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…

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 572.177 - 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...

49 CFR 572.177 - Test conditions and instrumentation.

Code of Federal Regulations, 2013 CFR

2013-10-01

...) 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...

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

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.

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.

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...

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),

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.

On periodic solutions of an Atwood's pendulum

NASA Astrophysics Data System (ADS)

Mittleman, Donald

1987-05-01

An Atwood's pendulum is defined as an Atwood's machine in which one of two masses is allowed to swing as a pendulum while the other remains constrained to move only in the vertical direction. The pendulum motion of the one mass induces a varying tension in the connecting wire; this, in turn, produces motion in the second mass. It is shown that this motion can be made periodic if the ratio of the two masses and the dependency of this ratio on the initial conditions are chosen as prescribed in this report. If this condition is not met, the motion consists of the superposition of two motions. The first is motion in a constant gravitational field where the effective gravity is kg; the factor k is determined explicitly. The second is the periodic motion that is the central theme of this report. During the course of the analysis, the fundamental frequency of the periodic motion is determined. It is shown to be slightly higher than the frequency of a pendulum of comparable length swinging in the Earth's gravitational field; the factor is given explicitly. This work is restricted to the extent that small approximations are introduced initially for trigonometric functions.

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.

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

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.

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

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.

Integrated Data Collection and Analysis Project: Friction Correlation Study

DTIC Science & Technology

2015-08-01

methods authorized in AOP-7 include Pendulum Friction, Rotary Friction, Sliding Friction (ABL), BAM Friction and Steel/Fiber Shoe Methods. The...sensitivity can be obtained by Pendulum Friction, Rotary Friction, Sliding Friction (such as the ABL), BAM Friction and Steel/Fiber Shoe Methods.3, 4 Within...Figure 4.16 A variable compressive force is applied downward through the wheel hydraulically (50-1995 psi). The 5 kg pendulum impacts (8 ft/sec is the

Improving the sensitivity of a torsion pendulum by using an optical spring method

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

Wang Qinglan; Yeh Hsienchi; Zhou Zebing

We present a scheme aiming at improving the sensitivity of a torsion pendulum by means of radiation-pressure-induced optical spring. Two partial-reflective mirrors are installed on the opposite sides of a torsion pendulum, and one high-reflective mirror is mounted at the end of the torsion beam so that two identical Fabry-Perot cavities can be formed and aligned in series. Due to the antisymmetric radiation pressures acting on the opposite sides of the torsion beam, a negative restoring coefficient can be generated within a certain dynamic range, such that both the resultant torsional rigidity and the resonant frequency of the torsion pendulummore » are reduced, and the minimum detectable response torque in high-frequency region can be reduced accordingly.« less

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.

Changes consequent to maxillary molar distalization with the bone-anchored pendulum appliance.

PubMed

Cambiano, Aldo Otazú; Janson, Guilherme; Fuziy, Acácio; Garib, Daniela Gamba; Lorenzoni, Diego Coelho

2017-01-01

This retrospective study aimed to evaluate the dentoalveolar, skeletal, and soft tissue effects obtained with bone-anchored pendulum appliance in patients with Class II malocclusion. A total of 18 patients (4 male, 14 female) at a mean pretreatment age of 14.0 years (+1.08) were enrolled in this study. All patients were treated with the bone-anchored pendulum appliance for an average duration of 4.8 months. Only the active distalization period was evaluated with predistalization and postdistalization lateral cephalograms. Skeletal, dentoalveolar, and soft tissue variables were obtained. Based on these variables, the treatment effects were evaluated with dependent t -test. Correction of Class II molar relationship resulted from distal movement of 3.45 mm and tipping of 11.24° of the first maxillary molars. The premolars were distalized accompanying the molars. The bone-anchored pendulum appliance proved to be an effective method for distalization of maxillary molars in cases that require maximum anchorage, avoiding reciprocal mesial movement of premolars and incisors.

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

Non-contact thrust stand calibration method for repetitively pulsed electric thrusters.

PubMed

Wong, Andrea R; Toftul, Alexandra; Polzin, Kurt A; Pearson, J Boise

2012-02-01

A thrust stand calibration technique for use in testing repetitively pulsed electric thrusters for in-space propulsion has been developed and tested using a modified hanging pendulum thrust stand. In the implementation of this technique, current pulses are applied to a solenoid to produce a pulsed magnetic field that acts against a permanent magnet mounted to the thrust stand pendulum arm. The force on the magnet is applied in this non-contact manner, with the entire pulsed force transferred to the pendulum arm through a piezoelectric force transducer to provide a time-accurate force measurement. Modeling of the pendulum arm dynamics reveals that after an initial transient in thrust stand motion the quasi-steady average deflection of the thrust stand arm away from the unforced or "zero" position can be related to the average applied force through a simple linear Hooke's law relationship. Modeling demonstrates that this technique is universally applicable except when the pulsing period is increased to the point where it approaches the period of natural thrust stand motion. Calibration data were obtained using a modified hanging pendulum thrust stand previously used for steady-state thrust measurements. Data were obtained for varying impulse bit at constant pulse frequency and for varying pulse frequency. The two data sets exhibit excellent quantitative agreement with each other. The overall error on the linear regression fit used to determine the calibration coefficient was roughly 1%.

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.

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.

Mechanical monolithic compact sensors for real-time linear and angular broadband low frequency monitoring and control of spacecrafts and satellites

NASA Astrophysics Data System (ADS)

Barone, F.; Giordano, G.

2017-09-01

In this paper we describe the characteristics and performances of a monolithic sensor designed for low frequency motion measurement of spacecrafts and satellites, whose mechanics is based on the UNISA Folded Pendulum. The latter, developed for ground-based applications, exhibits unique features (compactness, lightness, scalability, low resonance frequency and high quality factor), consequence of the action of the gravitational force on its inertial mass. In this paper we introduce and discuss the general methodology used to extend the application of ground-based folded pendulums to space, also in total absence of gravity, still keeping all their peculiar features and characteristics.

Changes consequent to maxillary molar distalization with the bone-anchored pendulum appliance

PubMed Central

Cambiano, Aldo Otazú; Janson, Guilherme; Fuziy, Acácio; Garib, Daniela Gamba; Lorenzoni, Diego Coelho

2017-01-01

OBJECTIVES: This retrospective study aimed to evaluate the dentoalveolar, skeletal, and soft tissue effects obtained with bone-anchored pendulum appliance in patients with Class II malocclusion. MATERIALS AND METHODS: A total of 18 patients (4 male, 14 female) at a mean pretreatment age of 14.0 years (+1.08) were enrolled in this study. All patients were treated with the bone-anchored pendulum appliance for an average duration of 4.8 months. Only the active distalization period was evaluated with predistalization and postdistalization lateral cephalograms. Skeletal, dentoalveolar, and soft tissue variables were obtained. Based on these variables, the treatment effects were evaluated with dependent t-test. RESULTS: Correction of Class II molar relationship resulted from distal movement of 3.45 mm and tipping of 11.24° of the first maxillary molars. The premolars were distalized accompanying the molars. CONCLUSIONS: The bone-anchored pendulum appliance proved to be an effective method for distalization of maxillary molars in cases that require maximum anchorage, avoiding reciprocal mesial movement of premolars and incisors. PMID:29119095

The sympathy of two pendulum clocks: beyond Huygens’ observations

PubMed Central

Peña Ramirez, Jonatan; Olvera, Luis Alberto; Nijmeijer, Henk; Alvarez, Joaquin

2016-01-01

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. PMID:27020903

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.

A low-frequency vibration insensitive pendulum bench based on translation-tilt compensation in measuring the performances of inertial sensors

NASA Astrophysics Data System (ADS)

Liu, L.; Ye, X.; Wu, S. C.; Bai, Y. Z.; Zhou, Z. B.

2015-10-01

The performance test of precision space inertial sensors on the ground is inevitably affected by seismic noise. A traditional vibration isolation platform, generally with a resonance frequency of several Hz, cannot satisfy the requirements for testing an inertial sensor at low frequencies. In this paper, we present a pendulum bench for inertial sensor testing based on translation-tilt compensation. A theoretical analysis indicates that the seismic noise effect on inertial sensors located on this bench can be attenuated by more than 40 dB below 0.1 Hz, which is very significant for investigating the performance of high-precision inertial sensors. We demonstrate this attenuation with a dedicated experiment.

Resonance frequency broadening of wave-particle interaction in tokamaks due to Alfvénic eigenmode

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

Meng, Guo; Gorelenkov, Nikolai N.; Duarte, Vinicius N.

We use the guiding center code ORBIT to study the broadening of resonances and the parametric dependence of the resonance frequency broadening widthmore » $$\\Delta\\Omega$$ on the nonlinear particle trapping frequency $$\\omega_b$$ of wave-particle interaction with specific examples using realistic equilibrium DIII-D shot 159243 (Collins et al. 2016 Phys. Rev. Lett. 116 095001). When the mode amplitude is small, the pendulum approximation for energetic particle dynamics near the resonance is found to be applicable and the ratio of the resonance frequency width to the deeply trapped bounce frequency $$\\Delta\\Omega/\\omega_b$$ equals 4, as predicted by theory. Lastly, it is found that as the mode amplitude increases, the coefficient $$a=\\Delta\\Omega/\\omega_b$$ becomes increasingly smaller because of the breaking down of the nonlinear pendulum approximation for the wave-particle interaction.« less

Resonance frequency broadening of wave-particle interaction in tokamaks due to Alfvénic eigenmode

DOE PAGES

Meng, Guo; Gorelenkov, Nikolai N.; Duarte, Vinicius N.; ...

2018-01-19

We use the guiding center code ORBIT to study the broadening of resonances and the parametric dependence of the resonance frequency broadening widthmore » $$\\Delta\\Omega$$ on the nonlinear particle trapping frequency $$\\omega_b$$ of wave-particle interaction with specific examples using realistic equilibrium DIII-D shot 159243 (Collins et al. 2016 Phys. Rev. Lett. 116 095001). When the mode amplitude is small, the pendulum approximation for energetic particle dynamics near the resonance is found to be applicable and the ratio of the resonance frequency width to the deeply trapped bounce frequency $$\\Delta\\Omega/\\omega_b$$ equals 4, as predicted by theory. Lastly, it is found that as the mode amplitude increases, the coefficient $$a=\\Delta\\Omega/\\omega_b$$ becomes increasingly smaller because of the breaking down of the nonlinear pendulum approximation for the wave-particle interaction.« less

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.

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.

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.

Noise Performance of a 72 m Suspended FABRY-PÉROT Cavity

NASA Astrophysics Data System (ADS)

Dumas, Jean-Charles; Ju, Li; Barriga, Pablo; Zhao, Chunnong; Woolley, Andrew A.; Blair, David G.

We report on a seismic isolator with a relatively compact 3 m stack, combining new passive isolation techniques. It consists of three cascaded passive 3D isolator stages suspended from an Ultra Low Frequency (ULF) horizontal Robert linkage stage which itself is suspended from a ULF 3D pre-isolator. The 3D isolators use self-damping pendulums and Euler springs for the horizontal and vertical stages respectively, while the 3D pre-isolator is the combination of an inverse pendulum which provides low frequency horizontal pre-isolation, and a LaCoste linkage for low frequency vertical pre-isolation. Two isolators suspending mirror test masses have been built to form a 72 m optical cavity in order to test their performance. We report results which demonstrate residual motion at nanometer level at frequencies above 1 Hz.

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.

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.

Human balancing of an inverted pendulum: is sway size controlled by ankle impedance?

PubMed Central

Loram, Ian D; Kelly, Sue M; Lakie, Martin

2001-01-01

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. Two main questions were addressed. Can subjects systematically change sway size in response to instruction and availability of visual feedback? If so, do subjects decrease sway size by increasing ankle impedance or by some alternative mechanism? The position of the pendulum, the torque generated at each ankle and the soleus and tibialis anterior EMG were recorded. Results showed that subjects could significantly reduce the mean sway size of the pendulum by giving full attention to that goal. With visual feedback sway size could be minimised significantly more than without visual feedback. In changing sway size, the frequency of the sways was not changed. Results also revealed that ankle impedance and muscle co-contraction were not significantly changed when the sway size was decreased. As the ankle impedance and sway frequency do not change when the sway size is decreased, this implies no change in ankle stiffness or viscosity. Increasing ankle impedance, stiffness or viscosity are not the only methods by which sway size could be reduced. A reduction in torque noise or torque inaccuracy via a predictive process which provides active damping could reduce sway size without changing ankle impedance and is plausible given the data. Such a strategy involving motion recognition and generation of an accurate motor response may require higher levels of control than changing ankle impedance by altering reflex or feedforward gain. PMID:11313453

Non-Contact Thrust Stand Calibration Method for Repetitively-Pulsed Electric Thrusters

NASA Technical Reports Server (NTRS)

Wong, Andrea R.; Toftul, Alexandra; Polzin, Kurt A.; Pearson, J. Boise

2011-01-01

A thrust stand calibration technique for use in testing repetitively-pulsed electric thrusters for in-space propulsion has been developed and tested using a modified hanging pendulum thrust stand. In the implementation of this technique, current pulses are applied to a solenoidal coil to produce a pulsed magnetic field that acts against the magnetic field produced by a permanent magnet mounted to the thrust stand pendulum arm. The force on the magnet is applied in this non-contact manner, with the entire pulsed force transferred to the pendulum arm through a piezoelectric force transducer to provide a time-accurate force measurement. Modeling of the pendulum arm dynamics reveals that after an initial transient in thrust stand motion the quasisteady average deflection of the thrust stand arm away from the unforced or zero position can be related to the average applied force through a simple linear Hooke s law relationship. Modeling demonstrates that this technique is universally applicable except when the pulsing period is increased to the point where it approaches the period of natural thrust stand motion. Calibration data were obtained using a modified hanging pendulum thrust stand previously used for steady-state thrust measurements. Data were obtained for varying impulse bit at constant pulse frequency and for varying pulse frequency. The two data sets exhibit excellent quantitative agreement with each other as the constant relating average deflection and average thrust match within the errors on the linear regression curve fit of the data. Quantitatively, the error on the calibration coefficient is roughly 1% of the coefficient value.

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.

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.

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.

Parametric vibrations of a mechanical system and their stability for an arbitrary modulation coefficient

NASA Astrophysics Data System (ADS)

Akulenko, L. D.; Nesterov, S. V.

2013-03-01

The natural frequencies and modes of parametric vibrations of a mechanical system are studied, by way of example, for a pendulum of variable length with modulation coefficient varying from arbitrarily small to maximum admissible values. Analytic and numerical methods are used to construct and study the boundaries of the resonance domains for the first four vibration modes, and the main qualitative properties of higher modes are found. The complete degeneration of modes with even numbers, i.e., the coincidence of the frequencies of symmetric and nonsymmetric naturalmodes for admissible values of the modulation parameter, is proved. The global picture of boundaries of stability domains for the lower equilibriumis constructed, and a significant difference from the Ince-Strutt diagram is shown. Specific properties of the natural modes are established.

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.

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.

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.

Spherical Pendulum Small Oscillations for Slewing Crane Motion

PubMed Central

Perig, Alexander V.; Stadnik, Alexander N.; Deriglazov, Alexander I.

2014-01-01

The present paper focuses on the Lagrange mechanics-based description of small oscillations of a spherical pendulum with a uniformly rotating suspension center. The analytical solution of the natural frequencies' problem has been derived for the case of uniform rotation of a crane boom. The payload paths have been found in the inertial reference frame fixed on earth and in the noninertial reference frame, which is connected with the rotating crane boom. The numerical amplitude-frequency characteristics of the relative payload motion have been found. The mechanical interpretation of the terms in Lagrange equations has been outlined. The analytical expression and numerical estimation for cable tension force have been proposed. The numerical computational results, which correlate very accurately with the experimental observations, have been shown. PMID:24526891

Magnetically driven oscillator and resonance: a teaching tool

NASA Astrophysics Data System (ADS)

Erol, M.; Çolak, İ. Ö.

2018-05-01

This paper reports a simple magnetically driven oscillator, designed and resolved in order to achieve a better student understanding and to overcome certain instructional difficulties. The apparatus is mainly comprised of an ordinary spring pendulum with a neodymium magnet attached to the bottom, a coil placed in the same vertical direction, an ordinary function generator, an oscilloscope and a smartphone. Driven oscillation and resonance is basically managed by applying a sinusoidal voltage to the coil and tuning the driving frequency to the natural frequency of the pendulum. The resultant oscillation is recorded by a smartphone video application and analyzed via a video analysis programme. The designed apparatus can easily be employed in basic physics laboratories to achieve an enhanced and deeper understanding of driven oscillation and resonance.

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.

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.

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.

A high-sensitivity torsional pendulum for polymeric films and fibres

NASA Technical Reports Server (NTRS)

Aghili-Kermani, H.; Obrien, T.; Armeniades, C. D.; Roberts, J. M.

1976-01-01

A free oscillation torsion pendulum is described, which has been designed to measure accurately the dynamic shear modulus and logarithmic decrement of polymeric thin films and fibers, at frequencies of 0.1 to 10 Hz and a temperature range of 4.2 to 450 K. The instrument can also provide in situ tensile deformations of up to 5%. The specimen geometry necessary to obtain reliable modulus measurements with thin films is discussed, and typical data are presented which exhibit hitherto unreported relaxation processes, discernible by this instrument.

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

Measuring Low Frequency Tilts

PubMed Central

Kohl, M. L.; Levine, J.

1993-01-01

A borehole tiltmeter with a sensitivity of a few nanoradians is described. It is composed of two orthogonal horizontal pendulums with free periods of 1 s. The pendulums are insensitive to barometric pressure fluctuations, and the measured temperature coefficient is less than 30 nrad/°C. The range of the pendulums is about ±5 μ rad, and their response is linear within 1% and stable over several years. The performance of the tiltmeter in the field was evaluated using tidal data obtained from a closely spaced array of boreholes in Southern California. The long-term stability of the tiltmeter is generally better than 1 μ rad/yr. The data also indicate that instruments in boreholes at least 24 m deepare independent of surface effects. Several different capsules designed to couple the instrument to the surrounding material have been tested. In addition, an experimental method for estimating the magnitudes of local perturbation in the regional tilt field is described. PMID:28053466

Molecular and agronomic analysis of intraspecific variability in Capsicum baccatum var. pendulum accessions.

PubMed

Leite, P S S; Rodrigues, R; Silva, R N O; Pimenta, S; Medeiros, A M; Bento, C S; Gonçalves, L S A

2016-10-05

Capsicum baccatum is one of the most important chili peppers in South America, since this region is considered to be the center of origin and diversity of this species. In Brazil, C. baccatum has been widely explored by family farmers and there are different local names for each fruit phenotype, such as cambuci and dedo-de-moça (lady's finger). Although very popular among farmers and consumers, C. baccatum has been less extensively studied than other Capsicum species. This study describes the phenotypic and genotypic variability in C. baccatum var. pendulum accessions. Twenty-nine accessions from the Universidade Estadual do Norte Fluminense Darcy Ribeiro gene bank, and one commercial genotype ('BRS-Mari') were evaluated for 53 morphoagronomic descriptors (31 qualitative and 22 quantitative traits). In addition, accessions were genotyped using 30 microsatellite primers. Three accessions from the C. annuum complex were included in the molecular characterization. Nine of 31 qualitative descriptors were monomorphic, while all quantitative descriptors were highly significant different between accessions (P < 0.01). Using the unweighted pair group method using arithmetic averages, four groups were obtained based on multicategoric variables and five groups were obtained based on quantitative variables. In the genotyping analysis, 12 polymorphic simple sequence repeat primers amplified in C. baccatum with dissimilarity between accessions ranging from 0.13 to 0.91, permitting the formation of two distinct groups for Bayesian analysis. These results indicate wide variability among the accessions comparing phenotypic and genotypic data and revealed distinct patterns of dissimilarity between matrices, indicating that both steps are valuable for the characterization of C. baccatum var. pendulum accessions.

Variability among Capsicum baccatum accessions from Goiás, Brazil, assessed by morphological traits and molecular markers.

PubMed

Martinez, A L A; Araújo, J S P; Ragassi, C F; Buso, G S C; Reifschneider, F J B

2017-07-06

Capsicum peppers are native to the Americas, with Brazil being a significant diversity center. Capsicum baccatum accessions at Instituto Federal (IF) Goiano represent a portion of the species genetic resources from central Brazil. We aimed to characterize a C. baccatum working collection comprising 27 accessions and 3 commercial cultivars using morphological traits and molecular markers to describe its genetic and morphological variability and verify the occurrence of duplicates. This set included 1 C. baccatum var. praetermissum and 29 C. baccatum var. pendulum with potential for use in breeding programs. Twenty-two morphological descriptors, 57 inter-simple sequence repeat, and 34 random amplified polymorphic DNA markers were used. Genetic distance was calculated through the Jaccard similarity index and genetic variability through cluster analysis using the unweighted pair group method with arithmetic mean, resulting in dendrograms for both morphological analysis and molecular analysis. Genetic variability was found among C. baccatum var. pendulum accessions, and the distinction between the two C. baccatum varieties was evident in both the morphological and molecular analyses. The 29 C. baccatum var. pendulum genotypes clustered in four groups according to fruit type in the morphological analysis. They formed seven groups in the molecular analysis, without a clear correspondence with morphology. No duplicates were found. The results describe the genetic and morphological variability, provide a detailed characterization of genotypes, and discard the possibility of duplicates within the IF Goiano C. baccatum L. collection. This study will foment the use of this germplasm collection in C. baccatum breeding programs.

Flight-Time Identification of a UH-60A Helicopter and Slung Load

NASA Technical Reports Server (NTRS)

Cicolani, Luigi S.; McCoy, Allen H.; Tischler, Mark B.; Tucker, George E.; Gatenio, Pinhas; Marmar, Dani

1998-01-01

This paper describes a flight test demonstration of a system for identification of the stability and handling qualities parameters of a helicopter-slung load configuration simultaneously with flight testing, and the results obtained.Tests were conducted with a UH-60A Black Hawk at speeds from hover to 80 kts. The principal test load was an instrumented 8 x 6 x 6 ft cargo container. The identification used frequency domain analysis in the frequency range to 2 Hz, and focussed on the longitudinal and lateral control axes since these are the axes most affected by the load pendulum modes in the frequency range of interest for handling qualities. Results were computed for stability margins, handling qualities parameters and load pendulum stability. The computations took an average of 4 minutes before clearing the aircraft to the next test point. Important reductions in handling qualities were computed in some cases, depending, on control axis and load-slung combination. A database, including load dynamics measurements, was accumulated for subsequent simulation development and validation.

A micro-machined gyroscope for rotating aircraft.

PubMed

Yan, Qingwen; Zhang, Fuxue; Zhang, Wei

2012-01-01

In this paper we present recent work on the design, fabrication by silicon micromachining, and packaging of a new gyroscope for stabilizing the autopilot of rotating aircraft. It operates based on oscillation of the silicon pendulum between two torsion girders for detecting the Coriolis force. The oscillation of the pendulum is initiated by the rolling and deflecting motion of the rotating carrier. Therefore, the frequency and amplitude of the oscillation are proportional to the rolling frequency and deflecting angular rate of the rotating carrier, and are measured by the sensing electrodes. A modulated pulse with constant amplitude and unequal width is obtained by a linearizing process of the gyroscope output signal and used to control the deflection of the rotating aircraft. Experimental results show that the gyroscope has a resolution of 0.008 °/s and a bias of 56.18 °/h.

Trapping of a microsphere pendulum resonator in an optical potential

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

Ward, J. M.; Photonics Centre, Tyndall National Institute, Prospect Row, Cork; Wu, Y.

We propose a method to spatially confine or corral the movements of a micropendulum via the optical forces produced by two simultaneously excited optical modes of a photonic molecule comprising two microspherical cavities. We discuss how the cavity-enhanced optical force generated in the photonic molecule can create an optomechanical potential of about 10 eV deep and 30 pm wide, which can be used to trap the pendulum at any given equilibrium position by a simple choice of laser frequencies. This result presents opportunities for very precise all-optical self-alignment of microsystems.

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.

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.

Frequency modulation indicator, Arnold’s web and diffusion in the Stark Quadratic-Zeeman problem

NASA Astrophysics Data System (ADS)

Cordani, Bruno

2008-11-01

We notice that the fundamental frequencies of a slightly perturbed integrable Hamiltonian system are not time-constant inside a resonance but frequency modulated, as is evident from pendulum models and wavelet analysis. Exploiting an intrinsic imprecision inherent to the numerical frequency analysis algorithm itself, hence transforming a drawback into an opportunity, we define the Frequency Modulation Indicator, a very sensitive tool in detecting where fundamental frequencies are modulated, localizing so the resonances without having to resort, as in other methods, to the integration of variational equations. For the Kepler problem, the space of the orbits with a fixed energy has the topology of the product of two 2-spheres. The perturbation Hamiltonian, averaged over the mean anomaly, has surely a maximum and a minimum, to which correspond two periodic orbits in physical space. Studying the neighbourhood of these two elliptic stable points, we are able to define adapted action-angle variables, for example, the usual but “SO(4)-rotated” Delaunay variables. The procedure, implemented in the program KEPLER, is performed transparently for the user, providing a general scheme suited for generic perturbation. The method is then applied to the Stark-Quadratic-Zeeman problem, displaying very clearly the Arnold web of the resonances. Sectioning transversely one of the resonance strips so highlighted and performing a numerical frequency analysis, one is able to locate with great precision the thin stochastic layer surrounding a separatrix. Another very long (10 8 revolutions) frequency analysis on an orbit starting here reveals, as expected, a well defined pattern, which ensures that the integration errors do not eject the point out of the layer, and moreover a very slow drift in the frequency values, clearly due to Arnold diffusion.

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.

Motion estimation using point cluster method and Kalman filter.

PubMed

Senesh, M; Wolf, A

2009-05-01

The most frequently used method in a three dimensional human gait analysis involves placing markers on the skin of the analyzed segment. This introduces a significant artifact, which strongly influences the bone position and orientation and joint kinematic estimates. In this study, we tested and evaluated the effect of adding a Kalman filter procedure to the previously reported point cluster technique (PCT) in the estimation of a rigid body motion. We demonstrated the procedures by motion analysis of a compound planar pendulum from indirect opto-electronic measurements of markers attached to an elastic appendage that is restrained to slide along the rigid body long axis. The elastic frequency is close to the pendulum frequency, as in the biomechanical problem, where the soft tissue frequency content is similar to the actual movement of the bones. Comparison of the real pendulum angle to that obtained by several estimation procedures--PCT, Kalman filter followed by PCT, and low pass filter followed by PCT--enables evaluation of the accuracy of the procedures. When comparing the maximal amplitude, no effect was noted by adding the Kalman filter; however, a closer look at the signal revealed that the estimated angle based only on the PCT method was very noisy with fluctuation, while the estimated angle based on the Kalman filter followed by the PCT was a smooth signal. It was also noted that the instantaneous frequencies obtained from the estimated angle based on the PCT method is more dispersed than those obtained from the estimated angle based on Kalman filter followed by the PCT method. Addition of a Kalman filter to the PCT method in the estimation procedure of rigid body motion results in a smoother signal that better represents the real motion, with less signal distortion than when using a digital low pass filter. Furthermore, it can be concluded that adding a Kalman filter to the PCT procedure substantially reduces the dispersion of the maximal and minimal instantaneous frequencies.

Determination of the Glass-Transition Temperature of GRPS and CFRPS Using a Torsion Pendulum in Regimes of Freely Damped Vibrations and Quasi-Stastic Torsion of Specimens

NASA Astrophysics Data System (ADS)

Startsev, V. O.; Lebedev, M. P.; Molokov, M. V.

2018-03-01

A method to measure the glass-transition temperature of polymers and polymeric matrices of composite materials with the help of an inverse torsion pendulum over a wide range of temperatures is considered combining the method of free torsional vibrations and a quasi-static torsion of specimens. The glass-transition temperature Tg of a KMKS-1-80. T10 fiberglass, on increasing the frequency of freely damped torsional vibrations from 0.7 to 9.6 Hz, was found to increase from 132 to 140°C. The value of Tg of these specimens, determined by measuring the work of their torsion through a small fixed angle was 128.6°C ± 0.8°C. It is shown that the use of a torsion pendulum allows one to determine the glass-transition temperature of polymeric or polymer matrices of PCMs in dynamic and quasi-static deformation regimes of specimens.

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.

A double-inverted pendulum model for studying the adaptability of postural control to frequency during human stepping in place.

PubMed

Breniere, Y; Ribreau, C

1998-10-01

In order to analyze the influence of gravity and body characteristics on the control of center of mass (CM) oscillations in stepping in place, equations of motion in oscillating systems were developed using a double-inverted pendulum model which accounts for both the head-arms-trunk (HAT) segment and the two-legged system. The principal goal of this work is to propose an equivalent model which makes use of the usual anthropometric data for the human body, in order to study the ability of postural control to adapt to the step frequency in this particular paradigm of human gait. This model allows the computation of CM-to-CP amplitude ratios, when the center of foot pressure (CP) oscillates, as a parametric function of the stepping in place frequency, whose parameters are gravity and major body characteristics. Motion analysis from a force plate was used to test the model by comparing experimental and simulated values of variations of the CM-to-CP amplitude ratio in the frontal plane versus the frequency. With data from the literature, the model is used to calculate the intersegmental torque which stabilizes the HAT when the Leg segment is subjected to a harmonic torque with an imposed frequency.

Sinusoidal visuomotor tracking: intermittent servo-control or coupled oscillations?

PubMed

Russell, D M; Sternad, D

2001-12-01

In visuomotor tasks that involve accuracy demands, small directional changes in the trajectories have been taken as evidence of feedback-based error corrections. In the present study variability, or intermittency, in visuomanual tracking of sinusoidal targets was investigated. Two lines of analyses were pursued: First, the hypothesis that humans fundamentally act as intermittent servo-controllers was re-examined, probing the question of whether discontinuities in the movement trajectory directly imply intermittent control. Second, an alternative hypothesis was evaluated: that rhythmic tracking movements are generated by entrainment between the oscillations of the target and the actor, such that intermittency expresses the degree of stability. In 2 experiments, participants (N = 6 in each experiment) swung 1 of 2 different hand-held pendulums, tracking a rhythmic target that oscillated at different frequencies with a constant amplitude. In 1 line of analyses, the authors tested the intermittency hypothesis by using the typical kinematic error measures and spectral analysis. In a 2nd line, they examined relative phase and its variability, following analyses of rhythmic interlimb coordination. The results showed that visually guided corrective processes play a role, especially for slow movements. Intermittency, assessed as frequency and power components of the movement trajectory, was found to change as a function of both target frequency and the manipulandum's inertia. Support for entrainment was found in conditions in which task frequency was identical to or higher than the effector's eigenfrequency. The results suggest that it is the symmetry between task and effector that determines which behavioral regime is dominant.

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.

Nonlinear normal vibration modes in the dynamics of nonlinear elastic systems

NASA Astrophysics Data System (ADS)

Mikhlin, Yu V.; Perepelkin, N. V.; Klimenko, A. A.; Harutyunyan, E.

2012-08-01

Nonlinear normal modes (NNMs) are a generalization of the linear normal vibrations. By the Kauderer-Rosenberg concept in the regime of the NNM all position coordinates are single-values functions of some selected position coordinate. By the Shaw-Pierre concept, the NNM is such a regime when all generalized coordinates and velocities are univalent functions of a couple of dominant (active) phase variables. The NNMs approach is used in some applied problems. In particular, the Kauderer-Rosenberg NNMs are analyzed in the dynamics of some pendulum systems. The NNMs of forced vibrations are investigated in a rotor system with an isotropic-elastic shaft. A combination of the Shaw-Pierre NNMs and the Rauscher method is used to construct the forced NNMs and the frequency responses in the rotor dynamics.

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.

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.

LISA technology development using the UF precision torsion pendulum

NASA Astrophysics Data System (ADS)

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

2015-04-01

LISA will directly observe low-frequency gravitational waves emitted by sources ranging from super-massive black hole mergers to compact galactic binaries. A laser interferometer will measure picometer changes in the distances between free falling test masses separated by millions of kilometers. A test mass and its associated sensing, actuation, charge control and caging subsystems are referred to as a gravitational reference sensor (GRS). The demanding acceleration noise requirement for the LISA GRS has motivated a rigorous testing campaign in Europe and a dedicated technology mission, LISA Pathfinder, scheduled for launch in the fall of 2015. At the University of Florida we are developing a nearly thermally noise limited torsion pendulum for testing GRS technology enhancements that may improve the performance and/or reduce the cost of the LISA GRS. This experimental facility is based on the design of a similar facility at the University of Trento, and consists of a vacuum enclosed torsion pendulum that suspends mock-ups of the LISA test masses, surrounded by electrode housings. Some of the technologies that will be demonstrated by this facility include a novel TM charge control scheme based on ultraviolet LEDs, an all-optical TM position and attitude sensor, and drift mode operation. This presentation will describe the design of the torsion pendulum facility, its current acceleration noise performance, and the status of the GRS technologies under development.

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.

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.

Mechanical monolithic horizontal sensor for low frequency seismic noise measurement

NASA Astrophysics Data System (ADS)

Acernese, Fausto; Giordano, Gerardo; Romano, Rocco; De Rosa, Rosario; Barone, Fabrizio

2008-07-01

This paper describes a mechanical monolithic horizontal sensor for geophysical applications developed at the University of Salerno. The instrument is basically a monolithic tunable folded pendulum, shaped with precision machining and electric discharge machining, that can be used both as seismometer and, in a force-feedback configuration, as accelerometer. The monolithic mechanical design and the introduction of laser interferometric techniques for the readout implementation makes it a very compact instrument, very sensitive in the low frequency seismic noise band, with a very good immunity to environmental noises. Many changes have been produced since last version (2007), mainly aimed to the improvement of the mechanics and of the optical readout of the instrument. In fact, we have developed and tested a prototype with elliptical hinges and mechanical tuning of the resonance frequency together with a laser optical lever and a new laser interferometer readout system. The theoretical sensitivity curve for both laser optical lever and laser interferometric readouts, evaluated on the basis of suitable theoretical models, shows a very good agreement with the experimental measurements. Very interesting scientific result is the measured natural resonance frequency of the instrument of 70mHz with a Q =140 in air without thermal stabilization. This result demonstrates the feasibility of a monolithic folded pendulum sensor with a natural resonance frequency of the order of millihertz with a more refined mechanical tuning.

Mechanical monolithic horizontal sensor for low frequency seismic noise measurement.

PubMed

Acernese, Fausto; Giordano, Gerardo; Romano, Rocco; De Rosa, Rosario; Barone, Fabrizio

2008-07-01

This paper describes a mechanical monolithic horizontal sensor for geophysical applications developed at the University of Salerno. The instrument is basically a monolithic tunable folded pendulum, shaped with precision machining and electric discharge machining, that can be used both as seismometer and, in a force-feedback configuration, as accelerometer. The monolithic mechanical design and the introduction of laser interferometric techniques for the readout implementation makes it a very compact instrument, very sensitive in the low frequency seismic noise band, with a very good immunity to environmental noises. Many changes have been produced since last version (2007), mainly aimed to the improvement of the mechanics and of the optical readout of the instrument. In fact, we have developed and tested a prototype with elliptical hinges and mechanical tuning of the resonance frequency together with a laser optical lever and a new laser interferometer readout system. The theoretical sensitivity curve for both laser optical lever and laser interferometric readouts, evaluated on the basis of suitable theoretical models, shows a very good agreement with the experimental measurements. Very interesting scientific result is the measured natural resonance frequency of the instrument of 70 mHz with a Q=140 in air without thermal stabilization. This result demonstrates the feasibility of a monolithic folded pendulum sensor with a natural resonance frequency of the order of millihertz with a more refined mechanical tuning.

Towards thermal noise free optomechanics

NASA Astrophysics Data System (ADS)

Page, Michael A.; Zhao, Chunnong; Blair, David G.; Ju, Li; Ma, Yiqiu; Pan, Huang-Wei; Chao, Shiuh; Mitrofanov, Valery P.; Sadeghian, Hamed

2016-11-01

Thermal noise generally greatly exceeds quantum noise in optomechanical devices unless the mechanical frequency is very high or the thermodynamic temperature is very low. This paper addresses the design concept for a novel optomechanical device capable of ultrahigh quality factors in the audio frequency band with negligible thermal noise. The proposed system consists of a minimally supported millimeter scale pendulum mounted in a double end-mirror sloshing cavity that is topologically equivalent to a membrane-in-the-middle cavity. The radiation pressure inside the high-finesse cavity allows for high optical stiffness, cancellation of terms which lead to unwanted negative damping and suppression of quantum radiation pressure noise. We solve the optical spring dynamics of the system using the Hamiltonian, find the noise spectral density and show that stable optical trapping is possible. We also assess various loss mechanisms, one of the most important being the acceleration loss due to the optical spring. We show that practical devices, starting from a centre-of-mass pendulum frequency of 0.1 Hz, could achieve a maximum quality factor of (1014) with optical spring stiffened frequency 1-10 kHz. Small resonators of mass 1 ≤ft(μ \\right) g or less could achieve a Q-factor of (1011) at a frequency of 100 kHz. Applications for such devices include white light cavities for improvement of gravitational wave detectors, or sensors able to operate near the quantum limit.

A simple pendulum borehole tiltmeter based on a triaxial optical-fibre displacement sensor

NASA Astrophysics Data System (ADS)

Chawah, P.; Chéry, J.; Boudin, F.; Cattoen, M.; Seat, H. C.; Plantier, G.; Lizion, F.; Sourice, A.; Bernard, P.; Brunet, C.; Boyer, D.; Gaffet, S.

2015-11-01

Sensitive instruments like strainmeters and tiltmeters are necessary for measuring slowly varying low amplitude Earth deformations. Nonetheless, laser and fibre interferometers are particularly suitable for interrogating such instruments due to their extreme precision and accuracy. In this paper, a practical design of a simple pendulum borehole tiltmeter based on laser fibre interferometric displacement sensors is presented. A prototype instrument has been constructed using welded borosilicate with a pendulum length of 0.85 m resulting in a main resonance frequency of 0.6 Hz. By implementing three coplanar extrinsic fibre Fabry-Perot interferometric probes and appropriate signal filtering, our instrument provides tilt measurements that are insensitive to parasitic deformations caused by temperature and pressure variations. This prototype has been installed in an underground facility (Rustrel, France) where results show accurate measurements of Earth strains derived from Earth and ocean tides, local hydrologic effects, as well as local and remote earthquakes. The large dynamic range and the high sensitivity of this tiltmeter render it an invaluable tool for numerous geophysical applications such as transient fault motion, volcanic strain and reservoir monitoring.

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

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.

Peak effect in untwinned YBa 2Cu 3O 7-δ single crystals

NASA Astrophysics Data System (ADS)

D'Anna, G.; André, M.-O.; Indenbom, M. V.; Benoit, W.

1994-12-01

We report on the observation of a weak effect of the critical current density in untwinned YBa 2Cu 3O 7-δ single crystals of different purity, using a low frequency torsion pendulum. We construct the peak effect line and the irreversibility line.

The time-delayed inverted pendulum: Implications for human balance control

NASA Astrophysics Data System (ADS)

Milton, John; Cabrera, Juan Luis; Ohira, Toru; Tajima, Shigeru; Tonosaki, Yukinori; Eurich, Christian W.; Campbell, Sue Ann

2009-06-01

The inverted pendulum is frequently used as a starting point for discussions of how human balance is maintained during standing and locomotion. Here we examine three experimental paradigms of time-delayed balance control: (1) mechanical inverted time-delayed pendulum, (2) stick balancing at the fingertip, and (3) human postural sway during quiet standing. Measurements of the transfer function (mechanical stick balancing) and the two-point correlation function (Hurst exponent) for the movements of the fingertip (real stick balancing) and the fluctuations in the center of pressure (postural sway) demonstrate that the upright fixed point is unstable in all three paradigms. These observations imply that the balanced state represents a more complex and bounded time-dependent state than a fixed-point attractor. Although mathematical models indicate that a sufficient condition for instability is for the time delay to make a corrective movement, τn, be greater than a critical delay τc that is proportional to the length of the pendulum, this condition is satisfied only in the case of human stick balancing at the fingertip. Thus it is suggested that a common cause of instability in all three paradigms stems from the difficulty of controlling both the angle of the inverted pendulum and the position of the controller simultaneously using time-delayed feedback. Considerations of the problematic nature of control in the presence of delay and random perturbations ("noise") suggest that neural control for the upright position likely resembles an adaptive-type controller in which the displacement angle is allowed to drift for small displacements with active corrections made only when θ exceeds a threshold. This mechanism draws attention to an overlooked type of passive control that arises from the interplay between retarded variables and noise.

Gravity field error analysis for pendulum formations by a semi-analytical approach

NASA Astrophysics Data System (ADS)

Li, Huishu; Reubelt, Tilo; Antoni, Markus; Sneeuw, Nico

2017-03-01

Many geoscience disciplines push for ever higher requirements on accuracy, homogeneity and time- and space-resolution of the Earth's gravity field. Apart from better instruments or new observables, alternative satellite formations could improve the signal and error structure compared to Grace. One possibility to increase the sensitivity and isotropy by adding cross-track information is a pair of satellites flying in a pendulum formation. This formation contains two satellites which have different ascending nodes and arguments of latitude, but have the same orbital height and inclination. In this study, the semi-analytical approach for efficient pre-mission error assessment is presented, and the transfer coefficients of range, range-rate and range-acceleration gravitational perturbations are derived analytically for the pendulum formation considering a set of opening angles. The new challenge is the time variations of the opening angle and the range, leading to temporally variable transfer coefficients. This is solved by Fourier expansion of the sine/cosine of the opening angle and the central angle. The transfer coefficients are further applied to assess the error patterns which are caused by different orbital parameters. The simulation results indicate that a significant improvement in accuracy and isotropy is obtained for small and medium initial opening angles of single polar pendulums, compared to Grace. The optimal initial opening angles are 45° and 15° for accuracy and isotropy, respectively. For a Bender configuration, which is constituted by a polar Grace and an inclined pendulum in this paper, the behaviour of results is dependent on the inclination (prograde vs. retrograde) and on the relative baseline orientation (left or right leading). The simulation for a sun-synchronous orbit shows better results for the left leading case.

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.

Seismometer using a vertical long natural-period rotational pendulum with magnetic levitation

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

Otake, Yuji; Araya, Akito; Hidano, Kazuo

We have demonstrated a highly sensitive/wideband vertical-component seismometer using an astatic rotational pendulum to obtain a long natural period. This seismometer employs magnetic levitation for removing any parasitic resonances of a spring to support a weight due to gravity and the thermal dependence of the spring constant. The pendulum has a cylindrical plunger-type permanent magnet that has a weight at one side of its end edge. The plunger magnet is inserted into a uniform magnetic field generated by a window-frame-type permanent magnet, and attached to two crossed-leaf spring hinges as a rotational axis outside of the bore of the magnet.more » Magnetic forces applied to the plunger magnet counterbalance the gravitational force at the weight. To realize stable operation of the rotational pendulum without any unnecessary movements of the plunger magnet, a tilt of lines of the magnetic force in the bore of the window-frame magnet was compensated by a tilted magnetic-pole surface near to its opening. The field uniformity reached 10{sup -4} owing to this compensation. The thermal dependence of a magnetic field strength of about 10{sup -3}/K was also compensated by as much as 9x10{sup -5}/K by Ni-Fe metal having a negative permeability coefficient. The metal was attached along the sidewalls of the window-frame magnet. To determine the feedback control parameters for a feedback control seismometer, the natural period of a prototype rotational pendulum was measured. It was more than 8 s, and was able to be changed from 5 to 8 s by using an additional magnetic spring, similar to the voice coil actuator of a speaker. This change was in accordance with theoretical calculations, and showed that the pendulum movement did not include a big nonlinearity caused by the tilt of the lines of the magnetic force. No parasitic resonances were found during experiments. A velocity feedback-control circuit and a capacitance position detector to measure the weight position were applied to the rotational pendulum for building a feedback control seismometer. Observations showed that the noise level of the seismometer was less than about 10{sup -8} m/s at 1 Hz. This fruitful value is close to the specifications of the most sensitive seismometer, such as STS-I. However, low-frequency noise of about 10{sup -7} m/s, caused by a buoyancy change at the pendulum weight arising from atmospheric pressure variation, could be recognized. To decrease the noise, a vacuum chamber to isolate the atmospheric pressure variation should be employed in the next step of the study.« less

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…

Acceleration Noise Measurements for LISA

NASA Astrophysics Data System (ADS)

Schlamminger, Stephan; Gundlach, Jens

2005-04-01

The close spacing between the proof mass and the housing in the LISA (Laser Interferometer Space Antenna) spacecraft has been a concern as there may be spurious feeble forces. Such forces may limit the performance of the gravity wave detector at frequencies below 3 mHz and must be studied experimentally. We are performing ultra sensitive torsion balance tests to investigate such effects. Our torsion pendulum and a nearby plate are designed to simulate the LISA proof mass with its adjacent housing surface. We study torque noise on the pendulum as a function of separation between the surfaces. In order to exceed the LISA requirement we are probing the acceleration noise at much closer separations, than those planned for LISA. We have taken data at separations as small as 0.15 mm.

Apparatus for Teaching Physics.

ERIC Educational Resources Information Center

Gottlieb, Herbert H., Ed.

1979-01-01

Describes the following: a device which converts the displacement of a pendulum into an electric signal and is used as a voltage generator of low frequencies; a turn-by-turn transformer demonstration; how to remove the buoyant force on a piece of cork immersed in water; and how to demonstrate Coulomb's Law on the overhead projector. (GA)

A method of measuring micro-impulse with torsion pendulum based on multi-beam laser heterodyne

NASA Astrophysics Data System (ADS)

Li, Yan-Chao; Wang, Chun-Hui

2012-02-01

In this paper, we propose a novel method of multi-beam laser heterodyne measurement for micro-impulse. The measurement of the micro-impulse, which is converted into the measurement of the small tuning angle of the torsion pendulum, is realized by considering the interaction between pulse laser and working medium. Based on Doppler effect and heterodyne technology, the information regarding the small tuning angle is loaded to the frequency difference of the multi-beam laser heterodyne signal by the frequency modulation of the oscillating mirror, thereby obtaining many values of the small tuning angle after the multi-beam laser heterodyne signal demodulation simultaneously. Processing these values by weighted-average, the small tuning angle can be obtained accurately and the value of the micro-impulse can eventually be calculated. Using Polyvinylchlorid+2%C as a working medium, this novel method is used to simulate the value of the micro-impulse by MATLAB which is generated by considering the interaction between the pulse laser and the working medium, the obtained result shows that the relative error of this method is just 0.5%.

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)

Nature's Autonomous Oscillators

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Yee, J.-H.; Mayr, M.; Schnetzler, R.

2012-01-01

Nonlinearity is required to produce autonomous oscillations without external time dependent source, and an example is the pendulum clock. The escapement mechanism of the clock imparts an impulse for each swing direction, which keeps the pendulum oscillating at the resonance frequency. Among nature's observed autonomous oscillators, examples are the quasi-biennial oscillation and bimonthly oscillation of the Earth atmosphere, and the 22-year solar oscillation. The oscillations have been simulated in numerical models without external time dependent source, and in Section 2 we summarize the results. Specifically, we shall discuss the nonlinearities that are involved in generating the oscillations, and the processes that produce the periodicities. In biology, insects have flight muscles, which function autonomously with wing frequencies that far exceed the animals' neural capacity; Stretch-activation of muscle contraction is the mechanism that produces the high frequency oscillation of insect flight, discussed in Section 3. The same mechanism is also invoked to explain the functioning of the cardiac muscle. In Section 4, we present a tutorial review of the cardio-vascular system, heart anatomy, and muscle cell physiology, leading up to Starling's Law of the Heart, which supports our notion that the human heart is also a nonlinear oscillator. In Section 5, we offer a broad perspective of the tenuous links between the fluid dynamical oscillators and the human heart physiology.

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.

Development of impact resistant boron/aluminum composites for turbojet engine fan blades

NASA Technical Reports Server (NTRS)

Melnyk, P.; Toth, I. J.

1975-01-01

Composite fabrication was performed by vacuum press diffusion bonding by both the foil-filament array and preconsolidated monotape methods. The effect of matrix material, fiber diameter, matrix enhancement, fiber volume reinforcement, test temperature, angle-plying, notch, impact orientation, processing variables and fabrication methods on tensile strength and Charpy impact resistance are evaluated. Root attachment concepts, were evaluated by room and elevated temperature tensile testing, as well as by pendulum-Izod and ballistic impact testing. Composite resistance to foreign object damage was also evaluated by ballistic impacting of panels using projectiles of gelatin, RTV rubber and steel at various velocities, and impingement angles. A significant improvement in the pendulum impact resistance of B-Al composites was achieved.

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.

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.

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

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.

Data-Driven Belief Revision in Children and Adults

ERIC Educational Resources Information Center

Masnick, Amy M.; Klahr, David; Knowles, Erica R.

2017-01-01

The ability to use numerical evidence to revise beliefs about the physical world is an essential component of scientific reasoning that begins to develop in middle childhood. In 2 studies, we explored how data variability and consistency with participants' initial beliefs about causal factors associated with pendulums affected their ability to…

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.

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.

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.

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

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…

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.

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

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.

A method for measuring the inertia properties of rigid bodies

NASA Astrophysics Data System (ADS)

Gobbi, M.; Mastinu, G.; Previati, G.

2011-01-01

A method for the measurement of the inertia properties of rigid bodies is presented. Given a rigid body and its mass, the method allows to measure (identify) the centre of gravity location and the inertia tensor during a single test. The proposed technique is based on the analysis of the free motion of a multi-cable pendulum to which the body under consideration is connected. The motion of the pendulum and the forces acting on the system are recorded and the inertia properties are identified by means of a proper mathematical procedure based on a least square estimation. After the body is positioned on the test rig, the full identification procedure takes less than 10 min. The natural frequencies of the pendulum and the accelerations involved are quite low, making this method suitable for many practical applications. In this paper, the proposed method is described and two test rigs are presented: the first is developed for bodies up to 3500 kg and the second for bodies up to 400 kg. A validation of the measurement method is performed with satisfactory results. The test rig holds a third part quality certificate according to an ISO 9001 standard and could be scaled up to measure the inertia properties of huge bodies, such as trucks, airplanes or even ships.

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.

Advanced Bridge Capacity and Structural Integrity Assessment Methodology

DTIC Science & Technology

2013-03-01

following major drawbacks to working stress design: • inability to account for variability of loads and resistance • lack of knowledge of the level of...CERL TR-13-3 81 Early inclinometers were simple pendulums or tubes of water with buckets on each end where the difference in water level between to

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.

A springy pendulum could describe the swing leg kinetics of human walking.

PubMed

Song, Hyunggwi; Park, Heewon; Park, Sukyung

2016-06-14

The dynamics of human walking during various walking conditions could be qualitatively captured by the springy legged dynamics, which have been used as a theoretical framework for bipedal robotics applications. However, the spring-loaded inverted pendulum model describes the motion of the center of mass (CoM), which combines the torso, swing and stance legs together and does not explicitly inform us as to whether the inter-limb dynamics share the springy legged dynamics characteristics of the CoM. In this study, we examined whether the swing leg dynamics could also be represented by springy mechanics and whether the swing leg stiffness shows a dependence on gait speed, as has been observed in CoM mechanics during walking. The swing leg was modeled as a spring-loaded pendulum hinged at the hip joint, which is under forward motion. The model parameters of the loaded mass were adopted from body parameters and anthropometric tables, whereas the free model parameters for the rest length of the spring and its stiffness were estimated to best match the data for the swing leg joint forces. The joint forces of the swing leg were well represented by the springy pendulum model at various walking speeds with a regression coefficient of R(2)>0.8. The swing leg stiffness increased with walking speed and was correlated with the swing frequency, which is consistent with previous observations from CoM dynamics described using the compliant leg. These results suggest that the swing leg also shares the springy dynamics, and the compliant walking model could be extended to better present swing leg dynamics. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

Apparatus for dynamic and static measurements of mechanical properties of solids and of flux-lattice in type-II superconductors at low frequency (10 - 5-10 Hz) and temperature (4.7-500 K)

NASA Astrophysics Data System (ADS)

D'Anna, G.; Benoit, W.

1990-12-01

A forced torsional pendulum which permits us to examine anelastic mechanical properties of solids as well as for flux-lattice in type-II superconductors, has been built to explore the low frequency and low temperature range. It works on the principle of dynamic frequency response function measurement and appears to be a powerful instrument for studying structural defect motions as well as flux line dynamics. As an additional quantity, the magnetization or the plastic strain can be statically measured by the same apparatus.

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.

Validation of Slosh Model Parameters and Anti-Slosh Baffle Designs of Propellant Tanks by Using Lateral Slosh Testing

NASA Technical Reports Server (NTRS)

Perez, Jose G.; Parks, Russel, A.; Lazor, Daniel R.

2012-01-01

The slosh dynamics of propellant tanks can be represented by an equivalent mass-pendulum-dashpot mechanical model. The parameters of this equivalent model, identified as slosh mechanical model parameters, are slosh frequency, slosh mass, and pendulum hinge point location. They can be obtained by both analysis and testing for discrete fill levels. Anti-slosh baffles are usually needed in propellant tanks to control the movement of the fluid inside the tank. Lateral slosh testing, involving both random excitation testing and free-decay testing, are performed to validate the slosh mechanical model parameters and the damping added to the fluid by the anti-slosh baffles. Traditional modal analysis procedures were used to extract the parameters from the experimental data. Test setup of sub-scale tanks will be described. A comparison between experimental results and analysis will be presented.

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.

Seismic shear waves as Foucault pendulum

NASA Astrophysics Data System (ADS)

Snieder, Roel; Sens-Schönfelder, Christoph; Ruigrok, Elmer; Shiomi, Katsuhiko

2016-03-01

Earth's rotation causes splitting of normal modes. Wave fronts and rays are, however, not affected by Earth's rotation, as we show theoretically and with observations made with USArray. We derive that the Coriolis force causes a small transverse component for P waves and a small longitudinal component for S waves. More importantly, Earth's rotation leads to a slow rotation of the transverse polarization of S waves; during the propagation of S waves the particle motion behaves just like a Foucault pendulum. The polarization plane of shear waves counteracts Earth's rotation and rotates clockwise in the Northern Hemisphere. The rotation rate is independent of the wave frequency and is purely geometric, like the Berry phase. Using the polarization of ScS and ScS2 waves, we show that the Foucault-like rotation of the S wave polarization can be observed. This can affect the determination of source mechanisms and the interpretation of observed SKS splitting.

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…

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.

Anomalous Thrust Production from an RF Test Device Measured on a Low-Thrust Torsion Pendulum

NASA Technical Reports Server (NTRS)

Brady, David; White, Harold G.; March, Paul; Lawrence, James T.; Davies, Frank J.

2014-01-01

This paper describes the eight-day August 2013 test campaign designed to investigate and demonstrate viability of using classical magnetoplasmadynamics to obtain a propulsive momentum transfer via the quantum vacuum virtual plasma. This paper will not address the physics of the quantum vacuum plasma thruster, but instead will describe the test integration, test operations, and the results obtained from the test campaign. Approximately 30-50 micro-Newtons of thrust were recorded from an electric propulsion test article consisting primarily of a radio frequency (RF) resonant cavity excited at approximately 935 megahertz. Testing was performed on a low-thrust torsion pendulum that is capable of detecting force at a single-digit micronewton level, within a stainless steel vacuum chamber with the door closed but at ambient atmospheric pressure. Several different test configurations were used, including two different test articles as well as a reversal of the test article orientation. In addition, the test article was replaced by an RF load to verify that the force was not being generated by effects not associated with the test article. The two test articles were designed by Cannae LLC of Doylestown, Pennsylvania. The torsion pendulum was designed, built, and operated by Eagleworks Laboratories at the NASA Johnson Space Center of Houston, Texas. Approximately six days of test integration were required, followed by two days of test operations, during which, technical issues were discovered and resolved. Integration of the two test articles and their supporting equipment was performed in an iterative fashion between the test bench and the vacuum chamber. In other words, the test article was tested on the bench, then moved to the chamber, then moved back as needed to resolve issues. Manual frequency control was required throughout the test. Thrust was observed on both test articles, even though one of the test articles was designed with the expectation that it would not produce thrust. Specifically, one test article contained internal physical modifications that were designed to produce thrust, while the other did not (with the latter being referred to as the "null" test article). Test data gathered includes torsion pendulum displacement measurements which are used to calculate generated force, still imagery in the visible spectrum to document the physical configuration, still imagery in the infrared spectrum to characterize the thermal environment, and video imagery. Post-test data includes static and animated graphics produced during RF resonant cavity characterization using the COMSOL Multiphysics® software application. Excerpts from all of the above are included and discussed in this paper. Lessons learned from test integration and operations include identification of the need to replace manual control of the resonant cavity target frequency with an automated frequency control capability. Future test plans include the development of an automatic frequency control circuit. Test results indicate that the RF resonant cavity thruster design, which is unique as an electric propulsion device, is producing a force that is not attributable to any classical electromagnetic phenomenon and therefore is potentially demonstrating an interaction with the quantum vacuum virtual plasma. Future test plans include independent verification and validation at other test facilities.

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.

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. 

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.

On the JWKB solution of the uniformly lengthening pendulum via change of independent variable in the Bessel's equation

NASA Astrophysics Data System (ADS)

Deniz, Coşkun

2017-01-01

Common recipe for the lengthening pendulum (LP) involves some change of variables to give a relationship with the Bessel's equation. In this work, conventional semiclassical JWKB solution (named after Jeffreys, Wentzel, Kramers and Brillouin) of the LP is being obtained by first transforming the related Bessel's equation into the normal form `via the suggested change of independent variable'. JWKB approximation of the first-order Bessel functions ( ν=1) of both types along with their zeros are being obtained analytically with a very good accuracy as a result of the appropriately chosen associated initial values and they are extended to the neighbouring orders ( ν=0 and 2) by the recursion relations. The required initial values are also being studied and a quantization rule regarding the experimental LP parameters is being determined. Although common numerical methods given in the literature require adiabatic LP systems where the lengthening rate is slow, JWKB solution presented here can safely be used for higher lengthening rates and a criterion for its validity is determined by the JWKB applicability criterion given in the literature. As a result, the semiclassical JWKB method which is normally used for the quantum mechanical and optical waveguide systems is applied to the classical LP system successfully.

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

Testing the gravitational inverse-square law at centimeter scales

NASA Astrophysics Data System (ADS)

Bonicalzi, Ricco

Many attempts to unify gravity with the Standard Model entail a gravitational inverse-square-law violation (ISLV) at some low level. This dissertation reports on the initial phase of a torsion-pendulum null experiment searching for such a violation in the interaction between two macroscopic bodies with a characteristic separation of 12 cm. Central to the experimental design is the special configuration of the mass distributions of both the pendulum and source mass to provide high-sensitivity to the horizontal gradient of the Laplacian of the interaction potential (a signature of ISLV), while strongly suppressing coupling through Newtonian gravity. Specifically, this design ensures that gravitational systematic effects arise only at second order in the fabrication errors of the pendulum and source mass. A key aspect of this work is the choice of the second-harmonic amplitude of pendulum oscillation as the torque observable, instead of the traditional oscillation frequency. This relatively recent torsion-pendulum method is markedly less sensitive to changes in torsion-fiber temperature and enables the ambient-temperature instrumentation of the initial phase to achieve necessary noise performance without heroic efforts to stabilize temperature. As details of the second-harmonic method have not yet been published, the presentation here dwells on a number of subtleties involved in analyzing the data. Experimental results are reported assuming a Yukawa-type interaction anomaly, where a is the strength of the Yukawa term relative to Newtonian gravity. A preliminary set of 34 data runs, each around a day in duration, produced a value of alpha = (-6.3 +/- 7.5) x 10-5. In the absence of significant systematic effects, even this interim result would have placed tighter bounds on ISLV than previously appearing in the literature. Unfortunately, an accelerated Department of Energy deadline for demolition of our Hanford laboratory facility compelled a shift of focus to the principal phase of this experiment before resolving two apparently marginal, but significant sources of systematic error. These and resolved systematic effects are discussed in the context of the second-harmonic method.

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.

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.

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.

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.

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.

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)

Experimental Evaluation of Balance Prediction Models for Sit-to-Stand Movement in the Sagittal Plane

PubMed Central

Pena Cabra, Oscar David; Watanabe, Takashi

2013-01-01

Evaluation of balance control ability would become important in the rehabilitation training. In this paper, in order to make clear usefulness and limitation of a traditional simple inverted pendulum model in balance prediction in sit-to-stand movements, the traditional simple model was compared to an inertia (rotational radius) variable inverted pendulum model including multiple-joint influence in the balance predictions. The predictions were tested upon experimentation with six healthy subjects. The evaluation showed that the multiple-joint influence model is more accurate in predicting balance under demanding sit-to-stand conditions. On the other hand, the evaluation also showed that the traditionally used simple inverted pendulum model is still reliable in predicting balance during sit-to-stand movement under non-demanding (normal) condition. Especially, the simple model was shown to be effective for sit-to-stand movements with low center of mass velocity at the seat-off. Moreover, almost all trajectories under the normal condition seemed to follow the same control strategy, in which the subjects used extra energy than the minimum one necessary for standing up. This suggests that the safety considerations come first than the energy efficiency considerations during a sit to stand, since the most energy efficient trajectory is close to the backward fall boundary. PMID:24187580

Moving beyond quiet stance: applicability of the inverted pendulum model to stooping and crouching postures.

PubMed

Weaver, Tyler B; Glinka, Michal N; Laing, Andrew C

2014-11-07

Currently, it is unknown whether the inverted pendulum model is applicable to stooping or crouching postures. Therefore, the aim of this study was to determine the degree of applicability of the inverted pendulum model to these postures, via examination of the relationship between the centre of mass (COM) acceleration and centre of pressure (COP)-COM difference. Ten young adults held static standing, stooping and crouching postures, each for 20s. For both the anterior-posterior (AP) and medio-lateral (ML) directions, the time-varying COM acceleration and the COP-COM were computed, and the relationship between these two variables was determined using Pearson's correlation coefficients. Additionally, in both directions, the average absolute COM acceleration, average absolute COP-COM signal, and the inertial component (i.e., -I/Wh) were compared across postures. Pearson correlation coefficients revealed a significant negative relationship between the COM acceleration and COP-COM signal for all comparisons, regardless of the direction (p<0.001). While no effect of posture was observed in the AP direction (p=0.463), in the ML direction, the correlation coefficients for stooping were different (i.e., stronger) than standing (p=0.008). Regardless of direction, the average absolute COM acceleration for both the stooping and crouching postures was greater than standing (p<0.002). The high correlations indicate that the inverted pendulum model is applicable to stooping and crouching postures. Due to their importance in completing activities of daily living, there is merit in determining what type of motor strategies are used to control such postures and whether these strategies change with age. Crown Copyright © 2014. Published by Elsevier Ltd. All rights reserved.

The hybrid mass-spring pendulum model of human leg swinging: stiffness in the control of cycle period.

PubMed

Obusek, J P; Holt, K G; Rosenstein, R M

1995-07-01

Human leg swinging is modeled as the harmonic motion of a hybrid mass-spring pendulum. The cycle period is determined by a gravitational component and an elastic component, which is provided by the attachment of a soft-tissue/muscular spring of variable stiffness. To confirm that the stiffness of the spring changes with alterations in the inertial properties of the oscillator and that stiffness is relevant for the control of cycle period, we conducted this study in which the simple pendulum equivalent length was experimentally manipulated by adding mass to the ankle of a comfortably swinging leg. Twenty-four young, healthy adults were videotaped as they swung their right leg under four conditions: no added mass and with masses of 2.27, 4.55, and 6.82kg added to the ankle. Strong, linear relationships between the acceleration and displacement of the swinging leg within subjects and conditions were found, confirming the motion's harmonic nature. Cycle period significantly increased with the added mass. However, the observed increases were not as large as would be predicted by the induced changes in the gravitational component alone. These differences were interpreted as being due to increases in the active muscular stiffness. Significant linear increases in the elastic component (and hence stiffness) were demonstrated with increases in the simple pendulum equivalent length in 20 of the individual subjects, with r2 values ranging between 0.89 and 0.99. Significant linear relationships were also demonstrated between the elastic and gravitational components in 22 subjects, with individual r2 values between 0.90 and 0.99.(ABSTRACT TRUNCATED AT 250 WORDS)

[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.

Rates of Charged Clocks in an Electric Field.

NASA Astrophysics Data System (ADS)

Ozer, Murat

2008-04-01

The gravitational arguments leading to time dilation, redshift, and spacetime curvature are adapted to electric fields. The energy levels of two identical positively charged atoms at different potentials in a static electric field are shown to undergo blueshift. Secondly, the period of a charged simple pendulum (clock) in the electric field of a metallic sphere is shown to vary with the electric potential. The spacetime diagram for the world lines of two photons emitted and absorbed by two pendulums at different potentials at different times and the world lines of the pendulums, as in Schild's argument, is shown to be not a parallelogram in Minkowski spacetime, concluding that spacetime must be curved. A Pound-Rebka-Snider experiment in an electric field is proposed to confirm that photons undergo a frequency shift in an electric field and hence the spacetime manifold is curved. Next, Torretti's gravitational argument that spacetime around a mass distribution concentrated at a point is curved is extended to electric charge distributions to conclude that the nonuniform electric fields of such charge distributions too curve spacetime. Finally, the local equivalence of a uniform electric field times the charge to mass ratio to a uniform acceleration is shown through spacetime transformations and the electrical redshift is obtained in a uniformly accelerated frame by using this principle. These arguments lead to the conclusion that special relativistic electromagnetism is an approximation to a general relativistic multi-metric theory.

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.

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

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.

Pendulum Mass Affects the Measurement of Articular Friction Coefficient

PubMed Central

Akelman, Matthew R.; Teeple, Erin; Machan, Jason T.; Crisco, Joseph J.; Jay, Gregory D.; Fleming, Braden C.

2012-01-01

Friction measurements of articular cartilage are important to determine the relative tribologic contributions made by synovial fluid or cartilage, and to assess the efficacy of therapies for preventing the development of post-traumatic osteoarthritis. Stanton’s equation is the most frequently used formula for estimating the whole joint friction coefficient (μ) of an articular pendulum, and assumes pendulum energy loss through a mass-independent mechanism. This study examines if articular pendulum energy loss is indeed mass independent, and compares Stanton’s model to an alternative model, which incorporates viscous damping, for calculating μ. Ten loads (25-100% body weight) were applied in a random order to an articular pendulum using the knees of adult male Hartley guinea pigs (n = 4) as the fulcrum. Motion of the decaying pendulum was recorded and μ was estimated using two models: Stanton’s equation, and an exponential decay function incorporating a viscous damping coefficient. μ estimates decreased as mass increased for both models. Exponential decay model fit error values were 82% less than the Stanton model. These results indicate that μ decreases with increasing mass, and that an exponential decay model provides a better fit for articular pendulum data at all mass values. In conclusion, inter-study comparisons of articular pendulum μ values should not be made without recognizing the loads used, as μ values are mass dependent. PMID:23122223

Pendulum mass affects the measurement of articular friction coefficient.

PubMed

Akelman, Matthew R; Teeple, Erin; Machan, Jason T; Crisco, Joseph J; Jay, Gregory D; Fleming, Braden C

2013-02-01

Friction measurements of articular cartilage are important to determine the relative tribologic contributions made by synovial fluid or cartilage, and to assess the efficacy of therapies for preventing the development of post-traumatic osteoarthritis. Stanton's equation is the most frequently used formula for estimating the whole joint friction coefficient (μ) of an articular pendulum, and assumes pendulum energy loss through a mass-independent mechanism. This study examines if articular pendulum energy loss is indeed mass independent, and compares Stanton's model to an alternative model, which incorporates viscous damping, for calculating μ. Ten loads (25-100% body weight) were applied in a random order to an articular pendulum using the knees of adult male Hartley guinea pigs (n=4) as the fulcrum. Motion of the decaying pendulum was recorded and μ was estimated using two models: Stanton's equation, and an exponential decay function incorporating a viscous damping coefficient. μ estimates decreased as mass increased for both models. Exponential decay model fit error values were 82% less than the Stanton model. These results indicate that μ decreases with increasing mass, and that an exponential decay model provides a better fit for articular pendulum data at all mass values. In conclusion, inter-study comparisons of articular pendulum μ values should not be made without recognizing the loads used, as μ values are mass dependent. Copyright © 2012 Elsevier Ltd. All rights reserved.

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.

Pinning in the flux-line-cutting regime of Bi 2Sr 2Ca 1Cu 2O 8 single crystals at high field

NASA Astrophysics Data System (ADS)

D'Anna, G.; André, M.-O.; Indenbom, M. V.; Benoit, W.

1994-09-01

Using a low-frequency torsion pendulum we show that in a Bi 2Sr 2Ca 1Cu 2O 8 single crystal the irreversibility line Birr( T) is frequency dependent down to 10 -5 Hz in the high-field regime. The activation energy has a logarithmic field dependence, U0( B)= U∗ 1n( B∗/ B). A microscopic model for flux-line-cutting and pancake collision yields quantitative expressions for U0 and for Birr( T)= B∗ exp(- T/T∗), which reproduce the experimental data very well.

The asymptotic structure of a slender coiling fluid thread

NASA Astrophysics Data System (ADS)

Blount, Maurice; Lister, John

2010-11-01

The buckling of a viscous fluid thread as it falls through air onto a stationary surface is a well-known breakfast-time phenomenon which exhibits a rich variety of dynamical regimes [1]. Since the bending resistance of a slender thread is small, bending motion is largely confined to a short region of coiling near the surface. If the height of fall is large enough, then the thread above the coiling region forms a `tail' that falls nearly vertically under gravity but is deflected slightly due to forces exerted on it by the coil. Although it is possible to use force balances in the coil to estimate scalings for the coiling frequency, we analyse the solution structure of the entire thread in the asymptotic limit of a very slender thread and thereby include the dynamic interaction between the coil and the tail. Quantitative predictions of the coiling frequency are obtained which demonstrate the existence of leading-order corrections to scalings previously derived. In particular, we show that in the regime where the deflection of the tail is governed by a balance between centrifugal acceleration, hoop stress and gravity, the tail behaves as a flexible circular pendulum that is forced by bending stress exerted by the coil. The amplitude of the response is calculated and the previously observed resonance when the coiling frequency coincides with one of the eigenfrequencies of a free flexible pendulum is thereby explained. [1] N.M. Ribe et al., J. Fluid Mech. 555, 275-297.

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)

Impaired Visual Motor Coordination in Obese Adults.

PubMed

Gaul, David; Mat, Arimin; O'Shea, Donal; Issartel, Johann

2016-01-01

Objective. To investigate whether obesity alters the sensory motor integration process and movement outcome during a visual rhythmic coordination task. Methods. 88 participants (44 obese and 44 matched control) sat on a chair equipped with a wrist pendulum oscillating in the sagittal plane. The task was to swing the pendulum in synchrony with a moving visual stimulus displayed on a screen. Results. Obese participants demonstrated significantly ( p < 0.01) higher values for continuous relative phase (CRP) indicating poorer level of coordination, increased movement variability ( p < 0.05), and a larger amplitude ( p < 0.05) than their healthy weight counterparts. Conclusion. These results highlight the existence of visual sensory integration deficiencies for obese participants. The obese group have greater difficulty in synchronizing their movement with a visual stimulus. Considering that visual motor coordination is an essential component of many activities of daily living, any impairment could significantly affect quality of life.

Determination of the dynamical behaviour of biological materials during impact using a pendulum device

NASA Astrophysics Data System (ADS)

Van Zeebroeck, M.; Tijskens, E.; Van Liedekerke, P.; Deli, V.; De Baerdemaeker, J.; Ramon, H.

2003-09-01

A pendulum device has been developed to measure contact force, displacement and displacement rate of an impactor during its impact on the sample. Displacement, classically measured by double integration of an accelerometer, was determined in an alternative way using a more accurate incremental optical encoder. The parameters of the Kuwabara-Kono contact force model for impact of spheres have been estimated using an optimization method, taking the experimentally measured displacement, displacement rate and contact force into account. The accuracy of the method was verified using a rubber ball. Contact force parameters for the Kuwabara-Kono model have been estimated with success for three biological materials, i.e., apples, tomatoes and potatoes. The variability in the parameter estimations for the biological materials was quite high and can be explained by geometric differences (radius of curvature) and by biological variation of mechanical tissue properties.

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.

A novel pendulum test for measuring roller chain efficiency

NASA Astrophysics Data System (ADS)

Wragge-Morley, R.; Yon, J.; Lock, R.; Alexander, B.; Burgess, S.

2018-07-01

This paper describes a novel pendulum decay test for determining the transmission efficiency of chain drives. The test involves releasing a pendulum with an initial potential energy and measuring its decaying oscillations: under controlled conditions the decay reveals the losses in the transmission to a high degree of accuracy. The main advantage over motorised rigs is that there are significantly fewer sources of friction and inertia and hence measurement error. The pendulum rigs have an accuracy around 0.6% for the measurement of the coefficient of friction, giving an accuracy of transmission efficiency measurement around 0.012%. A theoretical model of chain friction combined with the equations of motion enables the coefficient of friction to be determined from the decay rate of pendulum velocity. The pendulum rigs operate at relatively low speeds. However, they allow an accurate determination of the coefficient of friction to estimate transmission efficiency at higher speeds. The pendulum rig revealed a previously undetected rocking behaviour in the chain links at very small articulation angles. In this regime, the link interfaces were observed to roll against one another rather than slide. This observation indicates that a very high-efficiency transmission can be achieved if the articulation angle is very low.

A Vibrating Jaw Crusher with Auteresonant Electric Motor Drive of Swinging Movement

NASA Astrophysics Data System (ADS)

Zagrivniy, E. A.; Poddubniy, D. A.

2018-01-01

The article relates to a vibrating jaw crusher with pendulum vibrating exciter auteresonant electric motor drive and with elastic element rational force distribution, with limited peak-to-peak swing. Its design and its math model are presented. Also disclosed is the operating principle of a vibrating jaw crusher and the control algorithm for controlling the crushing jaw for maintaining the operating mode at resonant frequency.

A control method of the rotor re-levitation for different orbit responses during touchdowns in active magnetic bearings

NASA Astrophysics Data System (ADS)

Lyu, Mindong; Liu, Tao; Wang, Zixi; Yan, Shaoze; Jia, Xiaohong; Wang, Yuming

2018-05-01

Touchdown can make active magnetic bearings (AMB) unable to work, and bring severe damages to touchdown bearings (TDB). To resolve it, we presents a novel re-levitation method consisting of two operations, i.e., orbit response recognition and rotor re-levitation. In the operation of orbit response recognition, the three orbit responses (pendulum vibration, combined rub and bouncing, and full rub) can be identified by the expectation of radial displacement of rotor and expectation of instantaneous frequency (IF) of rotor motion in the sampling period. In the rotor re-levitation operation, a decentralized PID control algorithm is employed for pendulum vibration and combined rub and bouncing, and the decentralized PID control algorithm and another whirl damping algorithm, in which the weighting factor is determined by the whirl frequency, are jointly executed for the full rub. The method has been demonstrated by the simulation results of an AMB model. The results reveal that the method is effective in actively suppressing the whirl motion and promptly re-levitating the rotor. As the PID control algorithm and the simple operations of signal processing are employed, the algorithm has a low computation intensity, which makes it more easily realized in practical applications.

The Learning of Visually Guided Action: An Information-Space Analysis of Pole Balancing

ERIC Educational Resources Information Center

Jacobs, David M.; Vaz, Daniela V.; Michaels, Claire F.

2012-01-01

In cart-pole balancing, one moves a cart in 1 dimension so as to balance an attached inverted pendulum. We approached perception-action and learning in this task from an ecological perspective. This entailed identifying a space of informational variables that balancers use as they perform the task and demonstrating that they improve by traversing…

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.

Various methods of determining the natural frequencies and damping of composite cantilever plates. 1. Exact solution for the binomial model of deformation

NASA Astrophysics Data System (ADS)

Skel'chik, V. S.; Ryabov, V. M.

1996-11-01

On the basis of the classical theory of thin anisotropic laminated plates the article analyzes the free vibrations of rectangular cantilever plates made of fibrous composites. The application of Kantorovich's method for the binomial representation of the shape of the elastic surface of a plate yielded for two unknown functions a system of two connected differential equations and the corresponding boundary conditions at the place of constraint and at the free edge. The exact solution for the frequencies and forms of the free vibrations was found with the use of Laplace transformation with respect to the space variable. The magnitudes of several first dimensionless frequencies of the bending and torsional vibrations of the plate were calculated for a wide range of change of two dimensionless complexes, with the dimensions of the plate and the anisotropy of the elastic properties of the material taken into account. The article shows that with torsional vibrations the warping constraint at the fixed end explains the apparent dependence of the shear modulus of the composite on the length of the specimen that had been discovered earlier on in experiments with a torsional pendulum. It examines the interaction and transformation of the second bending mode and of the first torsional mode of the vibrations. It analyzes the asymptotics of the dimensionless frequencies when the length of the plate is increased, and it shows that taking into account the bending-torsion interaction in strongly anisotropic materials type unidirectional carbon reinforced plastic can reduce substantially the frequencies of the bending vibrations but has no effect (within the framework of the binomial model) on the frequencies of the torsional vibrations.

On the MAF solution of the uniformly lengthening pendulum via change of independent variable in the Bessel's equation

NASA Astrophysics Data System (ADS)

Deniz, Coşkun

Common recipe for the Lengthening Pendulum (LP) involves some change of variables to give a relationship with the Bessel's equation. In this work, semiclassical MAF (Modified Airy Function) solution of the LP is being obtained by first transforming the related Bessel's equation into the normal form via the suggested change of independent variable just as one of our recent work regarding the JWKB solution of the LP in (Deniz, 2017). MAF approximation of the first order Bessel Functions (ν = 1) of both type along with their zeros are being obtained analytically with a very good accuracy as a result of the appropriately chosen associated initial values and they are extended to the neighbouring orders (ν = 0 and 2) by the recursion relations. Although common numerical methods given in the literature require adiabatic LP systems where the lengthening rate is small, MAF solution presented here can safely be used for higher lengthening rates and a criterion for its validity is determined via the use of MAF applicability criterion given in the literature. As a result, the semiclassical MAF method which is normally used for the quantum mechanical and optical waveguide systems is applied to the classical LP system successfully just as our previous work regarding the JWKB solution of the LP. Interestingly, we have very accurate results in the entire domain except for x ≈ 0 .

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 .

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.

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.

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.

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.

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…

The organizational pendulum--healthcare management in Sweden 1865-1998.

PubMed

Axelsson, R

2000-03-01

In recent years, there have been a number of large-scale changes in the organization of healthcare in Sweden, as in many other countries. From a longer time perspective, however, there has been a more or less permanent oscillation between centralization and decentralization, and also between competition and co-operation, in Swedish healthcare organizations. In fact, there seems to be something like a pendulum moving all the time between opposite forms of organization. The frequency of these changes has been increasing during the last fifteen years, as different organizational models have replaced each other at shorter and shorter intervals. This development is partly due to the increasing rate of change in modern society, but partly also due to an element of fashion in the area of management. There is, however, a growing change fatigue in many healthcare organizations, and also increasing demands for empirical evidence on the efficiency and effectiveness of different organizational models before they are introduced into the healthcare system.

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.

"Catch the Pendulum": The Problem of Asymmetric Data Delivery in Electromagnetic Nanonetworks.

PubMed

Islam, Nabiul; Misra, Sudip

2016-09-01

The network of novel nano-material based nanodevices, known as nanoscale communication networks or nanonetworks has ushered a new communication paradigm in the terahertz band (0.1-10 THz). In this work, first we envisage an architecture of nanonetworks-based Coronary Heart Disease (CHD) monitoring, consisting of nano-macro interface (NM) and nanodevice-embedded Drug Eluting Stents (DESs), termed as nanoDESs. Next, we study the problem of asymmetric data delivery in such nanonetworks-based systems and propose a simple distance-aware power allocation algorithm, named catch-the-pendulum, which optimizes the energy consumption of nanoDESs for communicating data from the underlying nanonetworks to radio frequency (RF) based macro-scale communication networks. The algorithm exploits the periodic change in mean distance between a nanoDES, inserted inside the affected coronary artery, and the NM, fitted in the intercostal space of the rib cage of a patient suffering from a CHD. Extensive simulations confirm superior performance of the proposed algorithm with respect to energy consumption, packet delivery, and shutdown phase.

Interfacial fluid instabilities and Kapitsa pendula.

PubMed

Krieger, Madison S

2017-07-01

The onset and development of instabilities is one of the central problems in fluid mechanics. Here we develop a connection between instabilities of free fluid interfaces and inverted pendula. When acted upon solely by the gravitational force, the inverted pendulum is unstable. This position can be stabilized by the Kapitsa phenomenon, in which high-frequency low-amplitude vertical vibrations of the base creates a fictitious force which opposes the gravitational force. By transforming the dynamical equations governing a fluid interface into an appropriate pendulum-type equation, we demonstrate how stability can be induced in fluid systems by properly tuned vibrations. We construct a "dictionary"-type relationship between various pendula and the classical Rayleigh-Taylor, Kelvin-Helmholtz, Rayleigh-Plateau and the self-gravitational instabilities. This makes several results in control theory and dynamical systems directly applicable to the study of tunable fluid instabilities, where the critical wavelength depends on the external forces or the instability is suppressed entirely. We suggest some applications and instances of the effect ranging in scale from microns to the radius of a galaxy.

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...

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…

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…

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.

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.

Robust design of mass-uncertain rolling-pendulum TMDs for the seismic protection of buildings

NASA Astrophysics Data System (ADS)

Matta, Emiliano; De Stefano, Alessandro

2009-01-01

Commonly used for mitigating wind- and traffic-induced vibrations in flexible structures, passive tuned mass dampers (TMDs) are rarely applied to the seismic control of buildings, their effectiveness to impulsive loads being conditional upon adoption of large mass ratios. Instead of recurring to cumbersome metal or concrete devices, this paper suggests meeting that condition by turning into TMDs non-structural masses sometimes available atop buildings. An innovative roof-garden TMD, for instance, sounds a promising tool capable of combining environmental and structural protection in one device. Unfortunately, the amount of these masses being generally variable, the resulting mass-uncertain TMD (MUTMD) appears prone to mistuning and control loss. In an attempt to minimize such adverse effects, robust analysis and synthesis against mass variations are applied in this study to MUTMDs of the rolling-pendulum type, a configuration characterized by mass-independent natural period. Through simulations under harmonic and recorded ground motions of increasing intensity, the performance of circular and cycloidal rolling-pendulum MUTMDs is evaluated on an SDOF structure in order to illustrate their respective advantages as well as the drawbacks inherent in their non-linear behavior. A possible implementation of a roof-garden TMD on a real building structure is described and its control efficacy numerically demonstrated, showing that in practical applications MUTMDs can become a good alternative to traditional TMDs.

Numerical simulations of an elastica pendulum

NASA Astrophysics Data System (ADS)

Sinclair, R.

Folklore would have it that a massless clamped-free elastica undergoing planar motion with a point end mass possesses periodic solutions corresponding to a single mode of oscillation. We present a battery of numerical simulations leading to the single conclusion that these supposed periodic solutions do not exist, due to a strong nonlinear coupling of two modes, the frequency of one of which is apparently inversely proportional to the magnitude of the force acting on the elastica.

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…

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,…

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...

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…

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…

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…

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

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.

Testing new technologies for the LISA Gravitational Reference Senso

NASA Astrophysics Data System (ADS)

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

2015-01-01

LISA will directly observe low-frequency gravitational waves emitted by sources ranging from super-massive black hole mergers to compact galactic binaries. A laser interferometer will measure picometer changes in the distances between free falling test masses separated by millions of kilometers. A test mass and its associated sensing, actuation, charge control and caging subsystems are referred to as a gravitational reference sensor (GRS). The demanding acceleration noise requirement of < 3×10-15 m/sec2Hz1/2 for the LISA GRS has motivated a rigorous testing campaign in Europe and a dedicated technology mission, LISA Pathfinder, scheduled for launch in the summer of 2015. At the University of Florida we are developing a nearly thermally noise limited torsion pendulum for testing GRS technology enhancements and for understanding the dozens of acceleration noise sources that affect the performance of the GRS. This experimental facility is based on the design of a similar facility at the University of Trento, and consists of a vacuum enclosed torsion pendulum that suspends mock-ups of the LISA test masses, surrounded by electrode housings. Some of the technologies that will be demonstrated by this facility include a novel TM charge control scheme based on ultraviolet LEDs, an all-optical TM position and attitude sensor, and drift mode operation. This presentation will describe the design of the torsion pendulum facility, its current acceleration noise performance, and the status of the GRS technologies under development.

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.

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...

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…

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…

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…

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

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

Investigation of flux penetration in YBa 2Cu 3O 7-δ filaments

NASA Astrophysics Data System (ADS)

Devos, P.; Buekenhoudt, A.; D'Anna, G.; André, M.-O.; Indenbom, M. V.; Benoit, W.; De Batist, R.; Cornelis, J.

1994-12-01

ac Susceptibility measurements using a low frequency torsion pendulum and an ac susceptometer were conducted on YBa 2Cu 3O 7-δ filaments in low magnetic dc fields (≤1T). Different dissipation peaks are observed, dependent on the temperature and the applied amplitude. The peak at low temperatures, which is of intergranular nature is studied in detail. The penetration follows the Bean model and the intergranular creep is observed.

Probing Many-Body Interactions in an Optical Lattice Clock (Preprint)

DTIC Science & Technology

2013-10-23

impressive potential gain over their microwave counterparts. Optical frequencies on the other hand are very difficult to measure, as the oscillations ...source can be compared. Here, the laboratory radiation source is an ultra-stable continuous-wave laser. It acts as the local oscillator (or pendulum...where φ Z 0 is the ground longitudinal mode in a lattice site and φn are transverse harmonic oscillator eigenmodes. ĉ†αn creates a fermion in mode n

Biomechanical analysis of INFINITY rehabilitation method for treatment of low back pain

PubMed Central

Daniel, Matej; Tomanová, Michaela; Hornová, Jana; Novotná, Iva; Lhotská, Lenka

2017-01-01

[Purpose] Low back pain is a pervasive problem in modern societies. Physical rehabilitation in treatment of low back pain should reduce pain, muscle tension and restore spine stability and balance. The INFINITY® rehabilitation method that is based on a figure of eight movement pattern was proved to be effective in low back pain treatment. The aim of the paper is to estimate the effect of a figure of eight motion on the L5/S1 load and lumbar spine muscle activation in comparison to other motion patterns. [Subjects and Methods] Three-dimensional model of lumbar spine musculoskeletal system is used to simulate effect of various load motion pattern induced by displacement of the center of gravity of the upper body. Four motion patterns were examined: lateral and oblique pendulum-like motion, elliptical motion and figure of eight motion. [Results] The simple pendulum-like and elliptical-like patterns induce harmonic muscle activation and harmonic spinal load. The figure of eight motion pattern creates high-frequency spinal loading that activates remodeling of bones and tendons. The figure of eight pattern also requires muscle activity that differs from harmonic frequency and is more demanding on muscle control and could also improve muscle coordination. [Conclusion] The results of the study indicate that complex motion pattern during INFINITY® rehabilitation might enhance the spine stability by influencing its passive, active and neural components. PMID:28603355

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.…

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…

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...

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...

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

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)

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.

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).

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.

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.

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.

Anisotropic dielectric phase transition triggered by pendulum-like motion coupled with proton transfer in a layered hybrid crystalline material (4-nitroanilinium+) (18-crown-6) (H2PO4-) (H3PO4)2

NASA Astrophysics Data System (ADS)

Liu, Yang; Zhu, Chun-li; Qin, Liu-lei; Zheng, Xiao-yuan; Liu, Zun-qi

2018-07-01

The organic-inorganic hybrid phase-transition material, (4-nitroanilinium+) (18-crown-6) (H2PO4-) (H3PO4)2 (1), was successfully synthesized. The organic (4-nitroanilinium) (18-crown-6)+ supramolecular cation layer and inorganic phosphate anion layer were arranged alternately. Differential scanning calorimetry (DSC), temperature-dependent dielectric measurements, and variable-temperature single-crystal X-ray diffraction analysis confirmed the reversible isostructural phase transition of 1 with the same space group Pbca at 225 K, wherein the synergistic effect between the pendulum-like motion of organic cations and the proton transfer in the Osbnd H⋯O hydrogen bonding of inorganic anions was mainly responsible for the phase-transition behavior of 1. The most striking dielectric property was the remarkable anisotropy along various crystallographic axes. A potential-energy calculation further supported the possibility of dynamic motion of cations in the crystal.

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...

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.

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.

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.

Robust and novel two degree of freedom fractional controller based on two-loop topology for inverted pendulum.

PubMed

Dwivedi, Prakash; Pandey, Sandeep; Junghare, A S

2018-04-01

A rotary single inverted pendulum (RSIP) typically represents a space booster rocket, Segway and similar systems with unstable equilibrium. This paper proposes a novel two degree of freedom (2-DOF) fractional control strategy based on 2-loop topology for RSIP system which can be extended to control the systems with unstable equilibrium. It comprises feedback and feed-forward paths. Primary controller relates the perturbation attenuation while the secondary controller is accountable for set point tracking. To tune the parameters of proposed fractional controller a simple graphical tuning method based on frequency response is used. The study will serve the outstanding experimental results for both, stabilization and trajectory tracking tasks. The study will also serve to present a comparison of the performance of the proposed controller with the 1-DOF FOPID controller and sliding mode controller (SMC) for the RSIP system. Further to confirm the usability of the proposed controller and to avoid the random perturbations sensitivity, robustness, and stability analysis through fractional root-locus and Bode-plot is investigated. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

A Parametric Oscillator Experiment for Undergraduates

NASA Astrophysics Data System (ADS)

Huff, Alison; Thompson, Johnathon; Pate, Jacob; Kim, Hannah; Chiao, Raymond; Sharping, Jay

We describe an upper-division undergraduate-level analytic mechanics experiment or classroom demonstration of a weakly-damped pendulum driven into parametric resonance. Students can derive the equations of motion from first principles and extract key oscillator features, such as quality factor and parametric gain, from experimental data. The apparatus is compact, portable and easily constructed from inexpensive components. Motion control and data acquisition are accomplished using an Arduino micro-controller incorporating a servo motor, laser sensor, and data logger. We record the passage time of the pendulum through its equilibrium position and obtain the maximum speed per oscillation as a function of time. As examples of the interesting physics which the experiment reveals, we present contour plots depicting the energy of the system as functions of driven frequency and modulation depth. We observe the transition to steady state oscillation and compare the experimental oscillation threshold with theoretical expectations. A thorough understanding of this hands-on laboratory exercise provides a foundation for current research in quantum information and opto-mechanics, where damped harmonic motion, quality factor, and parametric amplification are central.

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

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...

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...

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

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.

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.

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.

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.

Testing of the LISA pathfinder GRS

NASA Astrophysics Data System (ADS)

Antonucci, Federica; Cavalleri, Antonella; Ciani, Giacomo; Congedo, Giuseppe; Dolesi, Rita; de Marchi, Fabrizio; Ferraioli, Luigi; Hueller, Mauro; Nicolodi, Daniele; Tombolato, David; Vitale, Stefano; Wass, Peter J.; Weber, William J.

The ESA/NASA mission,LISA (Laser Interferometric Space Antenna), will measure gravita-tional waves emitted by astronomical sources, galactic and extra-galactic, at frequencies 10-4 to 10-1 Hz. LISA is a 5-million-km arm-length interferometer whose mirrors are test masses which must be nominally free-falling to a level which does not exceed 3 · 10-15 ms-2 Hz -1/2 in acceleration. LISA Pathfinder is a technology demonstration mission which will show that the relative parasitic acceleration between two masses on one spacecraft can be lower than 3 · 10-14 ms-2 Hz -1/2 , at frequencies around 1 mHz -one order of magnitude larger than LISA's goal. At the core of the LISA Pathfinder experiment is the GRS (gravitational reference sensor), a capacitive sensor with mm gaps used to measure the position of the test mass and actuate its position in 6-degrees-of-freedom. Testing the purity of free-fall for LISA Pathfinder on-ground is achieved using a torsion pendulum which allows us to measure force disturbances at a level relevant to LISA Pathfinder. We will present the latest campaign of tests of the LISA Pathfinder GRS using the 4-test-mass torsion pendulum facility aimed at measuring force-noise sources (responsible for the parasitic acceleration) for LISA Pathfinder in its frequency band. Our GRS , is the LISA Pathfinder flight-model replica, and its testing is crucial in verifying the design and performance of the flight instrument and measuring many of the unwanted disturbances which can limit the performance of LISA and LISA pathfinder. The measurements concern the dependence of the force on the test mass position in the sensor and their electrostatic coupling, electrostatic fields due to surface-potential variations and thermal gradients.

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

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

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.

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.

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].

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

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.

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

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.

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.

Pulsed Electric Propulsion Thrust Stand Calibration Method

NASA Technical Reports Server (NTRS)

Wong, Andrea R.; Polzin, Kurt A.; Pearson, J. Boise

2011-01-01

The evaluation of the performance of any propulsion device requires the accurate measurement of thrust. While chemical rocket thrust is typically measured using a load cell, the low thrust levels associated with electric propulsion (EP) systems necessitate the use of much more sensitive measurement techniques. The design and development of electric propulsion thrust stands that employ a conventional hanging pendulum arm connected to a balance mechanism consisting of a secondary arm and variable linkage have been reported in recent publications by Polzin et al. These works focused on performing steady-state thrust measurements and employed a static analysis of the thrust stand response. In the present work, we present a calibration method and data that will permit pulsed thrust measurements using the Variable Amplitude Hanging Pendulum with Extended Range (VAHPER) thrust stand. Pulsed thrust measurements are challenging in general because the pulsed thrust (impulse bit) occurs over a short timescale (typically 1 micros to 1 millisecond) and cannot be resolved directly. Consequently, the imparted impulse bit must be inferred through observation of the change in thrust stand motion effected by the pulse. Pulsed thrust measurements have typically only consisted of single-shot operation. In the present work, we discuss repetition-rate pulsed thruster operation and describe a method to perform these measurements. The thrust stand response can be modeled as a spring-mass-damper system with a repetitive delta forcing function to represent the impulsive action of the thruster.

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.

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.

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.

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.

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 ...

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.

11. BUILDING NO. 620B. INTERIOR VIEW LOOKING NORTH, SHOWING PENDULUM ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

11. BUILDING NO. 620-B. INTERIOR VIEW LOOKING NORTH, SHOWING PENDULUM AND FRAME IN FOREGROUND, SHIELD FOR OPERATORS IN BACKGROUND. FRICTION TEST IS OBSERVED FROM BEHIND BLAST SHIELD BY A SERIES OF MIRRORS. ANVIL IN CENTER OF PENDULUM FRAME HOLDS EXPLOSIVE WHOSE SENSITIVITY TO FRICTION IS TO BE TESTED. PANS ON EITHER SIDE CATCH ANY UNBURNT EXPLOSIVE SLUNG FROM ANVIL DURING TEST TO PREVENT EXPLOSIVE HAZARD. - Picatinny Arsenal, 600 Area, Test Areas District, State Route 15 near I-80, Dover, Morris County, NJ

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

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

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

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.

Spectrum of Quantized Energy for a Lengthening Pendulum

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

Choi, Jeong Ryeol; Song, Ji Nny; Hong, Seong Ju

We considered a quantum system of simple pendulum whose length of string is increasing at a steady rate. Since the string length is represented as a time function, this system is described by a time-dependent Hamiltonian. The invariant operator method is very useful in solving the quantum solutions of time-dependent Hamiltonian systems like this. The invariant operator of the system is represented in terms of the lowering operator a(t) and the raising operator a{sup {dagger}}(t). The Schroedinger solutions {psi}{sub n}({theta}, t) whose spectrum is discrete are obtained by means of the invariant operator. The expectation value of the Hamiltonian inmore » the {psi}{sub n}({theta}, t) state is the same as the quantum energy. At first, we considered only {theta}{sup 2} term in the Hamiltonian in order to evaluate the quantized energy. The numerical study for quantum energy correction is also made by considering the angle variable not only up to {theta}{sup 4} term but also up to {theta}{sup 6} term in the Hamiltonian, using the perturbation theory.« less

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.

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...

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 572.155 - Test conditions and instrumentation.

Code of Federal Regulations, 2012 CFR

2012-10-01

...) 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 572.146 - Test conditions and instrumentation.

Code of Federal Regulations, 2012 CFR

2012-10-01

...) 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 572.146 - Test conditions and instrumentation.

Code of Federal Regulations, 2014 CFR

2014-10-01

...) 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, 2011 CFR

2011-10-01

...) 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 572.146 - Test conditions and instrumentation.

Code of Federal Regulations, 2010 CFR

2010-10-01

...) 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 572.146 - Test conditions and instrumentation.

Code of Federal Regulations, 2011 CFR

2011-10-01

...) 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, 2010 CFR

2010-10-01

...) 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...

Health Information in Somali (Af-Soomaali )

MedlinePlus

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

Finite element analysis of unnotched charpy impact tests

DOT National Transportation Integrated Search

2008-10-01

This paper describes nonlinear finite element analysis (FEA) to examine the energy to : fracture unnotched Charpy specimens under pendulum impact loading. An oversized, : nonstandard pendulum impactor, called the Bulk Fracture Charpy Machine (BFCM), ...

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

Segmented Hoop as a Physical Pendulum

NASA Astrophysics Data System (ADS)

Layton, William; Rodriguez, Nuria

2013-10-01

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 segmented horizontally (as illustrated in Fig. 1) into smaller pieces that are symmetrical about the point of suspension, each smaller segment will also have the same period. Constructing such a demonstration can be difficult, but thanks to a suggestion from a fellow physics teacher a dissectible hula hoop can be purchased that serves well in this demonstration.2 A setup that has been repeated many times at various physics teacher meetings in Southern California is illustrated below.

[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.

Comparison of two different methods of preoperative marking for toric intraocular lens implantation: bubble marker versus pendulum marker

PubMed Central

Farooqui, Javed Hussain; Koul, Archana; Dutta, Ranjan; Shroff, Noshir Minoo

2016-01-01

AIM 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. METHODS 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. RESULTS 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). CONCLUSION Both preoperative marking techniques result in approximately 3 of alignment error. Both marking techniques are simple, predictable, reproducible and easy to perform. PMID:27275425

Pendulum migration and healthcare in border área.

PubMed

Zaslavsky, Ricardo; Goulart, Bárbara Niegia Garcia de

2017-12-01

This article aims to reflect about the importance and the potential impact of pendulum migration in the pursuance for healthcare, and, specifically, about the peculiarity of this kind of mobility in border areas. It describes the context in which the pendulum migration is inserted for the modification of the urban space in the 20th century, makes initial comments about legal aspects of the theme in health sector, and describes the reality of the Brazil-Argentina-Paraguay triple border as an important location of pendulum migration for the pursuance of healthcare as an illustrative fact. In this way, hypotheses are formulated about the causes of the pendulum migration impact on patient's health like the effect of the distance covered from home to healthcare facilities, and organizational aspects related to healthcare like the uncertainty about having or not health assistance due to international mobility. It concludes that this kind of mobility is very common in the pursuance of healthcare despite the traditional approach to the theme mentioning only work or study. Besides that, it is very important to study its impact on health and to include this theme on the cross border healthcare debate.

30 CFR 15.20 - Technical requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... temperature is between 68 and 86 °F. (f) Pendulum-friction test. The explosive shall show no perceptible reaction in the pendulum-friction test with the hard fiber-faced shoe. Ten trials of the test are conducted...

30 CFR 15.20 - Technical requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... temperature is between 68 and 86 °F. (f) Pendulum-friction test. The explosive shall show no perceptible reaction in the pendulum-friction test with the hard fiber-faced shoe. Ten trials of the test are conducted...

30 CFR 15.20 - Technical requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... temperature is between 68 and 86 °F. (f) Pendulum-friction test. The explosive shall show no perceptible reaction in the pendulum-friction test with the hard fiber-faced shoe. Ten trials of the test are conducted...

30 CFR 15.20 - Technical requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

... temperature is between 68 and 86 °F. (f) Pendulum-friction test. The explosive shall show no perceptible reaction in the pendulum-friction test with the hard fiber-faced shoe. Ten trials of the test are conducted...

30 CFR 15.20 - Technical requirements.

Code of Federal Regulations, 2010 CFR

2010-07-01

... temperature is between 68 and 86 °F. (f) Pendulum-friction test. The explosive shall show no perceptible reaction in the pendulum-friction test with the hard fiber-faced shoe. Ten trials of the test are conducted...

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.

Self-excited electrostatic pendulum showing electrohydrodynamic-force-induced oscillation

NASA Astrophysics Data System (ADS)

Stephan, Karl D.; Hernandez Guerrero, José M.

2017-12-01

The electrohydrodynamic (EHD) effect ("ion wind") associated with corona discharges in air has been extensively investigated and modeled. We present a simple experiment that shows how both the magnitude and direction of EHD forces can change in such a way as to impart energy continuously to an oscillating electrostatic pendulum. The amplitude of oscillations of an electrostatic pendulum subject to EHD forces can grow approximately exponentially over a period of minutes, and we describe a qualitative theory to account for this effect, along with implications of these experiments for theories of ball lightning.

Analysis of pendulum period with an iPod touch/iPhone

NASA Astrophysics Data System (ADS)

Briggle, Justin

2013-05-01

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. Moreover, the principles described may be carried out with any number of smartphone devices containing an integrated accelerometer and paired with an appropriate application for collecting and sending accelerometer data as a comma-separated value file.

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.

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.

Resonant frequency calculations using a hybrid perturbation-Galerkin technique

NASA Technical Reports Server (NTRS)

Geer, James F.; Andersen, Carl M.

1991-01-01

A two-step hybrid perturbation Galerkin technique is applied to the problem of determining the resonant frequencies of one or several degree of freedom nonlinear systems involving a parameter. In one step, the Lindstedt-Poincare method is used to determine perturbation solutions which are formally valid about one or more special values of the parameter (e.g., for large or small values of the parameter). In step two, a subset of the perturbation coordinate functions determined in step one is used in Galerkin type approximation. The technique is illustrated for several one degree of freedom systems, including the Duffing and van der Pol oscillators, as well as for the compound pendulum. For all of the examples considered, it is shown that the frequencies obtained by the hybrid technique using only a few terms from the perturbation solutions are significantly more accurate than the perturbation results on which they are based, and they compare very well with frequencies obtained by purely numerical methods.

Misura di g con pendolo non in regime caotico

NASA Astrophysics Data System (ADS)

Sigismondi, Costantino

2017-02-01

The measurement of the gravity acceleration with pendulum is a basic experiment in Newtonian physics, but the correct choice of wire and weight to suspend can avoid to have a cahotic instead of simple pendulum.

Deck the Halls. Animated Displays: Coupled Mechanical Oscillators.

ERIC Educational Resources Information Center

Pizzo, Joe, Ed.

1992-01-01

Describes a set of displays on the theme of coupled mechanical oscillators. Displays encompass three common demonstrations: (1) a coupled pair of identical pendulums; (2) a multiple-pendulum resonance demonstration; and (3) a Wilberforce coupled oscillator. (MDH)

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.

Recommended Practices in Thrust Measurements

NASA Technical Reports Server (NTRS)

Polk, James E.; Pancotti, Anthony; Haag, Thomas; King, Scott; Walker, Mitchell; Blakely, Joseph; Ziemer, John

2013-01-01

Accurate, direct measurement of thrust or impulse is one of the most critical elements of electric thruster characterization, and one of the most difficult measurements to make. The American Institute of Aeronautics and Astronautics has started an initiative to develop standards for many important measurement processes in electric propulsion, including thrust measurements. This paper summarizes recommended practices for the design, calibration, and operation of pendulum thrust stands, which are widely recognized as the best approach for measuring micro N- to mN-level thrust and micro Ns-level impulse bits. The fundamentals of pendulum thrust stand operation are reviewed, along with its implementation in hanging pendulum, inverted pendulum, and torsional balance configurations. Methods of calibration and recommendations for calibration processes are presented. Sources of error are identified and methods for data processing and uncertainty analysis are discussed. This review is intended to be the first step toward a recommended practices document to help the community produce high quality thrust measurements.

Design and analysis of a torsion braid pendulum displacement transducer

NASA Technical Reports Server (NTRS)

Rind, E.; Bryant, E. L.

1981-01-01

The dynamic properties at various temperatures of braids impregnated with polymer can be measured by using the braid as the suspension of a torsion pendulum. This report describes the electronic and mechanical design of a torsional braid pendulum displacement transducer which is an advance in the state of the art. The transducer uses a unique optical design consisting of refracting quartz windows used in conjunction with a differential photocell to produce a null signal. The release mechanism for initiating free torsional oscillation of the pendulum has also been improved. Analysis of the precision and accuracy of the transducer indicated that the maximum relative error in measuring torsional amplitude was approximately 0. A serious problem inherent in all instruments which use a torsional suspension was analyzed: misalignment of the physical and torsional axes of the torsional member which results in modulation of the amplitude of the free oscillation.

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%.

On the efficiency of the golf swing

NASA Astrophysics Data System (ADS)

White, Rod

2006-12-01

A non-driven double pendulum model is used to explain the principle underlying the surprising efficiency of the golf swing. The principle can be described as a parametric energy transfer between the arms and the club head due to the changing moment of inertia of the club. The transfer is a consequence of conservation of energy and angular momentum. Because the pendulum is not driven by an external force, it shows that the golfer need do little more than accelerate the arms with the wrists cocked and let the double pendulum transfer kinetic energy to the club head. A driven double pendulum model is used to study factors affecting the efficiency of a real golf swing. It is concluded that the wrist-cock angle is the most significant efficiency-determining parameter under the golfer's control and that improvements in golf technology have had a significant impact on driving distance.

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.

A novel control algorithm for interaction between surface waves and a permeable floating structure

NASA Astrophysics Data System (ADS)

Tsai, Pei-Wei; Alsaedi, A.; Hayat, T.; Chen, Cheng-Wu

2016-04-01

An analytical solution is undertaken to describe the wave-induced flow field and the surge motion of a permeable platform structure with fuzzy controllers in an oceanic environment. In the design procedure of the controller, a parallel distributed compensation (PDC) scheme is utilized to construct a global fuzzy logic controller by blending all local state feedback controllers. A stability analysis is carried out for a real structure system by using Lyapunov method. The corresponding boundary value problems are then incorporated into scattering and radiation problems. They are analytically solved, based on separation of variables, to obtain series solutions in terms of the harmonic incident wave motion and surge motion. The dependence of the wave-induced flow field and its resonant frequency on wave characteristics and structure properties including platform width, thickness and mass has been thus drawn with a parametric approach. From which mathematical models are applied for the wave-induced displacement of the surge motion. A nonlinearly inverted pendulum system is employed to demonstrate that the controller tuned by swarm intelligence method can not only stabilize the nonlinear system, but has the robustness against external disturbance.

Investigation of Learning Behaviors and Achievement of Vocational High School Students Using an Ubiquitous Physics Tablet PC App

NASA Astrophysics Data System (ADS)

Purba, Siska Wati Dewi; Hwang, Wu-Yuin

2017-06-01

In this study, we designed and developed an app called Ubiquitous-Physics (U-Physics) for mobile devices like tablet PC or smart phones to help students learn the principles behind a simple pendulum in Physics. The unique characteristic of U-Physics is the use of sensors on mobile devices to collect acceleration and velocity data during pendulum swings. The data collected are transformed to facilitate students' understanding of the pendulum time period. U-Physics helped students understand the effects of pendulum mass, length, and angle in relation to its time period. In addition, U-Physics was equipped with an annotation function such as textual annotation to help students interpret and understand the concepts and phenomena of the simple pendulum. U-Physics also generated graphs automatically to demonstrate the time period during which the pendulum was swinging. Results showed a significant positive correlation between interpreting graphs and applying formula. This finding indicated that the ability to interpret graphs has an important role in scientific learning. Therefore, we strongly recommend that physics teachers use graphs to enrich students' information content and understanding and negative correlation between pair coherence and interpreting graphs. It may be that most of the participants (vocational high school students) have limited skill or confidence in physics problem solving; so, they often seek help from teachers or their high-achieving peers. In addition, the findings also indicated that U-Physics can enhance students' achievement during a 3-week time period. We hope that this app can be globally used to learn physics in the future.

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

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.

Human balancing of an inverted pendulum with a compliant linkage: neural control by anticipatory intermittent bias

PubMed Central

Lakie, Martin; Caplan, Nicholas; Loram, Ian D

2003-01-01

These experiments were prompted by the recent discovery that the intrinsic stiffness of the ankle is inadequate to stabilise passively the body in standing. Our hope was that showing how a large inverted pendulum was manually balanced with low intrinsic stiffness would elucidate the active control of human standing. The results show that the pendulum can be satisfactorily stabilised when intrinsic stiffness is low. Analysis of sway size shows that intrinsic stiffness actually plays little part in stabilisation. The sway duration is also substantially independent of intrinsic stiffness. This suggests that the characteristic sway of the pendulum, rather than being dictated by stiffness and inertia, may result from the control pattern of hand movements. The key points revealed by these experiments are that with low intrinsic stiffness the hand provides pendulum stability by intermittently altering the bias of the spring and, on average, the hand moves in opposition to the load. The results lead to a new and testable hypothesis; namely that in standing, the calf muscle shortens as the body sways forward and lengthens as it sways backwards. These findings are difficult to reconcile with stretch reflex control of the pendulum and are of particular relevance to standing. They may also be relevant to postural maintenance in general whenever the CNS controls muscles which operate through compliant linkages. The results also suggest that in standing, rather than providing passive stability, the intrinsic stiffness acts as an energy efficient buffer which provides decoupling between muscle and body. PMID:12832494

[Evaluation of pendulum testing of spasticity].

PubMed

Le Cavorzin, P; Hernot, X; Bartier, O; Carrault, G; Chagneau, F; Gallien, P; Allain, H; Rochcongar, P

2002-11-01

To identify valid measurements of spasticity derived from the pendulum test of the leg in a representative population of spastic patients. Pendulum testing was performed in 15 spastic and 10 matched healthy subjects. The reflex-mediated torque evoked in quadriceps femoris, as well as muscle mechanical parameters (viscosity and elasticity), were calculated using mathematical modelling. Correlation with the two main measures derived from the pendulum test reported in the literature (the Relaxation Index and the area under the curve) was calculated in order to select the most valid. Among mechanical parameters, only viscosity was found to be significantly higher in the spastic group. As expected, the computed integral of the reflex-mediated torque was found to be larger in spastics than in healthy subjects. A significant non-linear (logarithmic) correlation was found between the clinically-assessed muscle spasticity (Ashworth grading) and the computed reflex-mediated torque, emphasising the non-linear behaviour of this scale. Among measurements derived from the pendulum test which are proposed in the literature for routine estimation of spasticity, the Relaxation Index exhibited an unsuitable U-shaped pattern of variation with increasing reflex-mediated torque. On the opposite, the area under the curve revealed a linear regression, which is more convenient for routine estimation of spasticity. The pendulum test of the leg is a simple technique for the assessment of spastic hypertonia. However, the measurement generally used in the literature (the Relaxation Index) exhibits serious limitations, and would benefit to be replaced by more valid measures, such as the area under the goniometric curve, especially for the assessment of therapeutics.

A Sensitivity Analysis of an Inverted Pendulum Balance Control Model.

PubMed

Pasma, Jantsje H; Boonstra, Tjitske A; van Kordelaar, Joost; Spyropoulou, Vasiliki V; Schouten, Alfred C

2017-01-01

Balance control models are used to describe balance behavior in health and disease. We identified the unique contribution and relative importance of each parameter of a commonly used balance control model, the Independent Channel (IC) model, to identify which parameters are crucial to describe balance behavior. The balance behavior was expressed by transfer functions (TFs), representing the relationship between sensory perturbations and body sway as a function of frequency, in terms of amplitude (i.e., magnitude) and timing (i.e., phase). The model included an inverted pendulum controlled by a neuromuscular system, described by several parameters. Local sensitivity of each parameter was determined for both the magnitude and phase using partial derivatives. Both the intrinsic stiffness and proportional gain shape the magnitude at low frequencies (0.1-1 Hz). The derivative gain shapes the peak and slope of the magnitude between 0.5 and 0.9 Hz. The sensory weight influences the overall magnitude, and does not have any effect on the phase. The effect of the time delay becomes apparent in the phase above 0.6 Hz. The force feedback parameters and intrinsic stiffness have a small effect compared with the other parameters. All parameters shape the TF magnitude and phase and therefore play a role in the balance behavior. The sensory weight, time delay, derivative gain, and the proportional gain have a unique effect on the TFs, while the force feedback parameters and intrinsic stiffness contribute less. More insight in the unique contribution and relative importance of all parameters shows which parameters are crucial and critical to identify underlying differences in balance behavior between different patient groups.

Validation of the Inverted Pendulum Model in standing for transtibial prosthesis users.

PubMed

Rusaw, David F; Ramstrand, Simon

2016-01-01

Often in balance assessment variables associated with the center of pressure are used to draw conclusions about an individual's balance. Validity of these conclusions rests upon assumptions that movement of the center of pressure is inter-dependent on movement of the center of mass. This dependency is mechanical and is referred to as the Inverted Pendulum Model. The following study aimed to validate this model both kinematically and kinetically, in transtibial prosthesis users and a control group. Prosthesis users (n=6) and matched control participants (n=6) stood quietly while force and motion data were collected under three conditions (eyes-open, eyes-closed, and weight-bearing feedback). Correlation coefficients were used to investigate the relationships between height and excursion of markers and center of masses in mediolateral/anteroposterior-directions, difference between center of pressure and center of mass and the center of mass acceleration in mediolateral/anteroposterior directions, magnitude of mediolateral/anteroposterior-component forces and center of mass acceleration, angular position of ankle and excursion in mediolateral/anteroposterior-directions, and integrated force signals. Results indicate kinematic validity of similar magnitudes (mean (SD) marker-displacement) between prosthesis users and control group for mediolateral- (r=0.77 (0.17); 0.74 (0.19)) and anteroposterior-directions (r=0.88 (0.18); 0.88 (0.19)). Correlation between difference of center of pressure and center of mass and the center of mass acceleration was negligible on the prosthetic side (r = 0.08 (0.06)) vs. control group (r=-0.51(0.13)). Results indicate kinematic validity of the Inverted Pendulum Model in transtibial prosthesis users but kinetic validity is questionable, particularly on the side with a prosthesis. Copyright © 2015 Elsevier Ltd. All rights reserved.

9. BUILDING NO. 620B, FRICTION PENDULUM BUILDING. 29FOOT DROP TOWER ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

9. BUILDING NO. 620-B, FRICTION PENDULUM BUILDING. 29-FOOT DROP TOWER SITS BEHIND BLAST SHIELD IN FRONT OF BUILDING. - Picatinny Arsenal, 600 Area, Test Areas District, State Route 15 near I-80, Dover, Morris County, NJ

Acceleration of neutrons in a scheme of a tautochronous mathematical pendulum (physical principles)

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

Rivlin, Lev A

We consider the physical principles of neutron acceleration through a multiple synchronous interaction with a gradient rf magnetic field in a scheme of a tautochronous mathematical pendulum. (laser applications and other aspects of quantum electronics)

The Slinky Wilberforce pendulum: A simple coupled oscillator

NASA Astrophysics Data System (ADS)

Mewes, Matthew

2014-03-01

The Wilberforce pendulum is an effective classroom demonstration of coupled oscillations and the beat-like behavior that arises in weakly coupled tuned oscillators. We describe a simple and inexpensive version constructed from a Slinky spring toy and a soup can.

Magnetic shielding in a low temperature torsion pendulum experiment. [superconducting cylinders for attenuation earth field

NASA Technical Reports Server (NTRS)

Phillips, P. R.

1979-01-01

A new type of ether drift experiment searches for anomalous torques on a permanent magnet. A torsion pendulum is used at liquid helium temperature, so that superconducting cylinders can be used to shield magnetic fields. Lead shields attenuate the earth's field, while Nb-Sn shields fastened to the pendulum contain the fields of the magnet. The paper describes the technique by which the earth's field can be reduced below 0.0001 G while simultaneously the moment of the magnet can be reduced by a factor 7 x 10 to the 4th.

Non-extraction treatment of severe crowding with pendulum appliance.

PubMed

Gandikota, Chandrasekhar; Venkata, Yudhister Palla; Challa, Padmalatha; Juvvadi, Shubhaker Rao

2013-07-01

An extraction case was planned for non-extraction treatment using pendulum appliance and the effect of appliance was evaluated in a 14-year-old girl with a severe maxillary and mandibular crowding followed by non-extraction fixed appliance preadjusted edgewise appliance mechanotherapy. Total treatment time was for 22 months. The obtuse nasolabial angle was maintained intact. Correction of crowding, co-ordinated arch forms was achieved with molar distalization. The impetus on soft-tissue paradigm is stressed in this case report and pendulum appliance can indeed boost our clinical acumen and swing our priorities toward non-extraction treatment.

What Makes the Foucault Pendulum Move among the Stars?

NASA Astrophysics Data System (ADS)

Phillips, Norman

2004-11-01

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 respect to the stars. Two simple mechanical principles describe why the path of oscillation is fixed only at the poles; the principle of centripetal acceleration and the principle of conservation of angular momentum. A sky map is used to describe the elegant path among the stars produced by these principles.

Long period nodal motion of sun synchronous orbits

NASA Technical Reports Server (NTRS)

Duck, K. I.

1975-01-01

An approximative model is formulated for assessing these perturbations that significantly affect long term modal motion of sun synchronous orbits. Computer simulations with several independent computer programs consider zonal and tesseral gravitational harmonics, third body gravitational disturbances induced by the sun and the moon, and atmospheric drag. A pendulum model consisting of evenzonal harmonics through order 4 and solar gravity dominated nodal motion approximation. This pendulum motion results from solar gravity inducing an inclination oscillation which couples into the nodal precession induced by the earth's oblateness. The pendulum model correlated well with simulations observed flight data.

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.

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.

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.

Technical strategy of triple jump: differences of inverted pendulum model between hop-dominated and balance techniques.

PubMed

Fujibayashi, Nobuaki; Otsuka, Mitsuo; Yoshioka, Shinsuke; Isaka, Tadao

2017-10-24

The present study aims to cross-sectionally clarify the characteristics of the motions of an inverted pendulum model, a stance leg, a swing leg and arms in different triple-jumping techniques to understand whether or not hop displacement is relatively longer rather than step and jump displacements. Eighteen male athletes performed the triple jump with a full run-up. Based on the technique of the jumpers, they were classified as hop-dominated (n = 10) or balance (n = 8) jumpers. The kinematic data were calculated using motion capture and compared between the two techniques using the inverted pendulum model. The hop-dominated jumpers had a significantly longer hop displacement and faster vertical centre-of-mass (COM) velocity of their whole body at hop take-off, which was generated by faster rotation behaviours of inverted pendulum model and faster swinging behaviours of arms. Conversely, balance jumpers had a significantly longer jump displacement and faster horizontal COM velocity of their whole body at take-off, which was generated by a stiffer inverted pendulum model and stance leg. The results demonstrate that hop-dominated and balance jumpers enhanced each dominated-jump displacement using different swing- and stance-leg motions. This information may help to enhance the actual displacement of triple jumpers using different jumping techniques.

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.

Decoupling the structure from the ground motion during earthquakes by employing friction pendulums

NASA Astrophysics Data System (ADS)

Gillich, G. R.; Iancu, V.; Gillich, N.; Korka, Z. I.; Chioncel, C. P.; Hatiegan, C.

2018-01-01

Avoiding dynamic loads on structures during earthquakes is an actual issue since seismic actions can harm or destroy the built environment. Several attempts to prevent this are possible, the essence being to decouple the structure from the ground motion during earthquakes and preventing in this way large deflections and high accelerations. A common approach is the use of friction pendulums, with cylindrical or spherical surfaces but not limited to that, inserted between the ground and the structure, respectively between the pillar and the superstructure. This type of bearings permits small pendulum motion and in this way, earthquake-induced displacements that occur in the bearings are not integrally transmitted to the structure. The consequence is that the structure is subject to greatly reduced lateral loads and shaking movements. In the experiments, conducted to prove the efficiency of the friction pendulums, we made use of an own designed and manufactured shaking table. Two types of sliding surfaces are analyzed, one polynomial of second order (i.e. circular) and one of a superior order. For both pendulum types, analytical models were developed. The results have shown that the structure is really decoupled from the ground motion and has a similar behaviour as that described by the analytic model.

Acceleration control system for semi-active in-car crib with joint application of regular and inverted pendulum mechanisms

NASA Astrophysics Data System (ADS)

Kawashima, T.

2016-09-01

To reduce the risk of injury to an infant in an in-car crib (or in a child safety bed) collision shock during a car crash, it is necessary to maintain a constant force acting on the crib below a certain allowable value. To realize this objective, we propose a semi-active in-car crib system with the joint application of regular and inverted pendulum mechanisms. The arms of the proposed crib system support the crib like a pendulum while the pendulum system itself is supported like an inverted pendulum by the arms. In addition, the friction torque of each arm is controlled using a brake mechanism that enables the proposed in-car crib to decrease the acceleration of the crib gradually and maintain it around the target value. This system not only reduces the impulsive force but also transfers the force to the infant's back using a spin control system, i.e., the impulse force acts is made to act perpendicularly on the crib. The spin control system was developed in our previous work. This work focuses on the acceleration control system. A semi-active control law with acceleration feedback is introduced, and the effectiveness of the system is demonstrated using numerical simulation and model experiment.

A method for the determination of the coefficient of rolling friction using cycloidal pendulum

NASA Astrophysics Data System (ADS)

Ciornei, M. C.; Alaci, S.; Ciornei, F. C.; Romanu, I. C.

2017-08-01

The paper presents a method for experimental finding of coefficient of rolling friction appropriate for biomedical applications based on the theory of cycloidal pendulum. When a mobile circle rolls over a fixed straight line, the points from the circle describe trajectories called normal cycloids. To materialize this model, it is sufficient that a small region from boundary surfaces of a moving rigid body is spherical. Assuming pure rolling motion, the equation of motion of the cycloidal pendulum is obtained - an ordinary nonlinear differential equation. The experimental device is composed by two interconnected balls rolling over the material to be studied. The inertial characteristics of the pendulum can be adjusted via weights placed on a rod. A laser spot oscillates together to the pendulum and provides the amplitude of oscillations. After finding the experimental parameters necessary in differential equation of motion, it can be integrated using the Runge-Kutta of fourth order method. The equation was integrated for several materials and found values of rolling friction coefficients. Two main conclusions are drawn: the coefficient of rolling friction influenced significantly the amplitude of oscillation but the effect upon the period of oscillation is practically imperceptible. A methodology is proposed for finding the rolling friction coefficient and the pure rolling condition is verified.

Apparatus for Teaching Physics: A Very Short, Portable Foucault Pendulum.

ERIC Educational Resources Information Center

Kruglak, Haym

1983-01-01

Describes the construction of a small (portable), inexpensive, and easy to build Foucault pendulum. Includes photographs of the apparatus, a schematic of the electrical circuit used, and discussion of the amount of accuracy to be expected during classroom investigation. (JM)

Viscous-pendulum damper suppresses structural vibrations

NASA Technical Reports Server (NTRS)

Reed, W. H., III

1964-01-01

The viscous pendulum damper consists of a cylinder containing round trays on which round lead slugs rest. When assembled, the container is filled with a viscous liquid and attached, with axis vertical, to the structure. The device permits varying the damping of structural vibrations.

29 CFR Appendix E to Subpart M of... - Sample Fall Protection Plan

Code of Federal Regulations, 2014 CFR

2014-07-01

... edge of the floor or beam and swing the worker like a pendulum until the line has moved to a position... points. Accompanying this pendulum swing is a lowering of the worker, with the attendant danger that he...

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)

Learning an Intermittent Control Strategy for Postural Balancing Using an EMG-Based Human-Computer Interface

PubMed Central

Asai, Yoshiyuki; Tateyama, Shota; Nomura, Taishin

2013-01-01

It has been considered that the brain stabilizes unstable body dynamics by regulating co-activation levels of antagonist muscles. Here we critically reexamined this established theory of impedance control in a postural balancing task using a novel EMG-based human-computer interface, in which subjects were asked to balance a virtual inverted pendulum using visual feedback information on the pendulum's position. The pendulum was actuated by a pair of antagonist joint torques determined in real-time by activations of the corresponding pair of antagonist ankle muscles of subjects standing upright. This motor-task raises a frustrated environment; a large feedback time delay in the sensorimotor loop, as a source of instability, might favor adopting the non-reactive, preprogrammed impedance control, but the ankle muscles are relatively hard to co-activate, which hinders subjects from adopting the impedance control. This study aimed at discovering how experimental subjects resolved this frustrated environment through motor learning. One third of subjects adapted to the balancing task in a way of the impedance-like control. It was remarkable, however, that the majority of subjects did not adopt the impedance control. Instead, they acquired a smart and energetically efficient strategy, in which two muscles were inactivated simultaneously at a sequence of optimal timings, leading to intermittent appearance of periods of time during which the pendulum was not actively actuated. Characterizations of muscle inactivations and the pendulum¡Çs sway showed that the strategy adopted by those subjects was a type of intermittent control that utilizes a stable manifold of saddle-type unstable upright equilibrium that appeared in the state space of the pendulum when the active actuation was turned off. PMID:23717398

Harvesting wind energy to detect weak signals using mechanical stochastic resonance.

PubMed

Breen, Barbara J; Rix, Jillian G; Ross, Samuel J; Yu, Yue; Lindner, John F; Mathewson, Nathan; Wainwright, Elliot R; Wilson, Ian

2016-12-01

Wind is free and ubiquitous and can be harnessed in multiple ways. We demonstrate mechanical stochastic resonance in a tabletop experiment in which wind energy is harvested to amplify weak periodic signals detected via the movement of an inverted pendulum. Unlike earlier mechanical stochastic resonance experiments, where noise was added via electrically driven vibrations, our broad-spectrum noise source is a single flapping flag. The regime of the experiment is readily accessible, with wind speeds ∼20 m/s and signal frequencies ∼1 Hz. We readily obtain signal-to-noise ratios on the order of 10 dB.

Are the initial frequency-modulated components of the mustached bat's biosonar pulses important for ranging?

PubMed

Fitzpatrick, D C; Suga, N; Misawa, H

1991-12-01

1. FM-FM neurons in the auditory cortex of the mustached bat, Pteronotus parnellii, are specialized to process target range. They respond when the terminal frequency-modulated component (TFM) of a biosonar pulse is paired with the TFM of the echo at a particular echo delay. Recently, it has been suggested that the initial FM components (IFMs) of biosonar signals may also be important for target ranging. To examine the possible role of IFMs in target ranging, we characterized the properties of IFMs and TFMs in biosonar pulses emitted by bats swung on a pendulum. We then studied responses of FM-FM neurons to synthesized biosonar signals containing IFMs and TFMs. 2. The mustached bat's biosonar signal consists of four harmonics, of which the second (H2) is the most intense. Each harmonic has an IFM in addition to a constant-frequency component (CF) and a TFM. Therefore each pulse potentially consists of 12 components, IFM1-4, CF1-4, and TFM1-4. The IFM sweeps up while the TFM sweeps down. 3. The IFM2 and TFM2 depths (i.e., bandwidths) were measured in 217 pulses from four animals. The mean IFM2 depth was much smaller than the mean TFM2 depth, 2.87 +/- 1.52 (SD) kHz compared with 16.27 +/- 1.08 kHz, respectively. The amplitude of the IFM2 continuously increased throughout its duration and was always less than the CF2 amplitude, whereas the TFM2 was relatively constant in amplitude over approximately three-quarters of its duration and was often the most intense part of the pulse. The maximum amplitude of the IFM2 was, on average, 11 dB smaller than that of the TFM2. Because range resolution increases with depth and the maximum detectable range increases with signal amplitude, the IFMs are poorly suited for ranging compared with the TFMs. 4. FM-FM neurons (n = 77) did not respond or responded very poorly to IFMs with depths and intensities similar to those emitted on the pendulum. The mean IFM2 depth at which a just-noticeable response appeared was 4.48 +/- 1.98 kHz. Only 14% of the pulses emitted on the pendulum had IFM2 depths that exceeded the mean IFM2 depth threshold of FM-FM neurons. 5. Most FM-FM neurons responded to IFMs that had depths comparable with those of TFMs. However, when all parameters were adjusted to optimize the response to TFMs and then readjusted to maximize the response to IFMs, 52% of 27 neurons tested responded significantly better to the optimal TFMs than to the optimal IFMs (P less than 0.05, t test).(ABSTRACT TRUNCATED AT 400 WORDS)

LETTERS AND COMMENTS: Note on the 'log formulae' for pendulum motion valid for any amplitude

NASA Astrophysics Data System (ADS)

Qing-Xin, Yuan; Pei, Ding

2010-01-01

In this note, we present an improved approximation to the solution of Lima (2008 Eur. J. Phys. 29 1091), which decreases the maximum relative error from 0.6% to 0.084% in evaluating the exact pendulum period.

Extraordinary Oscillations of an Ordinary Forced Pendulum

ERIC Educational Resources Information Center

Butikov, Eugene I.

2008-01-01

Several well-known and newly discovered counterintuitive regular and chaotic modes of the sinusoidally driven rigid planar pendulum are discussed and illustrated by computer simulations. The software supporting the investigation offers many interesting predefined examples that demonstrate various peculiarities of this famous physical model.…

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.

Influence of Partial Solar Eclipse 2016 on the surface gravity acceleration using photogate sensor on Kater's reversible pendulum

NASA Astrophysics Data System (ADS)

Nugraha, M. G.; Saepuzaman, D.; Sholihat, F. N.; Ramayanti, S.; Setyadin, A. H.; Ferahenki, A. R.; Samsudin, A.; Utama, J. A.; Susanti, H.; Kirana, K. H.

2016-11-01

This study was conducted to determine the Earth's surface gravitational acceleration (g) prior to, during, and after a partial solar eclipse. Data was collected in Basic Physics Laboratory Universitas Pendidikan Indonesia, Bandung with coordinates S 6°51'48", E 107°35'40" for three days on March 8 - 10, 2016, in time interval measurement from 6 a.m. to 9 a.m. This research used a standard pendulum, Kater's reversible pendulum, which deviated less than 3° so that the motion can be regarded harmonics oscillation. The period of pendulum oscillation motion is measured by a light sensor (photogate sensor) with accuracy until 10-13 seconds. The data analysis shows that there is small difference value of gravity acceleration at the Earth's surface from three days of observation, i.e. in the order of 10-3 ms-2. It means, there is a changes in the Earth's surface gravitational acceleration (g) due to the partial solar eclipse but not significant.

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.

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.

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,…

A passive pendulum wobble damper for a low spin rate Jupiter flyby spacecraft

NASA Technical Reports Server (NTRS)

Fowler, R. C.

1972-01-01

When the spacecraft has a low spin rate and precise pointing requirements, the wobble angle must be damped in a time period equivalent to a very few wobble cycles. The design, analysis, and test of a passive pendulum wobble damper are described.

Frozen Pendulum?

ERIC Educational Resources Information Center

Barker, Bernard

2012-01-01

This article examines the New Labour legacy in education, reviews the arguments of "The Pendulum Swings" in the light of contributions to this themed issue, examines early Coalition policymaking, and recommends four principles that should guide the search for a new approach to school improvement. Recent initiatives are found to be a…

Deterrence and Engagement: A Blended Strategic Approach to a Resurgent Russia

DTIC Science & Technology

2016-04-15

increasing the alliances’ hard power projection to contain and deter further aggression. This strategic approach represents an extreme pendulum ...This strategic approach represents an extreme pendulum swing that is a polar opposite of the U.S. administration’s 2009 approach to ‘Reset’ relations

Rendering the "Not-So-Simple" Pendulum Experimentally Accessible.

ERIC Educational Resources Information Center

Jackson, David P.

1996-01-01

Presents three methods for obtaining experimental data related to acceleration of a simple pendulum. Two of the methods involve angular position measurements and the subsequent calculation of the acceleration while the third method involves a direct measurement of the acceleration. Compares these results with theoretical calculations and…

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

Reinforcement learning for stabilizing an inverted pendulum naturally leads to intermittent feedback control as in human quiet standing.

PubMed

Michimoto, Kenjiro; Suzuki, Yasuyuki; Kiyono, Ken; Kobayashi, Yasushi; Morasso, Pietro; Nomura, Taishin

2016-08-01

Intermittent feedback control for stabilizing human upright stance is a promising strategy, alternative to the standard time-continuous stiffness control. Here we show that such an intermittent controller can be established naturally through reinforcement learning. To this end, we used a single inverted pendulum model of the upright posture and a very simple reward function that gives a certain amount of punishments when the inverted pendulum falls or changes its position in the state space. We found that the acquired feedback controller exhibits hallmarks of the intermittent feedback control strategy, namely the action of the feedback controller is switched-off intermittently when the state of the pendulum is located near the stable manifold of the unstable saddle-type upright equilibrium of the inverted pendulum with no active control: this action provides an opportunity to exploit transiently converging dynamics toward the unstable upright position with no help of the active feedback control. We then speculate about a possible physiological mechanism of such reinforcement learning, and suggest that it may be related to the neural activity in the pedunculopontine tegmental nucleus (PPN) of the brainstem. This hypothesis is supported by recent evidence indicating that PPN might play critical roles for generation and regulation of postural tonus, reward prediction, as well as postural instability in patients with Parkinson's disease.

Figuring the Acceleration of the Simple Pendulum

NASA Astrophysics Data System (ADS)

Lieberherr, Martin

2011-12-01

The centripetal acceleration has been known since Huygens' (1659) and Newton's (1684) time.1,2 The physics to calculate the acceleration of a simple pendulum has been around for more than 300 years, and a fairly complete treatise has been given by C. Schwarz in this journal.3 But sentences like "the acceleration is always directed towards the equilibrium position" beside the picture of a swing on a circular arc can still be found in textbooks, as e.g. in Ref. 4. Vectors have been invented by Grassmann (1844)5 and are conveniently used to describe the acceleration in curved orbits, but acceleration is more often treated as a scalar with or without sign, as the words acceleration/deceleration suggest. The component tangential to the orbit is enough to deduce the period of the simple pendulum, but it is not enough to discuss the forces on the pendulum, as has been pointed out by Santos-Benito and A. Gras-Marti.6 A suitable way to address this problem is a nice figure with a catch for classroom discussions or homework. When I plotted the acceleration vectors of the simple pendulum in their proper positions, pictures as in Fig. 1 appeared on the screen. The endpoints of the acceleration vectors, if properly scaled, seemed to lie on a curve with a familiar shape: a cardioid. Is this true or just an illusion?

Fact Sheet: FY2017 National Defense Authorization Act (NDAA) DOD Reform Proposals

DTIC Science & Technology

2016-05-25

this critical organizational framework, while still preserving its spirit and intent. For example, we can see in some areas how the pendulum between...or where subsequent world events suggest nudging the pendulum further, as in taking more steps to strengthen the capability of the Chairman and the

49 CFR 572.137 - Test conditions and instrumentation.

Code of Federal Regulations, 2011 CFR

2011-10-01

...—Class 1000 (2) Neck: (i) Forces—Class 1000 (ii) Moments—Class 600 (iii) Pendulum acceleration—Class 180... and pendulum accelerations—Class 180 (iii) Sternum deflection—Class 600 (iv) Forces—Class 1000 (v...—Class 180 (6) Femur forces and knee pendulum—Class 600 (n) Coordinate signs for instrumentation polarity...

49 CFR 572.137 - Test conditions and instrumentation.

Code of Federal Regulations, 2010 CFR

2010-10-01

...—Class 1000 (2) Neck: (i) Forces—Class 1000 (ii) Moments—Class 600 (iii) Pendulum acceleration—Class 180... and pendulum accelerations—Class 180 (iii) Sternum deflection—Class 600 (iv) Forces—Class 1000 (v...—Class 180 (6) Femur forces and knee pendulum—Class 600 (n) Coordinate signs for instrumentation polarity...

49 CFR 572.137 - Test conditions and instrumentation.

Code of Federal Regulations, 2013 CFR

2013-10-01

...—Class 1000 (2) Neck: (i) Forces—Class 1000 (ii) Moments—Class 600 (iii) Pendulum acceleration—Class 180... and pendulum accelerations—Class 180 (iii) Sternum deflection—Class 600 (iv) Forces—Class 1000 (v...—Class 180 (6) Femur forces and knee pendulum—Class 600 (n) Coordinate signs for instrumentation polarity...

49 CFR 572.137 - Test conditions and instrumentation.

Code of Federal Regulations, 2014 CFR

2014-10-01

...—Class 1000 (2) Neck: (i) Forces—Class 1000 (ii) Moments—Class 600 (iii) Pendulum acceleration—Class 180... and pendulum accelerations—Class 180 (iii) Sternum deflection—Class 600 (iv) Forces—Class 1000 (v...—Class 180 (6) Femur forces and knee pendulum—Class 600 (n) Coordinate signs for instrumentation polarity...

49 CFR 572.137 - Test conditions and instrumentation.

Code of Federal Regulations, 2012 CFR

2012-10-01

...—Class 1000 (2) Neck: (i) Forces—Class 1000 (ii) Moments—Class 600 (iii) Pendulum acceleration—Class 180... and pendulum accelerations—Class 180 (iii) Sternum deflection—Class 600 (iv) Forces—Class 1000 (v...—Class 180 (6) Femur forces and knee pendulum—Class 600 (n) Coordinate signs for instrumentation polarity...

New Approaches to Data Acquisitions in a Torsion Pendulum Experiment

ERIC Educational Resources Information Center

Jiang, Daya; Xiao, Jinghua; Li, Haihong; Dai, Qionglin

2007-01-01

In this paper, two simple non-contact and cost-effective methods to acquire data in the student laboratory are applied to investigate the motion of a torsion pendulum. The first method is based on a Hall sensor, while the second makes use of an optical mouse.

Recurrence Effects in the Parametric Spring Pendulum.

ERIC Educational Resources Information Center

Falk, Lars

1978-01-01

Gives a perturbation analysis to recurrence effects of the spring pendulum. The recurrence depends on two conservation laws which determine the motion in an intermediate region; oscillations outside this region are unstable and must return. Gives the relation to Fermi-Pasta-Ulam problem together with the explicit solution. (Author/GA)

Soup-Can Pendulum

ERIC Educational Resources Information Center

Peters, Randall D.

2004-01-01

In these studies, a vegetable can containing fluid was swung as a pendulum by supporting its end-lips with a pair of knife edges. The motion was measured with a capacitive sensor and the logarithmic decrement in free decay was estimated from computer-collected records. Measurements performed with nine different homogeneous liquids, distributed…

A Rolling Pendulum Bob: Conservation of Energy and Partitioning of Kinetic Energy.

ERIC Educational Resources Information Center

Helrich, Carl; Lehman, Thomas

1979-01-01

Describes a pendulum in which the spherical bob can roll on a track of the same arc as it swings when suspended by a cord. Comparison of the motion in the two mentioned cases shows the effect of rotational kinetic energy when the bob rolls. (GA)