Nonlinear Dynamics: The Richard Rand 50th Anniversary Volume
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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Stability of InPhase and OutofPhase Modes for
Perturbation Methods for Strongly Nonlinear Oscil
Momentum Transfer in TorqueFree Gyrostats
The Almost Complete Dynamics of the FitzHugh
Excitable Oscillators as Models for Central Pattern
Solitons Chaos and Modal Interactions in Periodic
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amplitude analysis analytical angular momentum approximate asymptotic axial beam behavior bifurcation diagrams brainstem branches buckling elements codimension coefficients computed constant corresponding damping defined differential equations displacement coupling dynamical systems elliptic functions energy equilibrium excitation experimental Figure fixed points force friction Guran gyrostat Hamiltonian homoclinic orbits in-phase mode initial conditions Journal layer Lie derivative Lie Transform limit cycle linear Lyapunov exponents maneuver Mathieu equation Mechanics method of averaging modal momentum sphere near-identity transformation NNMs Nonlinear Dynamics nutation obtained orbits order trig out-of-phase mode parameter periodic solution periodic system perturbation method phase portraits phase space phase-locked plane predicted R. H. Rand regions relaxation limit Relaxation Oscillations Richard Rand rotor separatrix shown single-rotor singularity Solitons spatial spinup torques stability transition stationary-platform stick-slip structure theory trajectories transition curve uncoupled unperturbed unstable values variables variational equation vector velocity vibrations wave zero