Strongly Nonlinear Oscillators
Analytical Solutions
Seiten
2014
|
2014
Springer International Publishing (Verlag)
978-3-319-05271-7 (ISBN)
Springer International Publishing (Verlag)
978-3-319-05271-7 (ISBN)
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This book outlines an analytical solution procedure of the pure nonlinear oscillator system, offering a solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter. Includes exercises.
This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author's method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for professionals and engineers who apply these techniques to the field of nonlinear oscillations.
This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author's method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for professionals and engineers who apply these techniques to the field of nonlinear oscillations.
Introduction.- Nonlinear Oscillators.- Pure Nonlinear Oscillator.- Free Vibrations.- Oscillators with Time-Variable Parameters.- Forced Vibrations.- Two-Degree-Of-Freedom Oscillator.- Chaos in Oscillators.
From the book reviews:
"This book is devoted to analysis of solutions of the second-order ordinary differential equations (or systems) which describe oscillations of mechanical (and related) systems. ... the book can be recommended to engineers as a good source of methods and examples." (Henryk oladek, Mathematical Reviews, January, 2015)
| Reihe/Serie | Undergraduate Lecture Notes in Physics |
|---|---|
| Zusatzinfo | IX, 239 p. 74 illus., 12 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 393 g |
| Themenwelt | Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik |
| Schlagworte | Chaos in Oscillators • Deterministic Chaos • Non-ideal Mechanical System • Oscillators with Time-Variable Parameters • Oszillator • Solving Nonlinear Oscillator Equations • Strong Nonlinear Vibration • Two-Degree-Of-Freedom Oscillator • Waves and Oscillations |
| ISBN-10 | 3-319-05271-3 / 3319052713 |
| ISBN-13 | 978-3-319-05271-7 / 9783319052717 |
| Zustand | Neuware |
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