Nonlinear oscillations in physical systems

Many of today's most exciting questions in the physical and life sciences concern the behavior of nonlinear systems, especially the onset of chaotic behavior under deterministic conditions. Available for the first time in paperback, this book offers a fundamental explanation of nonlinear oscillations in physical systems. Originally intended for electrical engineers, this book remains an important reference for the increasing numbers of researchers studying nonlinear phenomena in physics, chemical engineering, biology, medicine, and other fields. All problems in mechanics are basically nonlinear from the outset, and the linearizations commonly practiced are approximating devices. Focusing attention on those features of problems where nonlinearity results in distinctive new phenomena, the author stresses the relationship between analysis and experiment.

Originally published in 1953 under title: Forced oscillations in non-linear systems.

Reprint. Originally published: New York : McGraw-Hill, ©1964.

pt. I. Principal methods of nonlinear analysis. Analytical methods -- Topological methods and graphical solutions -- Stability of nonlinear systems -- pt. II. Forced oscillations in steady states. Stability of periodic oscillations in second-order systems -- Harmonic oscillations -- Higher-harmonic oscillations -- Subharmonic oscillations -- pt. III. Forced oscillations in transient states. Harmonic oscillations -- Subharmonic oscillations -- Initial conditions leading to different types of periodic oscillations -- Almost periodic oscillations -- pt. IV. Self-oscillatory systems with external force. Entrainment of frequency -- Almost periodic oscillations -- Appendix I. Expansions of the Mathieu functions -- Appendix II. Unstable solutions of Hill's equation -- Appendix III. Unstable solutions for the extended form of Hill's equation -- Appendix IV. Stability criterion obtained by using the perturbation method -- Appendix V. Remarks concerning integral curves and singular points -- Appendix VI. Electronic synchronous switch.