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Om Nonlinear Dynamics
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.Contents: Stability of In-Phase and Out-of-Phase Modes for a Pair of Linearly Coupled van der Pol Oscillators (D W Storti & P G Reinhall)Perturbation Methods for Strongly Nonlinear Oscillators Using Lie Transforms (V T Coppola)Momentum Transfer in Torque-Free Gyrostats (C D Hall)The (Almost) Complete Dynamics of the FitzHugh Nagumo Equations (D Armbruster)Excitable Oscillators as Models for Central Pattern Generators (D Taylor et al.)Solitons, Chaos and Modal Interactions in Periodic Structures (M A Davies & F C Moon)Two Applications of Nonlinear Normal Modes in Vibration Analysis (M E King et al. )Friction as a Nonlinearity in Dynamics: A Historical Review (B Fenny & A Guran)A Quasiperiodic Mathieu Equation (R Rand et al. )Readership: Engineers, applied mathematicians and physicists.Key Features:First comprehensive book on equivariant transversalityPresents general theories of equivariant steady state and Hopf bifurcation, including rather new results on bifurcation from relative equilibria and relative periodic orbitsContains sections on equivariant reversible systemsIntroduces a range of new geometric tools for the study of steady state and Hopf bifurcationIncludes exercises with many recent and useful examples given