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Regular and Chaotic Oscillations

  • Book
  • © 2001

Overview

Authors:
  1. Polina S. Landa

    1. Dept. of Physics, Moscow State University, Moscow, Russia

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  • Presented in a non-traditional manner with emphasis on the new result in the theory obtained partially by the author, who is one of the leading experts in the area
  • Includes modern topics such as synchronization and chaotization of self-oscillatory systems and the influence of weak random vibration
  • Includes supplementary material: sn.pub/extras

Part of the book series: Foundations of Engineering Mechanics (FOUNDATIONS)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    1. Introduction

      • Polina S. Landa
      Pages 1-7

  3. The main analytical methods of studies of nonlinear oscillations in near-conservative systems

    1. The main analytical methods of studies of nonlinear oscillations in near-conservative systems

      • Polina S. Landa
      Pages 9-23

  4. Oscillations in Autonomous Dynamical Systems

    1. Front Matter

      Pages 25-25
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    2. General properties of autonomous dynamical systems

      • Polina S. Landa
      Pages 27-47

    3. Examples of natural oscillations in systems with one degree of freedom

      • Polina S. Landa
      Pages 49-62

    4. Natural oscillations in systems with many degrees of freedom. Normal oscillations

      • Polina S. Landa
      Pages 63-88

    5. Self-oscillatory systems with one degree of freedom

      • Polina S. Landa
      Pages 89-106

    6. Self-oscillatory systems with one and a half degrees of freedom

      • Polina S. Landa
      Pages 107-136

    7. Examples of self-oscillatory systems with two or more degrees of freedom

      • Polina S. Landa
      Pages 137-160

    8. Synchronization and chaotization of self-oscillatory systems by an external harmonic force

      • Polina S. Landa
      Pages 161-203

    9. Interaction of two self-oscillatory systems. Synchronization and chaotization of self-oscillations

      • Polina S. Landa
      Pages 205-236

    10. Interaction of three or more self-oscillatory systems

      • Polina S. Landa
      Pages 237-251

  5. Oscillations in Nonautonomous Systems

    1. Front Matter

      Pages 253-253
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    2. Oscillations of nonlinear systems excited by external periodic forces

      • Polina S. Landa
      Pages 255-288

    3. Parametric excitation of oscillations

      • Polina S. Landa
      Pages 289-322

    4. Changes in the dynamical behavior of nonlinear systems induced by high-frequency vibration or by noise

      • Polina S. Landa
      Pages 323-372

  6. Back Matter

    Pages 373-397
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Keywords

About this book

In this book the modern theory of both regular and chaotic nonlinear oscillations is set out, primarily, as applied to mechanical problems. The material is presented in a nontraditional manner with emphasis on the new results of the theory obtained 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 systems and the influence of weak random vibrations on the modification of characteristics and behavior of nonlinear systems. One of the purposes of the book is to enable readers to gain a thorough understanding of this theory and to show that it can be very useful in engineering investigations. The primary audience for this book is researchers working with different oscillatory processes and students interested in a thorough study of the general laws and applications of the theory of nonlinear oscillations.

Reviews

From the reviews of the first edition:

"The present book … gives an up to date overview of recent developments, especially focusing on work done in the countries of the former Soviet Union. In this respect it is a gold mine for readers who have already some similarity with the theory of nonlinear oscillations, because 375 references are listed. … For those readers who want to get an overview on modern developments of oscillation theory and their applications in the sciences, the book will be certainly an excellent choice." (H. Troger, Zentralblatt MATH, Vol. 980, 2002)

Authors and Affiliations

  • Dept. of Physics, Moscow State University, Moscow, Russia

    Polina S. Landa

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