Dynamical Systems III

  • Vladimir I. Arnold

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 3)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Vladimir I. Arnold
    Pages 1-48
  3. Vladimir I. Arnold
    Pages 49-77
  4. Vladimir I. Arnold
    Pages 78-106
  5. Vladimir I. Arnold
    Pages 107-137
  6. Vladimir I. Arnold
    Pages 138-211
  7. Vladimir I. Arnold
    Pages 212-250
  8. Vladimir I. Arnold
    Pages 251-273
  9. Back Matter
    Pages 274-294

About this book

Introduction

This work describes the fundamental principles, problems, and methods of elassical mechanics focussing on its mathematical aspects. The authors have striven to give an exposition stressing the working apparatus of elassical mechanics, rather than its physical foundations or applications. This appara­ tus is basically contained in Chapters 1, 3,4 and 5. Chapter 1 is devoted to the fundamental mathematical models which are usually employed to describe the motion of real mechanical systems. Special consideration is given to the study of motion under constraints, and also to problems concerned with the realization of constraints in dynamics. Chapter 3 is concerned with the symmetry groups of mechanical systems and the corresponding conservation laws. Also discussed are various aspects of the theory of the reduction of order for systems with symmetry, often used in applications. Chapter 4 contains abrief survey of various approaches to the problem of the integrability of the equations of motion, and discusses some of the most general and effective methods of integrating these equations. Various elassical examples of integrated problems are outlined. The material pre­ sen ted in this chapter is used in Chapter 5, which is devoted to one of the most fruitful branches of mechanics - perturbation theory. The main task of perturbation theory is the investigation of problems of mechanics which are" elose" to exact1y integrable problems.

Keywords

dynamical systems integrable system integration mechanics n-body problem

Editors and affiliations

  • Vladimir I. Arnold
    • 1
  1. 1.Steklov Mathematical InstituteMoscowUSSR

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-02535-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-02537-6
  • Online ISBN 978-3-662-02535-2
  • Series Print ISSN 0938-0396
  • About this book