Truly nonlinear oscillations : harmonic balance, parameter expansions, iteration, and averaging methods / Ronald E. Mickens.

Format:

Book

Author/Creator:

Mickens, Ronald E., 1943-

Language:

English

Subjects (All):

Approximation theory.

Nonlinear oscillations.

Physical Description:

1 online resource (260 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; Hackensack, NJ : World Scientific, c2010.

Language Note:

English

Summary:

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 dire

Contents:

Preface; 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; Appendix B Gamma and Beta Functions; Appendix C Fourier Series; Appendix D Basic Theorems of the Theory of Second-Order Differential Equations; Appendix E Linear Second-Order Differential Equations; Appendix F Lindstedt-Poincar ́e Perturbation Method; Appendix G A Standard Averaging Method

Appendix H Discrete Models of Two TNL OscillatorsBibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786612761904

9781282761902

1282761900

9789814291668

9814291668

OCLC:

671655101