03012nam 2200601 a 450 991045586140332120200520144314.01-282-76190-09786612761904981-4291-66-8(CKB)2490000000001797(EBL)731306(OCoLC)671655101(SSID)ssj0000430115(PQKBManifestationID)11284820(PQKBTitleCode)TC0000430115(PQKBWorkID)10452832(PQKB)10176812(MiAaPQ)EBC731306(WSP)00007561(Au-PeEL)EBL731306(CaPaEBR)ebr10422530(CaONFJC)MIL276190(EXLCZ)99249000000000179720091005d2010 uy 0engur|n|---|||||txtccrTruly nonlinear oscillations[electronic resource] harmonic balance, parameter expansions, iteration, and averaging methods /Ronald E. MickensSingapore ;Hackensack, NJ World Scientificc20101 online resource (260 p.)Description based upon print version of record.981-4291-65-X Includes bibliographical references and index.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 MethodAppendix H Discrete Models of Two TNL OscillatorsBibliography; IndexThis 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 direApproximation theoryNonlinear oscillationsElectronic books.Approximation theory.Nonlinear oscillations.511/.4Mickens Ronald E.1943-497093MiAaPQMiAaPQMiAaPQBOOK9910455861403321Truly nonlinear oscillations2287666UNINA