Nonlinear Dynamics: The Richard Rand 50th Anniversary Volume

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World Scientific, 1997 - Science - 229 pages
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This book is a collection of papers on the subject of nonlinear dynamics and its applications written by experts in this field. It offers the reader a sampling of exciting research areas in this fast-growing field. The topics covered include chaos, tools to analyze motions, fractal boundaries, dynamics of the Fitzhugh-Nagumo equation, structural control, separation of contaminations from signal of interest, parametric excitation, stochastic bifurcation, mode localization in repetitive structures, Toda lattice, transition from soliton to chaotic motion, nonlinear normal modes, noise perturbations of nonlinear dynamical systems, and phase locking of coupled limit cycle oscillators. Mathematical methods include Lie transforms, Monte Carlo simulations, stochastic calculus, perturbation methods and proper orthogonal decomposition. Applications include gyrodynamics, tether connected satellites, shell buckling, nonlinear circuits, volume oscillations of a large lake, systems with stick-slip friction, imperfect or disordered structures, overturning of rigid blocks, central pattern generators, flow induced oscillations, shape control and vibration suppression of elastic structures.All of these diverse contributions have a common thread: the world of nonlinear behavior. Although linear dynamics is an invaluable tool, there are many problems where nonlinear effects are essential. Some examples include bifurcation of solutions, stability of motion, the effects of large displacements, and subharmonic resonance. This book shows how nonlinear dynamics is currently being utilized and investigated. It will be of interest to engineers, applied mathematicians and physicists.
 

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Contents

Stability of InPhase and OutofPhase Modes for
1
Perturbation Methods for Strongly Nonlinear Oscil
24
Momentum Transfer in TorqueFree Gyrostats
60
The Almost Complete Dynamics of the FitzHugh
89
Excitable Oscillators as Models for Central Pattern
103
Solitons Chaos and Modal Interactions in Periodic
119
Two Applications of Nonlinear Normal Modes in
144
Friction as a Nonlinearity in Dynamics A Historical
168
A Quasiperiodic Mathieu Equation
203
Author Index
222
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