Truly nonlinear oscillations: harmonic balance, parameter expansions, iteration, and averaging methods
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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World Scientific
©2010
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| Beschreibung: | Includes bibliographical references and index 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 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 |
| Beschreibung: | 1 Online-Ressource (xxi, 238 pages) |
| ISBN: | 9789814291651 9789814291668 981429165X 9814291668 |
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| 245 | 1 | 0 | |a Truly nonlinear oscillations |b harmonic balance, parameter expansions, iteration, and averaging methods |c Ronald E. Mickens |
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| 500 | |a Includes bibliographical references and index | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
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| 650 | 4 | |a Nonlinear oscillations | |
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Datensatz im Suchindex
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| institution | BVB |
| isbn | 9789814291651 9789814291668 981429165X 9814291668 |
| language | English |
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| spelling | Mickens, Ronald E. Verfasser aut Truly nonlinear oscillations harmonic balance, parameter expansions, iteration, and averaging methods Ronald E. Mickens Singapore World Scientific ©2010 1 Online-Ressource (xxi, 238 pages) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references and index 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 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 Parameter Mathematics MATHEMATICS / General bisacsh Mathematik Approximation theory Nonlinear oscillations http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=340700 Aggregator Volltext |
| spellingShingle | Mickens, Ronald E. Truly nonlinear oscillations harmonic balance, parameter expansions, iteration, and averaging methods Parameter Mathematics MATHEMATICS / General bisacsh Mathematik Approximation theory Nonlinear oscillations |
| title | Truly nonlinear oscillations harmonic balance, parameter expansions, iteration, and averaging methods |
| title_auth | Truly nonlinear oscillations harmonic balance, parameter expansions, iteration, and averaging methods |
| title_exact_search | Truly nonlinear oscillations harmonic balance, parameter expansions, iteration, and averaging methods |
| title_full | Truly nonlinear oscillations harmonic balance, parameter expansions, iteration, and averaging methods Ronald E. Mickens |
| title_fullStr | Truly nonlinear oscillations harmonic balance, parameter expansions, iteration, and averaging methods Ronald E. Mickens |
| title_full_unstemmed | Truly nonlinear oscillations harmonic balance, parameter expansions, iteration, and averaging methods Ronald E. Mickens |
| title_short | Truly nonlinear oscillations |
| title_sort | truly nonlinear oscillations harmonic balance parameter expansions iteration and averaging methods |
| title_sub | harmonic balance, parameter expansions, iteration, and averaging methods |
| topic | Parameter Mathematics MATHEMATICS / General bisacsh Mathematik Approximation theory Nonlinear oscillations |
| topic_facet | Parameter Mathematics MATHEMATICS / General Mathematik Approximation theory Nonlinear oscillations |
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