Presents underlying principles and theories using an easily understood approach. Focuses specifically on those features of the problems in which nonlinearity results in a variety of distinctive new phenomena that can be treated by techniques both interesting and instructive in themselves and which do not require the use of sophisticated mathematics. Recent work discussed includes the endeavors of Levinson and Smith on the existence and uniqueness of the periodic solution in a general case of the self-excited type, Haag and Dorodnitsyn on asymptotic developments and quantities associated with relaxation oscillations. Along with 5 appendices containing rigorous existence and uniqueness proofs, readers are both implicitly and explicitly supplied with hints regarding new problems to be tackled plus numerous ideas and techniques that can be used to solve them.
Table of Contents
Free Vibrations of Undamped Systems with Nonlinear Restoring Forces.
Free Oscillations with Damping and the Geometry of Integral Curves.
Forced Oscillations of Systems with Nonlinear Restoring Force.
Hill's Equation and Its Application to the Study of the Stability of Nonlinear Oscillations.