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This unique book provides a concise presentation of many of the fundamental strategies for calculating approximations to the oscillatory solutions of “truly nonlinear” (TNL) oscillator equations. The volume gives a general overview of the author's work on harmonic balance, iteration and combined linearization-averaging methods. However, full discussions are also presented on parameter expansion procedures and a first-order averaging technique for TNL oscillators. The calculational basis of each method is clarified by applying them to a set of standard TNL oscillator equations. This allows a direct comparison to be made among the various methods.
The book is self-contained and therefore suitable for both classroom use and self-study by students and professionals who desire to learn, understand, and apply these technique to the field of nonlinear oscillations.
Sample Chapter(s)
Chapter 1: Background and General Comments (255 KB)
Contents:
- Background and General Comments
- Establishing Periodicity
- Harmonic Balance
- Parameter Expansions
- Iteration Methods
- Averaging Methods
- Comparative Analysis
Readership: Researchers in approximation theory, differential equations and mechanical engineering.
