected mode softening in the double pendulum. This mode softening prompted us to look for chaos in the double pendulum at low energies-energies thatmore » are just sufficient to allow the outer pendulum to rotate (the double pendulum is known to be chaotic at high energies-energies that are greater than that needed to make both pendulums to rotate). The emergence of the chaos is strongly dependent on initial conditions.« less

Efficiency of SparkJet

NASA Technical Reports Server (NTRS)

Golbabaei-Asl, M.; Knight, D.; Wilkinson, S.

2013-01-01

The thermal efficiency of a SparkJet is evaluated by measuring the impulse response of a pendulum subject to a single spark discharge. The SparkJet is attached to the end of a pendulum. A laser displacement sensor is used to measure the displacement of the pendulum upon discharge. The pendulum motion is a function of the fraction of the discharge energy that is channeled into the heating of the gas (i.e., increasing the translational-rotational temperature). A theoretical perfect gas model is used to estimate the portion of the energy from the heated gas that results in equivalent pendulum displacement as in the experiment. The earlier results from multiple runs for different capacitances of C = 3, 5, 10, 20, and 40(micro)F demonstrate that the thermal efficiency decreases with higher capacitive discharges.1 In the current paper, results from additional run cases have been included and confirm the previous results

Development of enhanced piezoelectric energy harvester induced by human motion.

PubMed

Minami, Y; Nakamachi, E

2012-01-01

In this study, a high frequency piezoelectric energy harvester converted from the human low vibrated motion energy was newly developed. This hybrid energy harvester consists of the unimorph piezoelectric cantilever and a couple of permanent magnets. One magnet was attached at the end of cantilever, and the counterpart magnet was set at the end of the pendulum. The mechanical energy provided through the human walking motion, which is a typical ubiquitous presence of vibration, is converted to the electric energy via the piezoelectric cantilever vibration system. At first, we studied the energy convert mechanism and the performance of our energy harvester, where the resonance free vibration of unimorph cantilever with one permanent magnet under a rather high frequency was induced by the artificial low frequency vibration. The counterpart magnet attached on the pendulum. Next, we equipped the counterpart permanent magnet pendulum, which was fluctuated under a very low frequency by the human walking, and the piezoelectric cantilever, which had the permanent magnet at the end. The low-to-high frequency convert "hybrid system" can be characterized as an enhanced energy harvest one. We examined and obtained maximum values of voltage and power in this system, as 1.2V and 1.2 µW. Those results show the possibility to apply for the energy harvester in the portable and implantable Bio-MEMS devices.

Seismic performance assessment of base-isolated safety-related nuclear structures

USGS Publications Warehouse

Huang, Y.-N.; Whittaker, A.S.; Luco, N.

2010-01-01

Seismic or base isolation is a proven technology for reducing the effects of earthquake shaking on buildings, bridges and infrastructure. The benefit of base isolation has been presented in terms of reduced accelerations and drifts on superstructure components but never quantified in terms of either a percentage reduction in seismic loss (or percentage increase in safety) or the probability of an unacceptable performance. Herein, we quantify the benefits of base isolation in terms of increased safety (or smaller loss) by comparing the safety of a sample conventional and base-isolated nuclear power plant (NPP) located in the Eastern U.S. Scenario- and time-based assessments are performed using a new methodology. Three base isolation systems are considered, namely, (1) Friction Pendulum??? bearings, (2) lead-rubber bearings and (3) low-damping rubber bearings together with linear viscous dampers. Unacceptable performance is defined by the failure of key secondary systems because these systems represent much of the investment in a new build power plant and ensure the safe operation of the plant. For the scenario-based assessments, the probability of unacceptable performance is computed for an earthquake with a magnitude of 5.3 at a distance 7.5 km from the plant. For the time-based assessments, the annual frequency of unacceptable performance is computed considering all potential earthquakes that may occur. For both assessments, the implementation of base isolation reduces the probability of unacceptable performance by approximately four orders of magnitude for the same NPP superstructure and secondary systems. The increase in NPP construction cost associated with the installation of seismic isolators can be offset by substantially reducing the required seismic strength of secondary components and systems and potentially eliminating the need to seismically qualify many secondary components and systems. ?? 2010 John Wiley & Sons, Ltd.

The Pendulum in the 21st Century-Relic or Trendsetter

ERIC Educational Resources Information Center

Peters, Randall D.

2004-01-01

When identifying instruments that have had great influence on the history of physics, none comes to mind more quickly than the pendulum. Though first treated scientifically by Galileo in the 16th century, and in some respects nearly "dead" by the middle of the 20th century; the pendulum experienced "rebirth" by becoming an archetype of chaos. With…

Analysis of Pendulum Period with an iPod Touch/iPhone

ERIC Educational Resources Information Center

Briggle, Justin

2013-01-01

We describe the use of Apple's iPod touch/iPhone, acting as the pendulum bob, as a means of measuring pendulum period, making use of the device's three-axis digital accelerometer and the freely available SPARKvue app from PASCO scientific. The method can be readily incorporated into an introductory physics laboratory experiment.…

49 CFR 572.187 - Lumbar spine.

Code of Federal Regulations, 2013 CFR

2013-10-01

...-headform assembly to the Part 572 pendulum test fixture per procedure in § 572.183(b)(2) and as shown in... assembly (175-5506) to 50 ±5 in-lb; (3) Release the pendulum from a height sufficient to allow it to fall freely to achieve an impact velocity of 6.05 ±0.1 m/s measured at the center of the pendulum...

49 CFR 572.187 - Lumbar spine.

Code of Federal Regulations, 2012 CFR

2012-10-01

...-headform assembly to the Part 572 pendulum test fixture per procedure in § 572.183(b)(2) and as shown in... assembly (175-5506) to 50 ±5 in-lb; (3) Release the pendulum from a height sufficient to allow it to fall freely to achieve an impact velocity of 6.05 ±0.1 m/s measured at the center of the pendulum...

49 CFR 572.187 - Lumbar spine.

Code of Federal Regulations, 2011 CFR

2011-10-01

...-headform assembly to the Part 572 pendulum test fixture per procedure in § 572.183(b)(2) and as shown in... assembly (175-5506) to 50 ± 5 in-lb; (3) Release the pendulum from a height sufficient to allow it to fall freely to achieve an impact velocity of 6.05 ±0.1 m/s measured at the center of the pendulum...

The Bravais Pendulum: The Distinct Charm of an Almost Forgotten Experiment

ERIC Educational Resources Information Center

Babovic, V. M.; Mekic, S.

2011-01-01

In the year 1851 in Paris, the apparent change of the plane of oscillation of a linear pendulum was observed by Leon Foucault. In the same year, at the same place, the unequal duration of the oscillations of a right- and left-handed conical pendulum was observed by Bravais. Today, the Foucault pendula are common at universities, the Bravais…

49 CFR 572.187 - Lumbar spine.

Code of Federal Regulations, 2010 CFR

2010-10-01

...-headform assembly to the Part 572 pendulum test fixture per procedure in § 572.183(b)(2) and as shown in... assembly (175-5506) to 50 ± 5 in-lb; (3) Release the pendulum from a height sufficient to allow it to fall freely to achieve an impact velocity of 6.05 ±0.1 m/s measured at the center of the pendulum...

Approximate Expressions for the Period of a Simple Pendulum Using a Taylor Series Expansion

ERIC Educational Resources Information Center

Belendez, Augusto; Arribas, Enrique; Marquez, Andres; Ortuno, Manuel; Gallego, Sergi

2011-01-01

An approximate scheme for obtaining the period of a simple pendulum for large-amplitude oscillations is analysed and discussed. When students express the exact frequency or the period of a simple pendulum as a function of the oscillation amplitude, and they are told to expand this function in a Taylor series, they always do so using the…

49 CFR 572.187 - Lumbar spine.

Code of Federal Regulations, 2014 CFR

2014-10-01

...-headform assembly to the Part 572 pendulum test fixture per procedure in § 572.183(b)(2) and as shown in... assembly (175-5506) to 50 ±5 in-lb; (3) Release the pendulum from a height sufficient to allow it to fall freely to achieve an impact velocity of 6.05 ±0.1 m/s measured at the center of the pendulum...

Propagation-invariant beams with quantum pendulum spectra: from Bessel beams to Gaussian beam-beams.

PubMed

Dennis, Mark R; Ring, James D

2013-09-01

We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly periodic Mathieu functions in azimuth, depend on a field strength parameter. When the parameter is zero, pendulum beams are Bessel beams, and as the parameter approaches infinity, they resemble transversely propagating one-dimensional Gaussian wave packets (Gaussian beam-beams). Pendulum beams are the eigenfunctions of an operator that interpolates between the squared angular momentum operator and the linear momentum operator. The analysis reveals connections with Mathieu beams, and insight into the paraxial approximation.

Analysis of the linearity of half periods of the Lorentz pendulum

NASA Astrophysics Data System (ADS)

Wickramasinghe, T.; Ochoa, R.

2005-05-01

We analyze the motion of the Lorentz pendulum, a simple pendulum whose length is changed at a constant rate k. We show both analytically and numerically that the half period Tn, the time between half oscillations as measured from midpoint to midpoint, increases linearly with the oscillation number n such that Tn+1-Tn≈kπ2/2g, where g is the acceleration due to gravity. A video camera is used to record the motion of the oscillating bob of the pendulum and verify the linearity of Tn with oscillation number. The theory and the experiment are suitable for an advanced undergraduate laboratory.

World pendulum—a distributed remotely controlled laboratory (RCL) to measure the Earth's gravitational acceleration depending on geographical latitude

NASA Astrophysics Data System (ADS)

Gröber, S.; Vetter, M.; Eckert, B.; Jodl, H.-J.

2007-05-01

We suggest that different string pendulums are positioned at different locations on Earth and measure at each place the gravitational acceleration (accuracy Δg ~ 0.01 m s-2). Each pendulum can be remotely controlled via the internet by a computer located somewhere on Earth. The theoretical part describes the physical origin of this phenomenon g(phiv), that the Earth's effective gravitational acceleration g depends on the angle of latitude phiv. Then, we present all necessary formula to deduce g(phiv) from oscillations of a string pendulum. The technical part explains tips and tricks to realize such an apparatus to measure all necessary values with sufficient accuracy. In addition, we justify the precise dimensions of a physical pendulum such that the formula for a mathematical pendulum is applicable to determine g(phiv) without introducing errors. To conclude, we describe the internet version—the string pendulum as a remotely controlled laboratory. The teaching relevance and educational value will be discussed in detail at the end of this paper including global experimenting, using the internet and communication techniques in teaching and new ways of teaching and learning methods.

Ground Simulator Studies of the Effects of Valve Friction, Stick Friction, Flexibility, and Backwash on Power Control System Quality

NASA Technical Reports Server (NTRS)

Brown, B Porter

1958-01-01

Report presents results of tests made on a power control system by means of a ground simulator to determine the effects of various combinations of valve friction and stick friction on the ability of the pilot to control the system. Various friction conditions were simulated with a rigid control system, a flexible system, and a rigid system having some backlash. For the tests, the period and damping of the simulated airplane were held constant.

Computational Methods for Nonlinear Dynamic Problems in Solid and Structural Mechanics: Progress in the Theory and Modeling of Friction and in the Control of Dynamical Systems with Frictional Forces

DTIC Science & Technology

1989-03-31

present several numerical studies designed to reveal the effect that some of the governing parameters have on the behavior of the system and, whenever...Friction and in the Control of Dynamical Systems with Frictional Forces FINAL TECHNICAL REPORT March 31, 1989 _ -- I -.7: .-.- - : AFOSR Contract F49620...SOLID AND STRUCTURAL MECHANICS: Progress in the Theory and Modeling of Friction and in the Control of Dynamical Systems with Frictional Forces I I * FINAL

Dynamical stability of a many-body Kapitza pendulum

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

Citro, Roberta, E-mail: citro@sa.infn.it; Dalla Torre, Emanuele G., E-mail: emanuele.dalla-torre@biu.ac.il; Department of Physics, Harvard University, Cambridge, MA 02138

We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine–Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in contrast to the common belief that periodically-driven unbounded interacting systems should always tend to an absorbing infinite-temperature state. The transition to an unstable absorbing state is described by a change in the sign of the kinetic term in the Floquet Hamiltonian and controlled by the short-wavelength degrees of freedom. We investigate the stability phase diagram through an analytic high-frequency expansion, a self-consistent variational approach, and amore » numeric semiclassical calculation. Classical and quantum experiments are proposed to verify the validity of our results.« less

Testing and evaluation of the LES-6 pulsed plasma thruster by means of a torsion pendulum system

NASA Technical Reports Server (NTRS)

Hamidian, J. P.; Dahlgren, J. B.

1973-01-01

Performance characteristics of the LES-6 pulsed plasma thruster over a range of input conditions were investigated by means of a torsion pendulum system. Parameters of particular interest included the impulse bit and time average thrust (and their repeatability), specific impulse, mass ablated per discharge, specific thrust, energy per unit area, efficiency, and variation of performance with ignition command rate. Intermittency of the thruster as affected by input energy and igniter resistance were also investigated. Comparative experimental data correlation with the data presented. The results of these tests indicate that the LES-6 thruster, with some identifiable design improvements, represents an attractive reaction control thruster for attitude contol applications on long-life spacecraft requiring small metered impulse bits for precise pointing control of science instruments.

Is paramecium swimming autonomic?

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Promode R.; Toplosky, Norman; Hansen, Joshua

2010-11-01

We seek to explore if the swimming of paramecium has an underlying autonomic mechanism. Such robotic elements may be useful in capturing the disturbance field in an environment in real time. Experimental evidence is emerging that motion control neurons of other animals may be present in paramecium as well. The limit cycle determined using analog simulation of the coupled nonlinear oscillators of olivo-cerebellar dynamics (ieee joe 33, 563-578, 2008) agrees with the tracks of the cilium of a biological paramecium. A 4-motor apparatus has been built that reproduces the kinematics of the cilium motion. The motion of the biological cilium has been analyzed and compared with the results of the finite element modeling of forces on a cilium. The modeling equates applied torque at the base of the cilium with drag, the cilium stiffness being phase dependent. A low friction pendulum apparatus with a multiplicity of electromagnetic actuators is being built for verifying the maps of the attractor basin computed using the olivo-cerebellar dynamics for different initial conditions. Sponsored by ONR 33.

Microtexture diagnostics of asphalt pavement surfaces

NASA Astrophysics Data System (ADS)

Florková, Zuzana; Pepucha, L.'ubomír

2017-09-01

The microtexture of asphalt pavement surface is an essential parameter from the traffic safety point of view and it closely relates to a geometrical, petrological and physical properties of aggregate particle used in asphalt pavement. Microtexture has a significant influence for assurance basic friction values between tire and pavement in relation to a skid resistance properties. Therefore, the microtexture detecting methods are necessary. The British pendulum tester measurements have been carried out on selected sections of roads with different asphalt surfaces. Individual grains of aggregates were taken from the surface of each section from the sliding path and also from the core sample after the extraction. The laboratory profilometry measurements have been practiced on these aggregate samples and subsequently the surface microtexture was investigated based on commonly used texture characteristics and the filtration approach was applied in calculation process. The results have shown the degradation of microtexture values occurs due to polishing of aggregate under loading from traffic in relation to the type of used aggregate. Some correlation between BPN values and texture characteristics was found.

Double pendulum model for a tennis stroke including a collision process

NASA Astrophysics Data System (ADS)

Youn, Sun-Hyun

2015-10-01

By means of adding a collision process between the ball and racket in the double pendulum model, we analyzed the tennis stroke. The ball and the racket system may be accelerated during the collision time; thus, the speed of the rebound ball does not simply depend on the angular velocity of the racket. A higher angular velocity sometimes gives a lower rebound ball speed. We numerically showed that the proper time-lagged racket rotation increased the speed of the rebound ball by 20%. We also showed that the elbow should move in the proper direction in order to add the angular velocity of the racket.

Investigations of quantum pendulum dynamics in a spin-1 BEC

NASA Astrophysics Data System (ADS)

Hoang, Thai; Gerving, Corey; Land, Ben; Anquez, Martin; Hamley, Chris; Chapman, Michael

2013-05-01

We investigate the quantum spin dynamics of a spin-1 BEC initialized to an unstable critical point of the dynamical phase space. The subsequent evolution of the collective states of the system is analogous to an inverted simple pendulum in the quantum limit and yields non-classical states with quantum correlations. For short evolution times in the low depletion limit, we observe squeezed states and for longer times beyond the low depletion limit we observe highly non-Gaussian distributions. C.D. Hamley, C.S. Gerving, T.M. Hoang, E.M. Bookjans, and M.S. Chapman, ``Spin-Nematic Squeezed Vacuum in a Quantum Gas,'' Nature Physics 8, 305-308 (2012).

Sensing and actuation system for the University of Florida Torsion Pendulum for LISA

NASA Astrophysics Data System (ADS)

Chilton, Andrew; Shelley, Ryan; Olatunde, Taiwo; Ciani, Giacomo; Conklin, John; Mueller, Guido

2014-03-01

Space-based gravitational wave detectors like LISA are a necessity for understanding the low-frequency portion of the gravitational universe. They use test masses (TMs) which are separated by Gm and are in free fall inside their respective spacecraft. Their relative distance is monitored with laser interferometry at the pm/rtHz level in the LISA band, ranging from 0.1 to 100 mHz. Each TM is enclosed in a housing that provides isolation, capacitive sensing, and electrostatic actuation capabilities. The electronics must both be sensitive at the 1 nm/rtHz level and not induce residual acceleration noise above the requirement for LISA Pathfinder (3*10-15 m/sec2Hz1/2at 3 mHz). Testing and developing this technology is one of the roles of the University of Florida Torsion Pendulum, the only US testbed for LISA-like gravitational reference sensor technology. Our implementation of the sensing system functions by biasing our hollow LISA-like TMs with a 100 kHz sine wave and coupling a pair surrounding electrodes as capacitors to a pair of preamps and a differential amplifier; all other processing is done digitally. Here we report on the design of, implementation of, and preliminary results from the UF Torsion Pendulum.

Nano-Electromechanical Systems: Displacement Detection and the Mechanical Single Electron Shuttle

NASA Astrophysics Data System (ADS)

Blick, R. H.; Beil, F. W.; Höhberger, E.; Erbe, A.; Weiss, C.

For an introduction to nano-electromechanical systems we present measurements on nanomechanical resonators operating in the radio frequency range. We discuss in detail two different schemes of displacement detection for mechanical resonators, namely conventional reflection measurements of a probing signal and direct detection by capacitive coupling via a gate electrode. For capacitive detection we employ an on-chip preamplifier, which enables direct measurements of the resonator's disp lacement. We observe that the mechanical quality factor of the resonator depends on the detection technique applied, which is verified in model calculations and report on the detection of sub-harmonics. In the second part we extend our investigations to include transport of single electrons through an electron island on the tip of a nanomachined mechanical pendulum. The pendulum is operated by applying a modulating electromagnetic field in the range of 1 - 200 MHz, leading to mechanical oscillations between two laterally integrated source and drain contacts. Forming tunneling barriers the metallic tip shuttles single electrons from source to drain. The resulting tunneling current shows distinct features corresponding to the discrete mechanical eigenfrequencies of the pendulum. We report on measurements covering the temperature range from 300 K down to 4.2 K. The transport properties of the device are compared in detail to model calculations based on a Master-equation approach.

29 CFR 1928.53 - Protective enclosures for wheel-type agricultural tractors-test procedures and performance...

Code of Federal Regulations, 2013 CFR

2013-07-01

... accomplished by using a 4,410-lb (2,000-kg) weight acting as a pendulum. The impact face of the weight shall be... of the pendulum will swing, or alternatively, two sets of symmetrically located cables may be used at... from the rear, followed by a load to the side on the same enclosure structure. The pendulum swinging...

An Approximate Solution to the Equation of Motion for Large-Angle Oscillations of the Simple Pendulum with Initial Velocity

ERIC Educational Resources Information Center

Johannessen, Kim

2010-01-01

An analytic approximation of the solution to the differential equation describing the oscillations of a simple pendulum at large angles and with initial velocity is discussed. In the derivation, a sinusoidal approximation has been applied, and an analytic formula for the large-angle period of the simple pendulum is obtained, which also includes…

29 CFR 1928.53 - Protective enclosures for wheel-type agricultural tractors-test procedures and performance...

Code of Federal Regulations, 2010 CFR

2010-07-01

... accomplished by using a 4,410-lb (2,000-kg) weight acting as a pendulum. The impact face of the weight shall be... of the pendulum will swing, or alternatively, two sets of symmetrically located cables may be used at... from the rear, followed by a load to the side on the same enclosure structure. The pendulum swinging...

Fluid-Structure Interaction in a Fluid-Filled Composite Structure Subjected to Low Velocity Impact

DTIC Science & Technology

2016-06-01

for creating an E-glass composite cubic structure and a pendulum was designed and built to provide a repeatable low velocity impact. The behavior of...structure and a pendulum was designed and built to provide a repeatable low velocity impact. The behavior of the composite structure was studied at various...SET-UP .......................................................31  1.  Impact Pendulum

29 CFR 1928.53 - Protective enclosures for wheel-type agricultural tractors-test procedures and performance...

Code of Federal Regulations, 2014 CFR

2014-07-01

...,000-kg) weight acting as a pendulum. The impact face of the weight shall be 27 ±1 in. by 27 ±1 in... restraining cables shall be located in the plane in which the center of gravity of the pendulum will swing, or... side on the same enclosure structure. The pendulum swinging from the height determined by paragraph (d...

World Pendulum--A Distributed Remotely Controlled Laboratory (RCL) to Measure the Earth's Gravitational Acceleration Depending on Geographical Latitude

ERIC Educational Resources Information Center

Grober, S.; Vetter, M.; Eckert, B.; Jodl, H.-J.

2007-01-01

We suggest that different string pendulums are positioned at different locations on Earth and measure at each place the gravitational acceleration (accuracy [delta]g is approximately equal to 0.01 m s[superscript -2]). Each pendulum can be remotely controlled via the internet by a computer located somewhere on Earth. The theoretical part describes…

29 CFR 1928.53 - Protective enclosures for wheel-type agricultural tractors-test procedures and performance...

Code of Federal Regulations, 2012 CFR

2012-07-01

... accomplished by using a 4,410-lb (2,000-kg) weight acting as a pendulum. The impact face of the weight shall be... of the pendulum will swing, or alternatively, two sets of symmetrically located cables may be used at... from the rear, followed by a load to the side on the same enclosure structure. The pendulum swinging...

29 CFR 1928.53 - Protective enclosures for wheel-type agricultural tractors-test procedures and performance...

Code of Federal Regulations, 2011 CFR

2011-07-01

... accomplished by using a 4,410-lb (2,000-kg) weight acting as a pendulum. The impact face of the weight shall be... of the pendulum will swing, or alternatively, two sets of symmetrically located cables may be used at... from the rear, followed by a load to the side on the same enclosure structure. The pendulum swinging...

Robotic system construction with mechatronic components inverted pendulum: humanoid robot

NASA Astrophysics Data System (ADS)

Sandru, Lucian Alexandru; Crainic, Marius Florin; Savu, Diana; Moldovan, Cristian; Dolga, Valer; Preitl, Stefan

2017-03-01

Mechatronics is a new methodology used to achieve an optimal design of an electromechanical product. This methodology is collection of practices, procedures and rules used by those who work in particular branch of knowledge or discipline. Education in mechatronics at the Polytechnic University Timisoara is organized on three levels: bachelor, master and PhD studies. These activities refer and to design the mechatronics systems. In this context the design, implementation and experimental study of a family of mechatronic demonstrator occupy an important place. In this paper, a variant for a mechatronic demonstrator based on the combination of the electrical and mechanical components is proposed. The demonstrator, named humanoid robot, is equivalent with an inverted pendulum. Is presented the analyze of components for associated functions of the humanoid robot. This type of development the mechatronic systems by the combination of hardware and software, offers the opportunity to build the optimal solutions.

Ultra-Stable Beacon Source for Laboratory Testing of Optical Tracking

NASA Technical Reports Server (NTRS)

Aso, Yoichi; Marka, Szabolcs; Kovalik, Joseph

2008-01-01

The ultra-stable beacon source (USBS) provides a laser-beam output with a very low angular jitter and can be used as an absolute angular reference to simulate a beacon in the laboratory. The laser is mounted on the top of a very short (approximately equal to 1 m) inverted pendulum (IP) with its optical axis parallel to the carbon fiber pendulum leg. The 85-cm, carbon fiber rods making up the leg are very lightweight and rigid, and are supported by a flex-joint at the bottom (see figure). The gimbal-mounted laser is a weight-adjustable load of about 1.5 kg with its center of rotation co-located with the center of percussion of the inverted pendulum. This reduces the coupling of transverse motion at the base of the pendulum to angular motion of the laser at the top. The inverted pendulum is mounted on a gimbal with its center of rotation coinciding with the pivot position of the inverted pendulum flexure joint. This reduces coupling of ground tilt at the inverted pendulum base to motion of the laser mounted at the top. The mass of the top gimbal is adjusted to give the pendulum a very low resonant frequency (approximately equal to 10 mHz) that filters transverse seismic disturbances from the ground where the base is attached. The motion of the IP is monitored by an optical-lever sensor. The laser light is reflected by the mirror on the IP, and then is detected by a quadrant photo-detector (QPD). The position of the beam spot on the QPD corresponds to the tilt of the IP. Damping of this motion is provided by two coil and magnet pairs. The bottom gimbal mount consists of two plates. The IP is mounted on the second plate. The first plate is supported by two posts through needles and can be rotated about the axis connecting the tips of the needles. The second plate hangs from the first plate and can be rotated about the axis perpendicular to the first plate. As a result, the second plate acts as a two-axis rotation stage. Its center of rotation is located at the effective bending point of the flex-joint. The second plate is pressed against two screw actuators by the weight of the IP. The screw actuators are orthogonal to each other and are used to adjust the inclination of the second plate. The actuators are driven by stepper motors. The whole IP system is housed in a box made of Lexan plastic plates to provide isolation from air currents and temperature variations. The signals from the sensors are processed and recorded with a PC using the xPC Target realtime environment of Math- Works. The control algorithms are written using the Simulink package from The MathWorks.

Idealisation and Galileo's Pendulum Discoveries: Historical, Philosophical and Pedagogical Considerations

NASA Astrophysics Data System (ADS)

Matthews, Michael R.

2004-11-01

Galileo's discovery of the properties of pendulum motion depended on his adoption of the novel methodology of idealisation. Galileo's laws of pendulum motion could not be accepted until the empiricist methodological constraints placed on science by Aristotle, and by common sense, were overturned. As long as scientific claims were judged by how the world was immediately seen to behave, and as long as mathematics and physics were kept separate, then Galileo's pendulum claims could not be substantiated; the evidence was against them. Proof of the laws required not just a new science, but a new way of doing science, a new way of handling evidence, a new methodology of science. This was Galileo's method of idealisatioin. It was the foundation of the Galilean-Newtonian Paradigm which characterised the Scientific Revolution of the 17th century, and the subsequent centuries of modern science. As the pendulum was central to Galileo's and Newton's physics, appreciating the role of idealisation in their work is an instructive way to learn about the nature of science.

Comparative Research on Characteristics of the Isolation Systems with Dry Friction Damping and with Vicious Damping under Base Excitation

NASA Astrophysics Data System (ADS)

Hou, Junfang; jing, Min; Zhang, Weihua; Lu, Yahui; He, Haiwen

2017-12-01

As for the isolation problem of electronic equipments on vehicle, the vibration response characteristics of dry friction damping isolation system under base displacement excitation was analyzed in theory by harmonic balance method, and the displacement response was compared between the isolation systems with dry friction damping and vicious damping separately. The results show that the isolation system with small dry friction damping can’t meet the demands of displacement reduction close to the natural frequency, and it can realize full-frequency vibration isolation by improving dry friction damping when the lock frequency passes beyond the resonance frequency band. The results imply that the damping mechanism of dry friction isolator can’t be described only by dry friction damping, and the composite damping with dry friction and vicious damping is more appropriate.

29 CFR 1928.52 - Protective frames for wheel-type agricultural tractors-test procedures and performance requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... a 4,410-lb (2,000-kg) weight acting as a pendulum. The impact face of the weight shall be 27 ±1 in... restraining cables shall be located in the plane in which the center of gravity of the pendulum will swing, or... pendulum swinging from the height determined by paragraph (d)(3)(ii) of this section shall be used to...

29 CFR 1926.1002 - Protective frames (roll-over protective structures, known as ROPS) for wheel-type agricultural...

Code of Federal Regulations, 2012 CFR

2012-07-01

... produced by using a 4,410-lb (2,000-kg) weight acting as a pendulum. The impact face of the weight shall be... the center of gravity of the pendulum will swing, or more than one restraining cable shall give a... to the side on the same frame. The pendulum dropped from the height (see the definition of “H” in...

29 CFR 1926.1002 - Protective frames (roll-over protective structures, known as ROPS) for wheel-type agricultural...

Code of Federal Regulations, 2011 CFR

2011-07-01

... produced by using a 4,410-lb (2,000-kg) weight acting as a pendulum. The impact face of the weight shall be... the center of gravity of the pendulum will swing, or more than one restraining cable shall give a... to the side on the same frame. The pendulum dropped from the height (see the definition of “H” in...

29 CFR 1926.1002 - Protective frames (roll-over protective structures, known as ROPS) for wheel-type agricultural...

Code of Federal Regulations, 2010 CFR

2010-07-01

... produced by using a 4,410-lb (2,000-kg) weight acting as a pendulum. The impact face of the weight shall be... the center of gravity of the pendulum will swing, or more than one restraining cable shall give a... to the side on the same frame. The pendulum dropped from the height (see the definition of “H” in...

The experimental determination of the moments of inertia of airplanes by a simplified compound-pendulum method

NASA Technical Reports Server (NTRS)

Gracey, William

1948-01-01

A simplified compound-pendulum method for the experimental determination of the moments of inertia of airplanes about the x and y axes is described. The method is developed as a modification of the standard pendulum method reported previously in NACA report, NACA-467. A brief review of the older method is included to form a basis for discussion of the simplified method. (author)

29 CFR 1926.1002 - Protective frames (roll-over protective structures, known as ROPS) for wheel-type agricultural...

Code of Federal Regulations, 2013 CFR

2013-07-01

... produced by using a 4,410-lb (2,000-kg) weight acting as a pendulum. The impact face of the weight shall be... the center of gravity of the pendulum will swing, or more than one restraining cable shall give a... to the side on the same frame. The pendulum dropped from the height (see the definition of “H” in...

Theoretical Pressure Distribution, Apparent Mass, and Moment of Inertia of a Disk Pendulum Oscillating at Low Frequency. M.S. Thesis - George Washington Univ., Washington, D. C.

NASA Technical Reports Server (NTRS)

Dunning, R. S.

1973-01-01

Equations are developed which give the pressure profile, the forces and torques on a disk pendulum by means of point source wave theory from acoustics. The pressure, force and torque equations for an unbaffled disk are developed. These equations are then used to calculate the apparent mass and apparent inertia for the pendulum.

29 CFR 1926.1002 - Protective frames (roll-over protective structures, known as ROPS) for wheel-type agricultural...

Code of Federal Regulations, 2014 CFR

2014-07-01

... produced by using a 4,410-lb (2,000-kg) weight acting as a pendulum. The impact face of the weight shall be... the center of gravity of the pendulum will swing, or more than one restraining cable shall give a... to the side on the same frame. The pendulum dropped from the height (see the definition of “H” in...

Novel Out-Coupling Techniques for Terahertz Free Electron Lasers

DTIC Science & Technology

2012-06-01

4  1.   FEL “ Pendulum ” Equation and Electron Dynamics .......................4  2.   FEL...4 B. FEL THEORY 1. FEL “ Pendulum ” Equation and Electron Dynamics The dynamics of electron motion as it passes through the undulator are governed...I.5, then the FEL “ pendulum equation” is derived , (I.7) where is the dimensionless laser field amplitude[1]. From this, it is shown that changes

In full swing? How do pendulum migrant labourers in Vietnam adjust their sexual perspectives to their rural-urban lives?

PubMed

Nguyen, Huong Ngoc; Hardesty, Melissa; Hong, Khuat Thu

2011-11-01

Having emerged only recently due to fast urbanisation and globalisation, pendulum migrant labourers in Vietnam are economically, culturally and socially difficult to locate - though they are estimated to number in their millions. Defined by their frequent migration between village and city, pendulum migrant labourers occupy an extended period of liminality. Are they traditional villagers or liberal city people when it comes to sex? Does city life radically change their views on sexuality? Starting with the premise that living environments play a key role in structuring the practical and symbolic realities of sex, this paper explores how extended periods of circular migration between the village and city - living environments that differ markedly in terms of socioeconomic and cultural conditions - affect the sexual views and perspectives of Vietnamese pendulum migrant labourers. Analysis from in-depth interviews with 23 married pendulum migrant labourers revealed that even though they had been living the pendulum life for several years, they continued to identify themselves, sexually, as traditional villagers. Among labourers the link between sexuality and living environment was a matter of pragmatism - matching 'suitable' sexual behaviour to social, even if imagined, location - and of privilege or 'leagues' - matching behaviour and comportment to social pedigree.

Clinical Usefulness of the Pendulum Test Using a NK Table to Measure the Spasticity of Patients with Brain Lesions

PubMed Central

Kim, Yong-Wook

2013-01-01

. [Purpose] The purpose of the present study was to investigate the clinical usefulness (reliability and validity) of the pendulum test using a Noland-Kuckhoff (NK) table with an attached electrogoniometer to measure the spasticity of patients with brain lesions. [Subjects] The subjects were 31 patients with stroke or traumatic brain injury. [Methods] The intraclass correlation coefficient (ICC) was used to verify the test–retest reliability of spasticity measures obtained using the pendulum test. Pearson's product correlation coefficient was used to examine the validity of the pendulum test using the amplitude of the patellar tendon reflex (PTR) test, an objective and quantitative measure of spasticity. [Results] The test–retest reliability was high, reflecting a significant correlation between the test and the retest (ICCs = 0.95–0.97). A significant negative correlation was found between the amplitude of the PTR test and the four variables measured in the pendulum test (r = −0.77– −0.85). [Conclusion] The pendulum test using a NK table is an objective measure of spasticity and can be used in the clinical setting in place of more expensive and complicated equipment. Further studies are needed to investigate the therapeutic effect of this method on spasticity. PMID:24259775

Clinical usefulness of the pendulum test using a NK table to measure the spasticity of patients with brain lesions.

PubMed

Kim, Yong-Wook

2013-10-01

. [Purpose] The purpose of the present study was to investigate the clinical usefulness (reliability and validity) of the pendulum test using a Noland-Kuckhoff (NK) table with an attached electrogoniometer to measure the spasticity of patients with brain lesions. [Subjects] The subjects were 31 patients with stroke or traumatic brain injury. [Methods] The intraclass correlation coefficient (ICC) was used to verify the test-retest reliability of spasticity measures obtained using the pendulum test. Pearson's product correlation coefficient was used to examine the validity of the pendulum test using the amplitude of the patellar tendon reflex (PTR) test, an objective and quantitative measure of spasticity. [Results] The test-retest reliability was high, reflecting a significant correlation between the test and the retest (ICCs = 0.95-0.97). A significant negative correlation was found between the amplitude of the PTR test and the four variables measured in the pendulum test (r = -0.77- -0.85). [Conclusion] The pendulum test using a NK table is an objective measure of spasticity and can be used in the clinical setting in place of more expensive and complicated equipment. Further studies are needed to investigate the therapeutic effect of this method on spasticity.

Measurement of g using a magnetic pendulum and a smartphone magnetometer

NASA Astrophysics Data System (ADS)

Pili, Unofre; Violanda, Renante; Ceniza, Claude

2018-04-01

The internal sensors in smartphones for their advanced add-in functions have also paved the way for these gadgets becoming multifunctional tools in elementary experimental physics. For instance, the acceleration sensor has been used to analyze free-falling motion and to study the oscillations of a spring-mass system. The ambient light sensor on the other hand has been proven to be a capable tool in studying an astronomical phenomenon as well as in measuring speed and acceleration. In this paper we present an accurate, convenient, and engaging use of the smartphone magnetic field sensor to measure the acceleration due to gravity via measurement of the period of oscillations (simply called "period" in what follows) of a simple pendulum. Measurement of the gravitational acceleration via the simple pendulum is a standard elementary physics laboratory activity, but the employment of the magnetic field sensor of a smartphone device in measuring the period is quite new and the use of it is seen as fascinating among students. The setup and procedure are rather simple and can easily be replicated as a classroom demonstration or as a regular laboratory activity.

Human balancing of an inverted pendulum: position control by small, ballistic-like, throw and catch movements

PubMed Central

Loram, Ian D; Lakie, Martin

2002-01-01

In standing, there are small sways of the body. Our interest is to use an artificial task to illuminate the mechanisms underlying the sways and to account for changes in their size. Using the ankle musculature, subjects balanced a large inverted pendulum. The equilibrium of the pendulum is unstable and quasi-regular sway was observed like that in quiet standing. By giving full attention to minimising sway subjects could systematically reduce pendulum movement. The pendulum position, the torque generated at each ankle and the soleus and tibialis anterior EMGs were recorded. Explanations about how the human inverted pendulum is balanced usually ignore the fact that balance is maintained over a range of angles and not just at one angle. Any resting equilibrium position of the pendulum is unstable and in practice temporary; movement to a different resting equilibrium position can only be accomplished by a biphasic ‘throw and catch’ pattern of torque and not by an elastic mechanism. Results showed that balance was achieved by the constant repetition of a neurally generated ballistic-like biphasic pattern of torque which can control both position and sway size. A decomposition technique revealed that there was a substantial contribution to changes in torque from intrinsic mechanical ankle stiffness; however, by itself this was insufficient to maintain balance or to control position. Minimisation of sway size was caused by improvement in the accuracy of the anticipatory torque impulses. We hypothesise that examination of centre of mass and centre of pressure data for quiet standing will duplicate these results. PMID:11986396

University of Florida Torsion Pendulum for Testing Key LISA Technology

NASA Astrophysics Data System (ADS)

Apple, Stephen; Chilton, Andrew; Olatunde, Taiwo Janet; Hillsberry, Daniel; Parry, Samantha; Ciani, Giacomo; Wass, Peter; Mueller, Guido; Conklin, John

2018-01-01

This presentation will describe the design and performance of a new torsion pendulum at the University of Florida used for testing inertial sensors and associated technologies for use in space – based gravitational wave observatories and geodesy missions. In particular this new torsion pendulum facility is testing inertial sensors and associated technology for the upcoming LISA (laser interferometer space antenna) space-based gravitational wave observatory mission. The torsion pendulum apparatus is comprised of a suspended cross bar assembly that has LISA test mass mockups at each of its ends. Two of the test mass mockups are enclosed by capacitive sensors which provide actuation and position sensing. The entire assembly is housed in a vacuum chamber. The pendulum cross-bar converts rotational motion of the test masses about the suspension fiber axis into translational motion. The 22 cm cross bar arm length along with the extremely small torsional spring constant of the suspension fiber results in a near free fall condition in the translational degree-of-freedom orthogonal to both the member and the suspension fiber. The test masses are electrically isolated from the pendulum assembly and their charge is controlled via photoemission using fiber coupled UV LEDS. Position of the test masses is measured using both capacitive and interferometric readout. The broadband sensitivity of the capacitive readout and laser interferometer readout is 30 nm/√Hz and 0.5 nm/√Hz respectively. The performance of the pendulum measured in equivalent acceleration noise acting on a LISA test mass is approximately 3 × 10-13 ms-2/√Hz at 2 mHz. This presentation will also discuss the design and fabrication of a flight-like gravitational reference sensor that will soon be integrated into the torsion pendulum facility. This flight-like GRS will allow for noise performance measurements in a more LISA-like configuration.

Morphological evolution of spiders predicted by pendulum mechanics.

PubMed

Moya-Laraño, Jordi; Vinković, Dejan; De Mas, Eva; Corcobado, Guadalupe; Moreno, Eulalia

2008-03-26

Animals have been hypothesized to benefit from pendulum mechanics during suspensory locomotion, in which the potential energy of gravity is converted into kinetic energy according to the energy-conservation principle. However, no convincing evidence has been found so far. Demonstrating that morphological evolution follows pendulum mechanics is important from a biomechanical point of view because during suspensory locomotion some morphological traits could be decoupled from gravity, thus allowing independent adaptive morphological evolution of these two traits when compared to animals that move standing on their legs; i.e., as inverted pendulums. If the evolution of body shape matches simple pendulum mechanics, animals that move suspending their bodies should evolve relatively longer legs which must confer high moving capabilities. We tested this hypothesis in spiders, a group of diverse terrestrial generalist predators in which suspensory locomotion has been lost and gained a few times independently during their evolutionary history. In spiders that hang upside-down from their webs, their legs have evolved disproportionately longer relative to their body sizes when compared to spiders that move standing on their legs. In addition, we show how disproportionately longer legs allow spiders to run faster during suspensory locomotion and how these same spiders run at a slower speed on the ground (i.e., as inverted pendulums). Finally, when suspensory spiders are induced to run on the ground, there is a clear trend in which larger suspensory spiders tend to run much more slowly than similar-size spiders that normally move as inverted pendulums (i.e., wandering spiders). Several lines of evidence support the hypothesis that spiders have evolved according to the predictions of pendulum mechanics. These findings have potentially important ecological and evolutionary implications since they could partially explain the occurrence of foraging plasticity and dispersal constraints as well as the evolution of sexual size dimorphism and sociality.

Experimental Apparatus to Observe Dynamical Manifestations of Hamiltonian Monodromy

NASA Astrophysics Data System (ADS)

Nerem, M. Perry; Salmon, Danial; Delos, John; Aubin, Seth

An experiment to observe a topological change in a classical system with nontrivial monodromy is presented. Monodromy is the study of the topological behavior of a system as it evolves along a closed path. If the system does not return to the initial topological state at the end of the circuit, that system exhibits nontrivial monodromy. Such a topological change has been predicted in certain mechanical systems, but has not yet been observed experimentally. One such system is a family of paths in a cylindrically symmetric champagne-bottle potential, with a classically forbidden region centered at the origin. We constructed this system with a long spherically symmetric pendulum and a permanent magnet attached at the end. Magnetic fields from coils are used to create the potential barrier and the external forces to drive the pendulum about a monodromy circuit. A loop of initial conditions, that is initially on one side of the forbidden region, is driven smoothly about this circuit such that it continuously evolves into a loop that surrounds the forbidden region. We will display this phenomena through numerical simulations and hopefully experimental measurement.

Experimental Apparatus for the Observation of the Topological Change Associated with Dynamical Monodromy

NASA Astrophysics Data System (ADS)

Salmon, Daniel; Nerem, M. Perry; Aubin, Seth; Delos, John

Monodromy means ``once around a path,'' therefore systems that have non-trivial monodromy are systems such that, when taken around a closed circuit in some space, the system has changed state in some way. Classical systems that exhibit non-trivial Hamiltonian monodromy have action and angle variables that are multivalued functions. A family, or loop, of trajectories of this system has a topological change upon traversing a monodromy circuit. We present an experimental apparatus for observing this topological change. A family of particles moving in a cylindrically symmetric champagne-bottle potential exhibits non-trivial Hamiltonian monodromy. At the center of this system is a classically forbidden region. By following a monodromy circuit, a loop of initial conditions on one side of the forbidden region can be made to evolve continuously into a loop that surrounds the forbidden region. We realize this system using a spherical pendulum, having at its end a permanent magnet. Magnetic fields generated by coils can then be used to create the champagne-bottle potential, as well as drive the pendulum through the monodromy circuit.

Revolutionizing Space Propulsion Through the Characterization of Iodine as Fuel for Hall-Effect Thrusters

DTIC Science & Technology

2011-03-01

for controlled thruster operation at varying conditions. An inverted pendulum was used to take thrust measurements. Thrust to power ratio, anode...for comparison will include thrust, T. Thrust 21 can be measured by a sensitive inverted pendulum thrust stand. Specific impulse would be...to this pressure. III.4 Diagnostic Equipment The instrument used to take thrust measurements was the Busek T8 inverted pendulum thrust stand [13

An Empirical Model for Mine-Blast Loading

DTIC Science & Technology

2014-10-17

fledged experimental program. The numerical approach however suffers from several drawbacks in the mine blast simulations. First, it is a very...Suffield consisted in a pendulum type device to measure global impulse of buried mine [15]. One of the main purposes of the ONAGER pendulum was to study...TP-1 Terminal effects, KTA 1-34 report, 2004. [15] Bues, R., Hlady, S.L. and Bergeron, D.M., Pendulum Measurement of Land Mine Blast Output, Volume

Simple pendulum for blind students

NASA Astrophysics Data System (ADS)

Goncalves, A. M. B.; Cena, C. R.; Alves, D. C. B.; Errobidart, N. C. G.; Jardim, M. I. A.; Queiros, W. P.

2017-09-01

Faced with the need to teach physics to the visually impaired, in this paper we propose a way to demonstrate the dependence of distance and time in a pendulum experiment to blind students. The periodic oscillation of the pendulum is translated, by an Arduino and an ultrasonic sensor, in a periodic variation of frequency in a speaker. The main advantage of this proposal is the possibility that a blind student understands the movement without necessity of touching it.

Precision Measurement of Distribution of Film Thickness on Pendulum for Experiment of G

NASA Astrophysics Data System (ADS)

Liu, Lin-Xia; Guan, Sheng-Guo; Liu, Qi; Zhang, Ya-Ting; Shao, Cheng-Gang; Luo, Jun

2009-09-01

Distribution of film thickness coated on the pendulum of measuring the Newton gravitational constant G is determined with a weighing method by means of a precision mass comparator. The experimental result shows that the gold film on the pendulum will contribute a correction of -24.3 ppm to our G measurement with an uncertainty of 4.3 ppm, which is significant for improving the G value with high precision.

Biped Robot Gait Planning Based on 3D Linear Inverted Pendulum Model

NASA Astrophysics Data System (ADS)

Yu, Guochen; Zhang, Jiapeng; Bo, Wu

2018-01-01

In order to optimize the biped robot’s gait, the biped robot’s walking motion is simplify to the 3D linear inverted pendulum motion mode. The Center of Mass (CoM) locus is determined from the relationship between CoM and the Zero Moment Point (ZMP) locus. The ZMP locus is planned in advance. Then, the forward gait and lateral gait are simplified as connecting rod structure. Swing leg trajectory using B-spline interpolation. And the stability of the walking process is discussed in conjunction with the ZMP equation. Finally the system simulation is carried out under the given conditions to verify the validity of the proposed planning method.

Including Memory Friction in Single- and Two-State Quantum Dynamics Simulations.

PubMed

Brown, Paul A; Messina, Michael

2016-03-03

We present a simple computational algorithm that allows for the inclusion of memory friction in a quantum dynamics simulation of a small, quantum, primary system coupled to many atoms in the surroundings. We show how including a memory friction operator, F̂, in the primary quantum system's Hamiltonian operator builds memory friction into the dynamics of the primary quantum system. We show that, in the harmonic, semi-classical limit, this friction operator causes the classical phase-space centers of a wavepacket to evolve exactly as if it were a classical particle experiencing memory friction. We also show that this friction operator can be used to include memory friction in the quantum dynamics of an anharmonic primary system. We then generalize the algorithm so that it can be used to treat a primary quantum system that is evolving, non-adiabatically on two coupled potential energy surfaces, i.e., a model that can be used to model H atom transfer, for example. We demonstrate this approach's computational ease and flexibility by showing numerical results for both harmonic and anharmonic primary quantum systems in the single surface case. Finally, we present numerical results for a model of non-adiabatic H atom transfer between a reactant and product state that includes memory friction on one or both of the non-adiabatic potential energy surfaces and uncover some interesting dynamical effects of non-memory friction on the H atom transfer process.

Light rays and the tidal gravitational pendulum

NASA Astrophysics Data System (ADS)

Farley, A. N. St J.

2018-05-01

Null geodesic deviation in classical general relativity is expressed in terms of a scalar function, defined as the invariant magnitude of the connecting vector between neighbouring light rays in a null geodesic congruence projected onto a two-dimensional screen space orthogonal to the rays, where λ is an affine parameter along the rays. We demonstrate that η satisfies a harmonic oscillator-like equation with a λ-dependent frequency, which comprises terms accounting for local matter affecting the congruence and tidal gravitational effects from distant matter or gravitational waves passing through the congruence, represented by the amplitude, of a complex Weyl driving term. Oscillating solutions for η imply the presence of conjugate or focal points along the rays. A polarisation angle, is introduced comprising the orientation of the connecting vector on the screen space and the phase, of the Weyl driving term. Interpreting β as the polarisation of a gravitational wave encountering the light rays, we consider linearly polarised waves in the first instance. A highly non-linear, second-order ordinary differential equation, (the tidal pendulum equation), is then derived, so-called due to its analogy with the equation describing a non-linear, variable-length pendulum oscillating under gravity. The variable pendulum length is represented by the connecting vector magnitude, whilst the acceleration due to gravity in the familiar pendulum formulation is effectively replaced by . A tidal torque interpretation is also developed, where the torque is expressed as a coupling between the moment of inertia of the pendulum and the tidal gravitational field. Precessional effects are briefly discussed. A solution to the tidal pendulum equation in terms of familiar gravitational lensing variables is presented. The potential emergence of chaos in general relativity is discussed in the context of circularly, elliptically or randomly polarised gravitational waves encountering the null congruence.

Two-Pendulum Model of Propellant Slosh in Europa Clipper PMD Tank

NASA Technical Reports Server (NTRS)

Ng, Wanyi; Benson, David

2017-01-01

The objective of this fluids analysis is to model propellant slosh for the Europa Clipper mission using a two-pendulum model, such that controls engineers can predict slosh behavior during the mission. Propellant slosh causes shifts in center of mass and exerts forces and torques on the spacecraft which, if not adequately controlled, can lead to mission failure. The two-pendulum model provides a computationally simple model that can be used to predict slosh for the Europa Clipper tank geometry. The Europa Clipper tank is cylindrical with a domed top and bottom and includes a propellant management device (PMD). Due to the lack of experimental data in low gravity environments, computational fluid dynamics (CFD) simulation results were used as 'real' slosh behavior for two propellants at three fill fractions. Key pendulum parameters were derived that allow the pendulum model's center of mass, forces, and moments to closely match the CFD data. The parameter trends were examined as a function of tank fill fraction and compared with solutions to analytic equations that describe the frequency of slosh in tanks with simple geometries. The trends were monotonic as expected, and parameters resembled analytical predictions; any differences could be explained by the specific differences in the geometry of the tank. This paper summarizes the new method developed at Goddard Space Flight Center (GSFC) for deriving pendulum parameters for two-pendulum equivalent sloshing models. It presents the results of this method and discusses the validity of the results. This analysis is at a completed stage and will be applied in the immediate future to the evolving tank geometry as Europa Clipper moves past its preliminary design review (PDR) phase.

Learning and Understanding System Stability Using Illustrative Dynamic Texture Examples

ERIC Educational Resources Information Center

Liu, Huaping; Xiao, Wei; Zhao, Hongyan; Sun, Fuchun

2014-01-01

System stability is a basic concept in courses on dynamic system analysis and control for undergraduate students with computer science backgrounds. Typically, this was taught using a simple simulation example of an inverted pendulum. Unfortunately, many difficult issues arise in the learning and understanding of the concepts of stability,…

Reachability and Real-Time Actuation Strategies for the Active SLIP Model

DTIC Science & Technology

2015-06-01

spring leg, the Spring Loaded Inverted Pendulum (SLIP) is a prevalent model for analyzing running and hopping. In this work we consider an actuated...forced symmetry of the stance phase for the Spring-Loaded Inverted Pendulum , In Proceedings of the 2012 IEEE International Conference on Robotics and...Networks. Automatica, 49(1):206-213, 2013 (v) G. Piovan and K. Byl. Enforced symmetry of the stance phase for the spring-loaded inverted pendulum . In

Lyapunov optimal feedback control of a nonlinear inverted pendulum

NASA Technical Reports Server (NTRS)

Grantham, W. J.; Anderson, M. J.

1989-01-01

Liapunov optimal feedback control is applied to a nonlinear inverted pendulum in which the control torque was constrained to be less than the nonlinear gravity torque in the model. This necessitates a control algorithm which 'rocks' the pendulum out of its potential wells, in order to stabilize it at a unique vertical position. Simulation results indicate that a preliminary Liapunov feedback controller can successfully overcome the nonlinearity and bring almost all trajectories to the target.

UT Austin Villa 2011: 3D Simulation Team Report

DTIC Science & Technology

2011-01-01

inverted pendulum model omnidirectional walk engine based on one that was originally designed for the real Nao robot [7]. The omnidirectional walk is...using a double linear inverted pendulum , where the center of mass is swinging over the stance foot. In addition, as in Graf et al.’s work [7], we use...between the inverted pendulums formed by the respective stance feet. Notation Description maxStep∗i Maximum step sizes allowed for x, y, and θ y

String-Coupled Pendulum Oscillators: Theory and Experiment.

ERIC Educational Resources Information Center

Moloney, Michael J.

1978-01-01

A coupled-oscillator system is given which is readily set up, using only household materials. The normal-mode analysis of this system is worked out, and an experiment or demonstration is recommended in which one verifies the theory by measuring two times and four lengths. (Author/GA)

Comparison of two different methods of preoperative marking for toric intraocular lens implantation: bubble marker versus pendulum marker.

PubMed

Farooqui, Javed Hussain; Koul, Archana; Dutta, Ranjan; Shroff, Noshir Minoo

2016-01-01

To compare the accuracy of two different methods of preoperative marking for toric intraocular lens (IOL) implantation, bubble marker versus pendulum marker, as a means of establishing the reference point for the final alignment of the toric IOL to achieve an outcome as close as possible to emmetropia. Toric IOLs were implanted in 180 eyes of 110 patients. One group (55 patients) had preoperative marking of both eyes done with bubble marker (ASICO AE-2791TBL) and the other group (55 patients) with pendulum marker (Rumex(®)3-193). Reference marks were placed at 3-, 6-, and 9-o'clock positions on the limbus. Slit-lamp photographs were analyzed using Adobe Photoshop (version 7.0). Amount of alignment error (in degrees) induced in each group was measured. Mean absolute rotation error in the preoperative marking in the horizontal axis was 2.42±1.71 in the bubble marker group and 2.83±2.31in the pendulum marker group (P=0.501). Sixty percent of the pendulum group and 70% of the bubble group had rotation error ≤3 (P=0.589), and 90% eyes of the pendulum group and 96.7% of the bubble group had rotation error ≤5 (P=0.612). Both preoperative marking techniques result in approximately 3 of alignment error. Both marking techniques are simple, predictable, reproducible and easy to perform.

Modelling, Simulation, Animation, and Real-Time Control (Mosart) for a Class of Electromechanical Systems: A System-Theoretic Approach

ERIC Educational Resources Information Center

Rodriguez, Armando A.; Metzger, Richard P.; Cifdaloz, Oguzhan; Dhirasakdanon, Thanate; Welfert, Bruno

2004-01-01

This paper describes an interactive modelling, simulation, animation, and real-time control (MoSART) environment for a class of 'cart-pendulum' electromechanical systems that may be used to enhance learning within differential equations and linear algebra classes. The environment is useful for conveying fundamental mathematical/systems concepts…

Physics in the laundromat

NASA Astrophysics Data System (ADS)

McDonald, Kirk T.

1998-03-01

The spin cycle of a washing machine involves motion that is stabilized by the Coriolis force, similar to the case of the motion of shafts of large turbines. This system is an example of a stable inverted pendulum.

Seismic cross-coupling noise in torsion pendulums

NASA Astrophysics Data System (ADS)

Shimoda, Tomofumi; Aritomi, Naoki; Shoda, Ayaka; Michimura, Yuta; Ando, Masaki

2018-05-01

Detection of low-frequency gravitational waves around 0.1 Hz is one of the important targets for future gravitational wave observation. One of the main sources of the expected signals is gravitational waves from binary intermediate-mass black hole coalescences which is proposed as one of the formation scenarios of supermassive black holes. By using a torsion pendulum, which can have a resonance frequency of a few millihertz, such signals can be measured on the ground since its rotational motion can act as a free mass down to 0.01 Hz. However, sensitivity of a realistic torsion pendulum will suffer from torsional displacement noise introduced from translational ground motion in the main frequency band of interest. Such noise is called seismic cross-coupling noise, and there has been little research on it. In this paper, systematic investigation is performed to identify routes of cross-coupling transfer for standard torsion pendulums. Based on the results, this paper also proposes reduction schemes of cross-coupling noise, and they were demonstrated experimentally in agreement with theory. This result establishes a basic way to reduce seismic noise in torsion pendulums for the most significant coupling routes.

Neural network-based motion control of an underactuated wheeled inverted pendulum model.

PubMed

Yang, Chenguang; Li, Zhijun; Cui, Rongxin; Xu, Bugong

2014-11-01

In this paper, automatic motion control is investigated for one of wheeled inverted pendulum (WIP) models, which have been widely applied for modeling of a large range of two wheeled modern vehicles. First, the underactuated WIP model is decomposed into a fully actuated second order subsystem Σa consisting of planar movement of vehicle forward and yaw angular motions, and a nonactuated first order subsystem Σb of pendulum motion. Due to the unknown dynamics of subsystem Σa and the universal approximation ability of neural network (NN), an adaptive NN scheme has been employed for motion control of subsystem Σa . The model reference approach has been used whereas the reference model is optimized by the finite time linear quadratic regulation technique. The pendulum motion in the passive subsystem Σb is indirectly controlled using the dynamic coupling with planar forward motion of subsystem Σa , such that satisfactory tracking of a set pendulum tilt angle can be guaranteed. Rigours theoretic analysis has been established, and simulation studies have been performed to demonstrate the developed method.

Piaget and the Pendulum

NASA Astrophysics Data System (ADS)

Bond, Trevor G.

Piaget's investigations into children's understanding of the laws governing the movement of a simple pendulum were first reported in 1955 as part of a report into how children's knowledge of the physical world changes during development. Chapter 4 of Inhelder & Piaget (1955/1958) entitled `The Oscillation of a Pendulum and the Operations of Exclusion'' demonstrated how adolescents could construct the experimental strategies necessary to isolate each of the variables, exclude the irrelevant factors and conclude concerning the causal role of length. This became one of the most easily replicable tasks from the Genevan school and was used in a number of important investigations to detect the onset of formal operational thinking. While it seems that the pendulum investigation fits nicely into Piaget's sequence of studies of concepts such as time, distance and speed suggested to him by Einstein, more recent research (Bond 2001) shows Inhelder to be directly responsible for the investigations into children's induction of physical laws. The inter-relationship between the pendulum problem, developing thought and scientific method is revealed in a number of Genevan and post-Piagetian investigations.

Ratchet baryogenesis and an analogy with the forced pendulum

NASA Astrophysics Data System (ADS)

Bamba, Kazuharu; Barrie, Neil D.; Sugamoto, Akio; Takeuchi, Tatsu; Yamashita, Kimiko

2018-06-01

A new scenario of baryogenesis via the ratchet mechanism is proposed based on an analogy with the forced pendulum. The oscillation of the inflaton field during the reheating epoch after inflation plays the role of the driving force, while the phase 𝜃 of a scalar baryon field (a complex scalar field with baryon number) plays the role of the angle of the pendulum. When the inflaton is coupled to the scalar baryon, the behavior of the phase 𝜃 can be analogous to that of the angle of the forced pendulum. If the oscillation of the driving force is adjusted to the pendulum’s motion, a directed rotation of the pendulum is obtained with a nonvanishing value of 𝜃˙, which models successful baryogenesis since 𝜃˙ is proportional to the baryon number density. Similar ratchet models which lead to directed motion have been used in the study of molecular motors in biology. There, the driving force is supplied by chemical reactions, while in our scenario this role is played by the inflaton during the reheating epoch.

Stick-slip friction and ageing in Velcro®

NASA Astrophysics Data System (ADS)

Mariani, Lisa; Angiolillo, Paul

2014-03-01

The mesoscopic hook and loop system of Velcro® provides a model of stick-slip friction that exhibits behavior reminiscent of results seen in nanoscale model systems. The friction is linearly dependent on contact area and independent of driving velocity. Morever, there is a power law dependence of the friction on loading, with exponent between 1/4 and 1/3. Furthermore, the evolution of stick-slip to more smooth sliding, as controlled by contact area, is also noted. These transition predictions follow power law profiles, as well, with respect to increasing contact area. Thus, the hook-and-loop system shows to be a good mesoscale model system of stick-slip friction and provides a link between nanoscale and macroscale friction. Through an investigation into the ageing of the hooks in the system, the data suggests that the hooks age during the shearing regime and take a characteristic time to return to initial attachment strength. Additionally, there does not appear to be a significant affect of ageing on the kinetic friction experienced by the system.

Phase Transition of a Dynamical System with a Bi-Directional, Instantaneous Coupling to a Virtual System

NASA Astrophysics Data System (ADS)

Gintautas, Vadas; Hubler, Alfred

2006-03-01

As worldwide computer resources increase in power and decrease in cost, real-time simulations of physical systems are becoming increasingly prevalent, from laboratory models to stock market projections and entire ``virtual worlds'' in computer games. Often, these systems are meticulously designed to match real-world systems as closely as possible. We study the limiting behavior of a virtual horizontally driven pendulum coupled to its real-world counterpart, where the interaction occurs on a time scale that is much shorter than the time scale of the dynamical system. We find that if the physical parameters of the virtual system match those of the real system within a certain tolerance, there is a qualitative change in the behavior of the two-pendulum system as the strength of the coupling is increased. Applications include a new method to measure the physical parameters of a real system and the use of resonance spectroscopy to refine a computer model. As virtual systems better approximate real ones, even very weak interactions may produce unexpected and dramatic behavior. The research is supported by the National Science Foundation Grant No. NSF PHY 01-40179, NSF DMS 03-25939 ITR, and NSF DGE 03-38215.

Improving the performance of auto-parametric pendulum absorbers by means of a flexural beam

NASA Astrophysics Data System (ADS)

Mahmoudkhani, S.

2018-07-01

Auto-parametric pendulum absorbers perform well only in a very limited range of excitation amplitudes, above which their efficiency would be substantially degraded as a consequence of spillover effects or appearance of quasi-periodic and chaotic responses. For improving the performance against this drawback, the rigid pendulum is replaced in the present study with a low-stiffness viscoelastic beam. An additional one-to-three internal resonance between the almost non-flexural rotational and the first flexural modes of the beam is also introduced. With the aid of this internal resonance, the energy that has been transferred to the absorber due to the one-to-two internal resonance would be avoided from being transferred back to the primary system by faster dissipation of vibrations at a higher-frequency mode thereby leading to lower spillover effects. For modeling purpose, the tracking frame with the rigid-body constraint and also the third-order nonlinear beam theory are employed to account for arbitrarily large rotation angles coupled to moderately large elastic deformations. The assumed-mode method is also used to obtain discretized equations of motion. The numerical continuation of periodic solution is performed and the bifurcations with detrimental effects on the performance are determined. Various parametric studies are also conducted which show that by proper setting of the system parameters, higher efficiencies at much wider range of excitation amplitudes could be achieved.

The sympathy of two pendulum clocks: beyond Huygens' observations.

PubMed

Peña Ramirez, Jonatan; Olvera, Luis Alberto; Nijmeijer, Henk; Alvarez, Joaquin

2016-03-29

This paper introduces a modern version of the classical Huygens' experiment on synchronization of pendulum clocks. The version presented here consists of two monumental pendulum clocks--ad hoc designed and fabricated--which are coupled through a wooden structure. It is demonstrated that the coupled clocks exhibit 'sympathetic' motion, i.e. the pendula of the clocks oscillate in consonance and in the same direction. Interestingly, when the clocks are synchronized, the common oscillation frequency decreases, i.e. the clocks become slow and inaccurate. In order to rigorously explain these findings, a mathematical model for the coupled clocks is obtained by using well-established physical and mechanical laws and likewise, a theoretical analysis is conducted. Ultimately, the sympathy of two monumental pendulum clocks, interacting via a flexible coupling structure, is experimentally, numerically, and analytically demonstrated.

Parametric pendulum based wave energy converter

NASA Astrophysics Data System (ADS)

Yurchenko, Daniil; Alevras, Panagiotis

2018-01-01

The paper investigates the dynamics of a novel wave energy converter based on the parametrically excited pendulum. The herein developed concept of the parametric pendulum allows reducing the influence of the gravity force thereby significantly improving the device performance at a regular sea state, which could not be achieved in the earlier proposed original point-absorber design. The suggested design of a wave energy converter achieves a dominant rotational motion without any additional mechanisms, like a gearbox, or any active control involvement. Presented numerical results of deterministic and stochastic modeling clearly reflect the advantage of the proposed design. A set of experimental results confirms the numerical findings and validates the new design of a parametric pendulum based wave energy converter. Power harvesting potential of the novel device is also presented.

Earthquake Facts

MedlinePlus

... recordings of large earthquakes, scientists built large spring-pendulum seismometers in an attempt to record the long- ... are moving away from one another. The first “pendulum seismoscope” to measure the shaking of the ground ...

Dynamic Accuracy of Inertial Magnetic Sensor Modules

DTIC Science & Technology

2016-12-01

and the cost of the YEI 3-space data-logging sensor was justified. C. PREVIOUS WORK In [7], Jeremy Cookson built a low-cost pendulum with an optical...encoder to test the dynamic accuracy of MARG sensor modules. The pendulum was designed in order to execute dynamic, repeatable tests in a single...3DM-GX1 and 3DM-GX3-25 sensors. In [8], Leslie Landry developed similar repeatable tests and utilized the pendulum to test the dynamic accuracy of

Advancements of In-Flight Mass Moment of Inertia and Structural Deflection Algorithms for Satellite Attitude Simulators

DTIC Science & Technology

2015-03-26

pendulum [15] to estimate the MOI. The benefit to this methodology is that instead of a direct comparison to Euler’s equations when using an on-board ACS...the equations of motion of pendulum motion are evaluated to estimate the resistance to angular acceleration. Instead of attempting to compare noisy...sensor data instantaneously when using on-board ACS data, the pendulum oscillation frequency is estimated, which can be globally smoothed for highly

Measuring g Using a Magnetic Pendulum and Telephone Pickup

NASA Astrophysics Data System (ADS)

Sinacore, J.; Takai, H.

2010-10-01

The simple pendulum has long been used to measure g, the acceleration due to gravity, with a precision of a few percent. Achieving agreement with the accepted value of less than 1% is feasible in the high school laboratory, though it requires some care. The precision of the measurement is bound by how accurately the period and the pendulum length are determined. To improve on the period measurement, we have developed a simple and inexpensive method using a magnet and telephone pickup.2

Adaptive back-stepping control of the harmonic drive system with LuGre model-based friction compensation

NASA Astrophysics Data System (ADS)

Liu, Sen; Gang, Tieqiang

2018-03-01

Harmonic drives are widely used in aerospace and industrial robots. Flexibility, friction and parameter uncertainty will result in transmission performance degradation. In this paper, an adaptive back-stepping method with friction compensation is proposed to improve the tracking performance of the harmonic drive system. The nonlinear friction is described by LuGre model and compensated with a friction observer, and the uncertainty of model parameters is resolved by adaptive parameter estimation method. By using Lyapunov stability theory, it is proved that all the errors of the closed-loop system are uniformly ultimately bounded. Simulations illustrate the effectiveness of our friction compensation method.

A Unit on Deterministic Chaos for Student Teachers

ERIC Educational Resources Information Center

Stavrou, D.; Assimopoulos, S.; Skordoulis, C.

2013-01-01

A unit aiming to introduce pre-service teachers of primary education to the limited predictability of deterministic chaotic systems is presented. The unit is based on a commercial chaotic pendulum system connected with a data acquisition interface. The capabilities and difficulties in understanding the notion of limited predictability of 18…

Changes in stature following plyometric drop-jump and pendulum exercises.

PubMed

Fowler, N E; Lees, A; Reilly, T

1997-12-01

The aim of this study was to compare the changes in stature following the performance of plyometric exercises using drop-jumps and a pendulum swing. Eight male participants aged 21.7 +/- 1.8 years with experience of plyometric training gave their informed consent to act as participants. Participants undertook two exercise regimens and a 15-min standing test in a random order. The exercises entailed the performance of 50 drop-jumps from a height of 0.28 m or 50 pendulum rebounds. Participants were instructed to perform maximal jumps or rebounds using a 'bounce' style. Measurements of stature were performed after a 20-min period of standing (pre-exercise), 2-min after exercise (post-exercise) and after a 20-min standing recovery (recovery). Back pain and muscle soreness were assessed using an analogue-visual scale, at each of the above times and also 24 and 36 h after the test. Peak torque during isokinetic knee extension at 1.04 rads-1 was measured immediately before and after the exercise bouts, to assess the degree of muscular fatigue. Ground/wall reaction force data were recorded using a Kistler force platform mounted in the floor for drop-jumps and vertically on the rebound wall for pendulum exercises. Drop-jumps resulted in the greatest (p < 0.05) change in stature (-2.71 +/- 0.8 mm), compared to pendulum exercises (-1.77 +/- 0.7 mm) and standing (-0.39 +/- 0.2 mm). Both exercise regimens resulted in a significant (p < 0.01) decrease in stature when compared to the standing condition. Drop-jumps resulted in significantly greater peak impact forces (p < 0.05) than pendulum exercises (drop-jumps = 3.2 +/- 0.5 x body weight, pendulum = 2.6 +/- 0.5 x body weight). The two exercise conditions both invoked a small degree of muscle soreness but there were no significant differences between conditions. Both exercise regimens resulted in a non-significant decrease in peak torque indicating a similar degree of muscular fatigue. Based on the lower shrinkage resulted and lower peak forces, it can be concluded that pendulum exercises pose a lower injury potential to the lower back than drop-jumps performed from a height of 28 cm.

Enhancing power generation of floating wave power generators by utilization of nonlinear roll-pitch coupling

NASA Astrophysics Data System (ADS)

Yerrapragada, Karthik; Ansari, M. H.; Karami, M. Amin

2017-09-01

We propose utilization of the nonlinear coupling between the roll and pitch motions of wave energy harvesting vessels to increase their power generation by orders of magnitude. Unlike linear vessels that exhibit unidirectional motion, our vessel undergoes both pitch and roll motions in response to frontal waves. This significantly magnifies the motion of the vessel and thus improves the power production by several orders of magnitude. The ocean waves result in roll and pitch motions of the vessel, which in turn causes rotation of an onboard pendulum. The pendulum is connected to an electric generator to produce power. The coupled electro-mechanical system is modeled using energy methods. This paper investigates the power generation of the vessel when the ratio between pitch and roll natural frequencies is about 2 to 1. In that case, a nonlinear energy transfer occurs between the roll and pitch motions, causing the vessel to perform coupled pitch and roll motion even though it is only excited in the pitch direction. It is shown that co-existence of pitch and roll motions significantly enhances the pendulum rotation and power generation. A method for tuning the natural frequencies of the vessel is proposed to make the energy generator robust to variations of the frequency of the incident waves. It is shown that the proposed method enhances the power output of the floating wave power generators by multiple orders of magnitude. A small-scale prototype is developed for the proof of concept. The nonlinear energy transfer and the full rotation of the pendulum in the prototype are observed in the experimental tests.

A non-ideal portal frame energy harvester controlled using a pendulum

NASA Astrophysics Data System (ADS)

Iliuk, I.; Balthazar, J. M.; Tusset, A. M.; Piqueira, J. R. C.; Rodrigues de Pontes, B.; Felix, J. L. P.; Bueno, Á. M.

2013-09-01

A model of energy harvester based on a simple portal frame structure is presented. The system is considered to be non-ideal system (NIS) due to interaction with the energy source, a DC motor with limited power supply and the system structure. The nonlinearities present in the piezoelectric material are considered in the piezoelectric coupling mathematical model. The system is a bi-stable Duffing oscillator presenting a chaotic behavior. Analyzing the average power variation, and bifurcation diagrams, the value of the control variable that optimizes power or average value that stabilizes the chaotic system in the periodic orbit is determined. The control sensitivity is determined to parametric errors in the damping and stiffness parameters of the portal frame. The proposed passive control technique uses a simple pendulum to tuned to the vibration of the structure to improve the energy harvesting. The results show that with the implementation of the control strategy it is possible to eliminate the need for active or semi active control, usually more complex. The control also provides a way to regulate the energy captured to a desired operating frequency.

Insensitivity of synchronization to network structure in chaotic pendulum systems with time-delay coupling.

PubMed

Yao, Chenggui; Zhan, Meng; Shuai, Jianwei; Ma, Jun; Kurths, Jürgen

2017-12-01

It has been generally believed that both time delay and network structure could play a crucial role in determining collective dynamical behaviors in complex systems. In this work, we study the influence of coupling strength, time delay, and network topology on synchronization behavior in delay-coupled networks of chaotic pendulums. Interestingly, we find that the threshold value of the coupling strength for complete synchronization in such networks strongly depends on the time delay in the coupling, but appears to be insensitive to the network structure. This lack of sensitivity was numerically tested in several typical regular networks, such as different locally and globally coupled ones as well as in several complex networks, such as small-world and scale-free networks. Furthermore, we find that the emergence of a synchronous periodic state induced by time delay is of key importance for the complete synchronization.

Study of a Car Body Tilting System Using a Variable Link Mechanism: Fundamental Characteristics of Pendulum Motion and Strategy for Perfect Tilting

NASA Astrophysics Data System (ADS)

Yoshida, Hidehisa; Nagai, Masao

This paper analyzes the fundamental dynamic characteristics of a tilting railway vehicle using a variable link mechanism for compensating both the lateral acceleration experienced by passengers and the wheel load imbalance between the inner and outer rails. The geometric relations between the center of rotation, the center of gravity, and the positions of all four links of the tilting system are analyzed. Then, equations of the pendulum motions of the railway vehicle body with a four-link mechanism are derived. A theoretically discussion is given on the geometrical shapes employed in the link mechanism that can simultaneously provide zero lateral acceleration and zero wheel load fluctuation. Then, the perfect tilting condition, which is the control target of the feedforward tilting control, is derived from the linear equation of tilting motion.

Dynamical control of a quantum Kapitza pendulum in a spin-1 BEC

NASA Astrophysics Data System (ADS)

Hoang, Thai; Gerving, Corey; Land, Ben; Anquez, Martin; Hamley, Chris; Chapman, Michael

2013-05-01

We demonstrate dynamic stabilization of an unstable strongly interacting quantum many-body system by periodic manipulation of the phase of the collective states. The experiment employs a spin-1 atomic Bose condensate that has spin dynamics analogous to a non-rigid pendulum in the mean-field limit. The condensate spin is initialized to an unstable (hyperbolic) fixed point of the phase space, where subsequent free evolution gives rise to spin-nematic squeezing and quantum spin mixing. To stabilize the system, periodic microwave pulses are applied that manipulate the spin-nematic fluctuations and limit their growth. The range of pulse periods and phase shifts with which the condensate can be stabilized is measured and compares well with a linear stability analysis of the problem. C.D. Hamley, et al., ``Spin-Nematic Squeezed Vacuum in a Quantum Gas,'' Nature Physics 8, 305-308 (2012).

49 CFR 572.127 - Test conditions and instrumentation.

Code of Federal Regulations, 2010 CFR

2010-10-01

...) Forces—Class 1000; (ii) Moments—Class 600; (iii) Pendulum acceleration—Class 180; (iv) Rotation—Class 60 (if used). (3) Thorax: (i) Rib acceleration—Class 1000; (ii) Spine and pendulum accelerations—Class...

49 CFR 572.127 - Test conditions and instrumentation.

Code of Federal Regulations, 2014 CFR

2014-10-01

...) Forces—Class 1000; (ii) Moments—Class 600; (iii) Pendulum acceleration—Class 180; (iv) Rotation—Class 60 (if used). (3) Thorax: (i) Rib acceleration—Class 1000; (ii) Spine and pendulum accelerations—Class...

49 CFR 572.127 - Test conditions and instrumentation.

Code of Federal Regulations, 2011 CFR

2011-10-01

...) Forces—Class 1000; (ii) Moments—Class 600; (iii) Pendulum acceleration—Class 180; (iv) Rotation—Class 60 (if used). (3) Thorax: (i) Rib acceleration—Class 1000; (ii) Spine and pendulum accelerations—Class...

49 CFR 572.127 - Test conditions and instrumentation.

Code of Federal Regulations, 2013 CFR

2013-10-01

...) Forces—Class 1000; (ii) Moments—Class 600; (iii) Pendulum acceleration—Class 180; (iv) Rotation—Class 60 (if used). (3) Thorax: (i) Rib acceleration—Class 1000; (ii) Spine and pendulum accelerations—Class...

49 CFR 572.127 - Test conditions and instrumentation.

Code of Federal Regulations, 2012 CFR

2012-10-01

...) Forces—Class 1000; (ii) Moments—Class 600; (iii) Pendulum acceleration—Class 180; (iv) Rotation—Class 60 (if used). (3) Thorax: (i) Rib acceleration—Class 1000; (ii) Spine and pendulum accelerations—Class...

A submerged membrane bioreactor with pendulum type oscillation (PTO) for oily wastewater treatment: membrane permeability and fouling control.

PubMed

Qin, Lei; Fan, Zheng; Xu, Lusheng; Zhang, Guoliang; Wang, Guanghui; Wu, Dexin; Long, Xuwei; Meng, Qin

2015-05-01

In this study, a novel submerged membrane bioreactor (SMBR) with pendulum type oscillation (PTO) hollow fiber membrane modules was developed to treat oily wastewater and control the problem of membrane fouling. To assess the potential of PTO membrane modules, the effect of oscillation orientation and frequency on membrane permeability was investigated in detail. The forces exerted on sludge flocs in the oscillating SMBR were analyzed to evaluate the impact of membrane oscillating on the cake layer resistance reduction. Results showed that the optimized PTO SMBR system exhibited 11 times higher membrane permeability and better fouling controllability than the conventional MBR system. By hydrodynamic analysis, it was found that the cooperative effect of bubble-induced turbulence and membrane oscillation in PTO SMBR system generated strong shear stress at liquid-membrane interface in vertical and horizontal direction and effectively hindered the particles from depositing on membrane surface. Copyright © 2015 Elsevier Ltd. All rights reserved.

Interval type-2 fuzzy PID controller for uncertain nonlinear inverted pendulum system.

PubMed

El-Bardini, Mohammad; El-Nagar, Ahmad M

2014-05-01

In this paper, the interval type-2 fuzzy proportional-integral-derivative controller (IT2F-PID) is proposed for controlling an inverted pendulum on a cart system with an uncertain model. The proposed controller is designed using a new method of type-reduction that we have proposed, which is called the simplified type-reduction method. The proposed IT2F-PID controller is able to handle the effect of structure uncertainties due to the structure of the interval type-2 fuzzy logic system (IT2-FLS). The results of the proposed IT2F-PID controller using a new method of type-reduction are compared with the other proposed IT2F-PID controller using the uncertainty bound method and the type-1 fuzzy PID controller (T1F-PID). The simulation and practical results show that the performance of the proposed controller is significantly improved compared with the T1F-PID controller. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

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.

Measurement of the inertial properties of the Helios F-1 spacecraft

NASA Technical Reports Server (NTRS)

Gayman, W. H.

1975-01-01

A gravity pendulum method of measuring lateral moments of inertia of large structures with an error of less than 1% is outlined. The method is based on the fact that in a physical pendulum with a knife-edge support the distance from the axis of rotation to the system center of gravity determines the minimal period of oscillation and is equal to the system centroidal radius of gyration. The method is applied to results of a test procedure in which the Helios F-1 spacecraft was placed in a roll fixture with crossed flexure pivots as elastic constraints and system oscillation measurements were made with each of a set of added moment-of-inertia increments. Equations of motion are derived with allowance for the effect of the finite pivot radius and an error analysis is carried out to find the criterion for maximum accuracy in determining the square of the centroidal radius of gyration. The test procedure allows all measurements to be made with the specimen in upright position.

The Effect of a Variable Disc Pad Friction Coefficient for the Mechanical Brake System of a Railway Vehicle

PubMed Central

Lee, Nam-Jin; Kang, Chul-Goo

2015-01-01

A brake hardware-in-the-loop simulation (HILS) system for a railway vehicle is widely applied to estimate and validate braking performance in research studies and field tests. When we develop a simulation model for a full vehicle system, the characteristics of all components are generally properly simplified based on the understanding of each component’s purpose and interaction with other components. The friction coefficient between the brake disc and the pad used in simulations has been conventionally considered constant, and the effect of a variable friction coefficient is ignored with the assumption that the variability affects the performance of the vehicle braking very little. However, the friction coefficient of a disc pad changes significantly within a range due to environmental conditions, and thus, the friction coefficient can affect the performance of the brakes considerably, especially on the wheel slide. In this paper, we apply a variable friction coefficient and analyzed the effects of the variable friction coefficient on a mechanical brake system of a railway vehicle. We introduce a mathematical formula for the variable friction coefficient in which the variable friction is represented by two variables and five parameters. The proposed formula is applied to real-time simulations using a brake HILS system, and the effectiveness of the formula is verified experimentally by testing the mechanical braking performance of the brake HILS system. PMID:26267883

The Effect of a Variable Disc Pad Friction Coefficient for the Mechanical Brake System of a Railway Vehicle.

PubMed

Lee, Nam-Jin; Kang, Chul-Goo

2015-01-01

A brake hardware-in-the-loop simulation (HILS) system for a railway vehicle is widely applied to estimate and validate braking performance in research studies and field tests. When we develop a simulation model for a full vehicle system, the characteristics of all components are generally properly simplified based on the understanding of each component's purpose and interaction with other components. The friction coefficient between the brake disc and the pad used in simulations has been conventionally considered constant, and the effect of a variable friction coefficient is ignored with the assumption that the variability affects the performance of the vehicle braking very little. However, the friction coefficient of a disc pad changes significantly within a range due to environmental conditions, and thus, the friction coefficient can affect the performance of the brakes considerably, especially on the wheel slide. In this paper, we apply a variable friction coefficient and analyzed the effects of the variable friction coefficient on a mechanical brake system of a railway vehicle. We introduce a mathematical formula for the variable friction coefficient in which the variable friction is represented by two variables and five parameters. The proposed formula is applied to real-time simulations using a brake HILS system, and the effectiveness of the formula is verified experimentally by testing the mechanical braking performance of the brake HILS system.

49 CFR 572.146 - Test conditions and instrumentation.

Code of Federal Regulations, 2013 CFR

2013-10-01

...) Head acceleration—Class 1000 (2) Neck (i) Force—Class 1000 (ii) Moments—Class 600 (iii) Pendulum... acceleration—Class 1000 (ii) Spine and pendulum accelerations—Class 180 (iii) Sternum deflection—Class 600 (iv...

49 CFR 572.155 - Test conditions and instrumentation.

Code of Federal Regulations, 2014 CFR

2014-10-01

...) Moments—Class 600; (iii) Pendulum acceleration—Class 180; (iv) Rotation potentiometer response (if used)—CFC 60. (3) Thorax: (i) Spine and pendulum accelerations—Class 180; (ii) Shoulder forces—Class 600; (4...

49 CFR 572.155 - Test conditions and instrumentation.

Code of Federal Regulations, 2013 CFR

2013-10-01

...) Moments—Class 600; (iii) Pendulum acceleration—Class 180; (iv) Rotation potentiometer response (if used)—CFC 60. (3) Thorax: (i) Spine and pendulum accelerations—Class 180; (ii) Shoulder forces—Class 600; (4...

49 CFR 572.177 - Test conditions and instrumentation.

Code of Federal Regulations, 2012 CFR

2012-10-01

...) except as noted, with channel frequency classes as follows: (1) Pendulum acceleration, CFC 180, (2) Pendulum D-plane rotation (if transducer is used), CFC 60, (3) Torso flexion pulling force (if transducer...

49 CFR 572.177 - Test conditions and instrumentation.

Code of Federal Regulations, 2014 CFR

2014-10-01

...) except as noted, with channel frequency classes as follows: (1) Pendulum acceleration, CFC 180, (2) Pendulum D-plane rotation (if transducer is used), CFC 60, (3) Torso flexion pulling force (if transducer...