Regular and Chaotic Oscillations
In the present book the modern theory of non-linear oscilla- tions both regular and chaotic, is set out, primarily, as applied to mechanical problems. The material is presented in a non-traditional manner with emphasizing of the new results of the theory otained partially by the author, who is one o...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2001, 2001
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| Edition: | 1st ed. 2001 |
| Series: | Foundations of Engineering Mechanics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. Introduction
- 1.1 The importance of oscillation theory for engineering mechanics
- 1.2 Classification of dynamical systems. Systems with conservation of phase volume and dissipative systems
- 1.3 Different types of mathematical models and their functions in studies of concrete systems
- 1.4 Phase space of autonomous dynamical systems and the number of degrees of freedom
- 1.5 The subject matter of the book
- 2. The main analytical methods of studies of nonlinear oscillations in near-conservative systems
- 2.1 The van der Pol method
- 2.2 The asymptotic Krylov-Bogolyubov method
- 2.3 The averaging method
- 2.4 The averaging method in systems incorporating fast and slow variables
- 2.5 The Whitham method
- I. Oscillations in Autonomous Dynamical Systems
- 3. General properties of autonomous dynamical systems
- 4. Examples of natural oscillations in systems with one degree of freedom
- 5. Natural oscillations in systems with many degrees of freedom. Normal oscillations
- 6. Self-oscillatory systems with one degree of freedom
- 7. Self-oscillatory systems with one and a half degrees of freedom
- 8. Examples of self-oscillatory systems with two or more degrees of freedom
- 9. Synchronization and chaotization of self-oscillatory systems by an external harmonic force
- 10. Interaction of two self-oscillatory systems. Synchronization and chaotization of self-oscillations
- 11. Interaction of three or more self-oscillatory systems
- II. Oscillations in Nonautonomous Systems
- 12. Oscillations of nonlinear systems excited by external periodic forces
- 13. Parametric excitation of oscillations
- 14. Changes in the dynamical behavior of nonlinear systems induced by high-frequency vibration or by noise
- A. Derivation of the approximate equation for the one-dimensional probability density
- References