The noisy pendulum / Moshe Gitterman.

Format:

Book

Author/Creator:

Gitterman, M.

Language:

English

Subjects (All):

Pendulum.

Noise.

Mechanics.

Physics.

Physical Description:

1 online resource (132 p.)

Edition:

1st ed.

Place of Publication:

New Jersey : World Scientific, c2008.

Language Note:

English

Summary:

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 combinat

Contents:

Preface; Contents; 1. Formulation of the Problem; 1.1 Mathematical pendulum; 1.2 Isomorphicmodels; 1.2.1 Brownian motion in a periodic potential; 1.2.2 Josephson junction; 1.2.3 Fluxon motion in superconductors; 1.2.4 Charge density waves (CDWs); 1.2.5 Laser gyroscope; 1.2.6 Synchronization phenomena; 1.2.7 Parametric resonance in anisotropic systems; 1.2.8 The Frenkel-Kontorova model (FK); 1.2.9 Solitons in optical lattices; 1.3 Noise; 1.3.1 White noise and colored noise; 1.3.2 Dichotomous noise; 1.3.3 Langevin and Fokker-Planck equations; 2. Overdamped Pendulum; 2.1 Deterministic motion

2.2 Influence of noise2.2.1 Additive white noise; 2.2.2 Additive and multiplicative white noise; 2.2.3 Additive dichotomous noise; 2.2.4 Multiplicative dichotomous noise; 2.2.5 Joint action of multiplicative noise and additive noise; 2.2.6 Correlated additive noise and multiplicative noise; 2.3 Periodic driven force; 2.3.1 Deterministic equation; 2.3.2 Influence of noise; 2.3.3 Deterministic telegraph signal; 3. Underdamped Pendulum; 3.1 Pendulum with constant torque; 3.2 Pendulum with multiplicative noise; 3.3 Pendulum with additive noise; 3.3.1 Damped pendulum subject to additive noise

3.3.2 Damped pendulum subject to constant torque and noise3.4 Periodically driven pendulum; 3.5 Damped pendulum subject to constant torque, periodic force and noise; 3.6 Pendulum with oscillating suspension point; 3.6.1 Vertical oscillations; 3.6.2 Horizontal oscillations; 3.6.3 Pendulum with parametric damping; 3.7 Spring pendulum; 3.8 Resonance-type phenomena; 3.8.1 Stochastic resonance (SR); 3.8.2 Absolute negative mobility (ANM); 3.8.3 Ratchets; 3.8.4 Resonance activation (RA) and noise enhanced stability (NES); 4. Deterministic Chaos; 4.1 General concepts

4.1.1 Poincare sections and strange attractors4.1.2 Lyapunov exponent; 4.1.3 Correlation function; 4.1.4 Spectral analysis; 4.1.5 Period doubling and intermittency; 4.2 Transition to chaos; 4.2.1 Damped, periodically driven pendulum; 4.2.2 Driven pendulum subject to a periodic and constant torque; 4.2.3 Pendulum with vertically oscillating suspension point; 4.2.4 Pendulum with horizontally oscillating suspension point; 4.2.5 Pendulum with applied periodic force; 4.2.6 Spring pendulum; 4.3 Pendulum subject to two periodic fields; 4.3.1 Controlling chaos; 4.3.2 Erraticmotion

4.3.3 Vibrational resonance5. Inverted Pendulum; 5.1 Oscillations of the suspension axis; 5.2 The tilted parametric pendulum; 5.3 Random vibrations of the suspension axis; 5.4 Spring pendulum; 5.5 Spring pendulum driven by a periodic force; 6. Conclusions; Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 113-118) and index.

ISBN:

9789812833006

9812833005

OCLC:

747539689