Regular and Chaotic Oscillations

✍ Scribed by Polina S. Landa (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2001
• Tongue: English
• Leaves: 400
• Series: Foundations of Engineering Mechanics
• Edition: 1
• Category: Library

✦ Synopsis

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 of the leading experts in the area. Among the up-to-date topics are synchronization and chaotization of self-oscillatory sy- stems, the influence of weak random vibration on modificati- on of characteristics and behavior of the non-linear systems etc. One of the purposes of the book is to convince the rea- ders of the necessity of a thorough study of this theory and to show that it can be very useful in engineering investiga- tions. The primary readers for this book are researchers working with different oscillatory processes, and both un- der-graduate and post-graduate students interested in a deep study of the general laws and applications of the theory of nonlinear oscillations. The instructors can find here new materials for lecturess and optinal courses.

✦ Table of Contents

Front Matter....Pages i-xii
Introduction....Pages 1-7
The main analytical methods of studies of nonlinear oscillations in near-conservative systems....Pages 9-23
Front Matter....Pages 25-25
General properties of autonomous dynamical systems....Pages 27-47
Examples of natural oscillations in systems with one degree of freedom....Pages 49-62
Natural oscillations in systems with many degrees of freedom. Normal oscillations....Pages 63-88
Self-oscillatory systems with one degree of freedom....Pages 89-106
Self-oscillatory systems with one and a half degrees of freedom....Pages 107-136
Examples of self-oscillatory systems with two or more degrees of freedom....Pages 137-160
Synchronization and chaotization of self-oscillatory systems by an external harmonic force....Pages 161-203
Interaction of two self-oscillatory systems. Synchronization and chaotization of self-oscillations....Pages 205-236
Interaction of three or more self-oscillatory systems....Pages 237-251
Front Matter....Pages 253-253
Oscillations of nonlinear systems excited by external periodic forces....Pages 255-288
Parametric excitation of oscillations....Pages 289-322
Changes in the dynamical behavior of nonlinear systems induced by high-frequency vibration or by noise....Pages 323-372
Back Matter....Pages 373-397

✦ Subjects

Appl.Mathematics/Computational Methods of Engineering;Theoretical and Applied Mechanics;Statistical Physics, Dynamical Systems and Complexity;Mechanics;Dynamical Systems and Ergodic Theory