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Encyclopaedia of Mathematical Sciences

Dynamical Systems III

Editors: Arnol'd, Vladimir I. (Ed.)

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About this book

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.

Reviews

From the reviews: "... As an encyclopaedia article, this book does not seek to serve as a textbook, nor to replace the original articles whose results it describes. The book's goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising. ... The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview. ..." American Mathematical Monthly, Nov. 1989 "This is a book to curl up with in front of a fire on a cold winter's evening. ..." SIAM Reviews, Sept. 1989

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $74.99
price for USA in USD
  • ISBN 978-3-662-02535-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Dynamical Systems III
Editors
  • Vladimir I. Arnol'd
Translated by
Iacob, A.
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
3
Copyright
1988
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-02535-2
DOI
10.1007/978-3-662-02535-2
Series ISSN
0938-0396
Edition Number
1
Number of Pages
XIV, 294
Number of Illustrations
3 b/w illustrations
Additional Information
Original Russian edition published by VINITI, Moscow 1985
Topics