"Truly Nonlinear Oscillations: Harmonic Balance, Parameter Expansions, Iteration, and Averaging Methods" by Ronald E. Mickens
World Scientific Publishing | 2010 | ISBN: 981429165X 9789814291651 | 260 pages | PDF | 14 MB
This 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.
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.
Contents List of Figures
List of Tables
1. Background and General Comments
2. Establishing Periodicity
3. Harmonic Balance
4. Parameter Expansions
5. Iteration Methods
6. Averaging Methods
7. Comparative Analysis
Appendix
A. Mathematical Relations
B. Gamma and Beta Functions
C. Fourier Series
D. Basic Theorems of the Theory of Second-Order Differential Equations
E. Linear Second-Order Differential Equations
F. Lindstedt-Poincare Perturbation Method
G. A Standard Averaging Method
H. Discrete Models of Two TNL Oscillators
Bibliography
Index
with TOC BookMarkLinks
Download File Size:13.45 MB
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