The Nonlinear Simple Pendulum

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

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 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.

A Simple Pendulum Energy Experiment

1944 ◽  
Vol 12 (4) ◽  
pp. 215-217
Author(s):  
Albert Burris ◽  
W. J. Hargrave
Keyword(s):  
Simple Pendulum
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