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Truly nonlinear oscillations : harmonic balance, parameter expansions, iteration, and averaging methods /
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 a...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, NJ :
World Scientific,
©2010.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1. Background and general comments. 1.1. Truly nonlinear functions. 1.2. Truly nonlinear oscillators. 1.3. General remarks. 1.4. Scaling and dimensionless form of differential equations. 1.5. Exactly solvable TNL oscillators. 1.6. Overview of TNL oscillator methods. 1.7. Discussion
- 2. Establishing periodicity. 2.1. Phase-space. 2.2. Application of phase-space methods. 2.3. Dissipative systems : energy methods. 2.4. Resume
- 3. Harmonic balance. 3.1. Direct harmonic balance : methodology. 3.2. Worked examples. 3.3. Rational approximations. 3.4. Worked examples. 3.5. Third-order equations. 3.6. Resume
- 4. Parameter expansions. 4.1. Introduction. 4.2. Worked examples. 4.3. Discussion
- 5. Iteration methods. 5.1. General methodology. 5.2. Worked examples : direct iteration. 5.3. Worked examples : extended iteration. 5.4. Discussion
- 6. Averaging methods. 6.1. Elementary TNL averaging methods. 6.2. Worked examples. 6.3. Cveticanin's averaging method. 6.4. Worked examples. 6.5. Chronology of averaging methods. 6.6. Comments
- 7. Comparative analysis. 7.1. Purpose. 7.2. x + x[symbol] = 0. 7.3. x + x[symbol] = 0. 7.4. x + x[symbol] = -2[symbol]. 7.5. x + x[symbol] = -2[symbol]. 7.6. x + x[symbol] = [symbol]. 7.7. x + x[symbol] = [symbol]. 7.8. General comments and calculation strategies. 7.9. Research problems.