Noisy Pendulum, The

By: Moshe Gitterman

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Hardcover | 10 October 2008

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132 Pages

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15.9 x 23.8 x 1.5

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This book contains the general description of the mathematical pendulum subject to constant torque, periodic and random forces. The latter appear in additive and multiplicative form with their possible correlation. For the underdamped pendulum driven by periodic forces, a new phenomenon - deterministic chaos - comes into play, and the common action of this chaos and the influence of noise are taken into account. The inverted position of the pendulum can be stabilized either by periodic or random oscillations of the suspension axis or by inserting a spring into a rigid rod, or by their combination. The pendulum is one of the simplest nonlinear models, which has many applications in physics, chemistry, biology, medicine, communications, economics and sociology. A wide group of researchers working in these fields, along with students and teachers, will benefit from this book.

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Preface	p. v
Formulation of the Problem	p. 1
Mathematical pendulum	p. 1
Isomorphic models	p. 10
Brownian motion in a periodic potential	p. 10
Josephson junction	p. 10
Fluxon motion in superconductors	p. 11
Charge density waves (CDWs)	p. 11
Laser gyroscope	p. 12
Synchronization phenomena	p. 12
Parametric resonance in anisotropic systems	p. 12
The Frenkel-Kontorova model (FK)	p. 13
Solitons in optical lattices	p. 13
Noise	p. 13
White noise and colored noise	p. 13
Dichotomous noise	p. 15
Langevin and Fokker-Planck equations	p. 15
Overdamped Pendulum	p. 19
Deterministic motion	p. 19
Influence of noise	p. 20
Additive white noise	p. 21
Additive and multiplicative white noise	p. 23
Additive dichotomous noise	p. 30
Multiplicative dichotomous noise	p. 33
Joint action of multiplicative noise and additive noise	p. 34
Correlated additive noise and multiplicative noise	p. 37
Periodic driven force	p. 39
Deterministic equation	p. 39
Influence of noise	p. 40
Deterministic telegraph signal	p. 41
Underdamped Pendulum	p. 43
Pendulum with constant torque	p. 43
Pendulum with multiplicative noise	p. 45
Pendulum with additive noise	p. 46
Damped pendulum subject to additive noise	p. 46
Damped pendulum subject to constant torque and noise	p. 47
Periodically driven pendulum	p. 49
Damped pendulum subject to constant torque, periodic force and noise	p. 52
Pendulum with oscillating suspension point	p. 53
Vertical oscillations	p. 53
Horizontal oscillations	p. 57
Pendulum with parametric damping	p. 57
Spring pendulum	p. 60
Resonance-type phenomena	p. 66
Stochastic resonance (SR)	p. 66
Absolute negative mobility (ANM)	p. 68
Ratchets	p. 68
Resonance activation (RA) and noise enhanced stability (NES)	p. 70
Deterministic Chaos	p. 71
General concepts	p. 71
Poincare sections and strange attractors	p. 72
Lyapunov exponent	p. 73
Correlation function	p. 73
Spectral analysis	p. 73
Period doubling and intermittency	p. 74
Transition to chaos	p. 75
Damped, periodically driven pendulum	p. 75
Driven pendulum subject to a periodic and constant torque	p. 79
Pendulum with vertically oscillating suspension point	p. 80
Pendulum with horizontally oscillating suspension point	p. 81
Pendulum with applied periodic force	p. 84
Spring pendulum	p. 86
Pendulum subject to two periodic fields	p. 87
Controlling chaos	p. 87
Erratic motion	p. 88
Vibrational resonance	p. 90
Inverted Pendulum	p. 93
Oscillations of the suspension axis	p. 93
The tilted parametric pendulum	p. 95
Random vibrations of the suspension axis	p. 98
Spring pendulum	p. 100
Spring pendulum driven by a periodic force	p. 101
Conclusions	p. 109
Bibliography	p. 113
Index	p. 119
Table of Contents provided by Ingram. All Rights Reserved.

Noisy Pendulum, The

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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