scholarly journals The Lengthening Pendulum

1969 ◽  
Vol 9 (3-4) ◽  
pp. 331-336 ◽  
Author(s):  
A. Werner ◽  
C. J. Eliezer
Keyword(s):  
Simple Pendulum ◽  
Angular Amplitude

Some recent papers have revived interest in some questions concerning the motion of a simple pendulum which is oscillating with small angular amplitude under gravity, when the length of the pendulum changes with time in some prescribed manner.

Free Oscillations of a Damped Simple Pendulum: An Analog Simulation Experiment

2019 ◽  
Vol 01 (04) ◽  
pp. 1950015 ◽  
Author(s):  
Ivan Skhem Sawkmie ◽  
Mangal C. Mahato
Keyword(s):  
Harmonic Oscillator ◽  
Free Oscillation ◽  
Simulation Experiment ◽  
Free Oscillations ◽  
Analog Simulation ◽  
Simple Pendulum ◽  
Electronic Circuitry ◽  
Undergraduate Laboratory ◽  
Angular Amplitude ◽  
Theoretical Results

The frequency of free oscillation of a damped simple pendulum with large amplitude depends on its amplitude unlike the amplitude-independent frequency of oscillation of a damped simple harmonic oscillator. This aspect is not adequately emphasized in the undergraduate courses due to experimental and theoretical difficulties. We propose an analog simulation experiment to study the free oscillations of a simple pendulum that could be performed in an undergraduate laboratory. The needed sinusoidal potential is obtained approximately by using the available AD534 IC by suitably augmenting the electronic circuitry. To keep the circuit simple enough we restrict the initial angular amplitude of the simple pendulum to a maximum of [Formula: see text]. The results compare well qualitatively with the theoretical results. The small quantitative discrepancy is attributed to the inexact nature of the used “sinusoidal potential”.

Action-Minimizing Curves for Tonelli Lagrangians

2017 ◽  
Author(s):  
Alfonso Sorrentino
Keyword(s):  
Critical Value ◽  
The Other ◽  
Invariant Sets ◽  
Simple Pendulum ◽  
New Concepts ◽  
Peierls Barrier ◽  
Average Action

This chapter discusses the notion of action-minimizing orbits. In particular, it defines the other two families of invariant sets, the so-called Aubry and Mañé sets. It explains their main dynamical and symplectic properties, comparing them with the results obtained in the preceding chapter for the Mather sets. The relation between these new invariant sets and the Mather sets is described. As a by-product, the chapter introduces the Mañé's potential, Peierls' barrier, and Mañé's critical value. It discusses their properties thoroughly. In particular, it highlights how this critical value is related to the minimal average action and describes these new concepts in the case of the simple pendulum.

The Simple Pendulum

1913 ◽  
Vol 7 (108) ◽  
pp. 189
Author(s):  
G. Greenhill
Keyword(s):  
Simple Pendulum

The Nonlinear Simple Pendulum

1972 ◽  
Vol 79 (4) ◽  
pp. 348-355
Author(s):  
Fred Brauer
Keyword(s):  
Simple Pendulum

The Simple Pendulum at Any Amplitude

1956 ◽  
Vol 40 (331) ◽  
pp. 34
Author(s):  
P. J. Bulman
Keyword(s):  
Simple Pendulum

scholarly journals Tracking of pendulum using particle filter with residual resampling

2018 ◽  
Vol 7 (2.7) ◽  
pp. 12
Author(s):  
Penumarty Hiranmayi ◽  
Kola Sai Gowtham ◽  
S Koteswara Rao ◽  
V Gopi Tilak
Keyword(s):  
Monte Carlo ◽  
Kalman Filter ◽  
Particle Filter ◽  
Extended Kalman Filter ◽  
Horizontal Direction ◽  
Bayesian Filtering ◽  
Discrete State ◽  
Harmonic Motion ◽  
Simple Pendulum ◽  
Importance Resampling

The phenomenon of simple harmonic motion is more vigilantly explained using a simple pendulum. The angular motion of a pendulum is linear in nature. But the analysis of the motion along the horizontal direction is non-linear. To estimate this, several algorithms like the Kalman filter, Extended Kalman Filter etc. are adopted. Here in this paper, Particle filter is chosen which is a method to form Monte Carlo approximations to the solutions of Bayesian filtering equations. Sequential importance resampling based Particle filters are used where the filtering distributions are multi-nodal or consist of discrete state components since under these circumstances the Bayesian approximations do not always work well.

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