Mathematical Aspects of Classical and Celestial Mechanics

Third Edition

  • Vladimir I. Arnold
  • Valery V. Kozlov
  • Anatoly I. Neishtadt
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 3)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Vladimir I. Arnold, Valery V. Kozlov, Anatoly I. Neishtadt
    Pages 1-60
  3. Vladimir I. Arnold, Valery V. Kozlov, Anatoly I. Neishtadt
    Pages 61-101
  4. Vladimir I. Arnold, Valery V. Kozlov, Anatoly I. Neishtadt
    Pages 103-133
  5. Vladimir I. Arnold, Valery V. Kozlov, Anatoly I. Neishtadt
    Pages 135-170
  6. Vladimir I. Arnold, Valery V. Kozlov, Anatoly I. Neishtadt
    Pages 171-206
  7. Vladimir I. Arnold, Valery V. Kozlov, Anatoly I. Neishtadt
    Pages 207-349
  8. Vladimir I. Arnold, Valery V. Kozlov, Anatoly I. Neishtadt
    Pages 351-399
  9. Vladimir I. Arnold, Valery V. Kozlov, Anatoly I. Neishtadt
    Pages 401-429
  10. Vladimir I. Arnold, Valery V. Kozlov, Anatoly I. Neishtadt
    Pages 431-468
  11. Back Matter
    Pages 469-518

About this book

Introduction

In this book we describe the basic principles, problems, and methods of cl- sical mechanics. Our main attention is devoted to the mathematical side of the subject. Although the physical background of the models considered here and the applied aspects of the phenomena studied in this book are explored to a considerably lesser extent, we have tried to set forth ?rst and foremost the “working” apparatus of classical mechanics. This apparatus is contained mainly in Chapters 1, 3, 5, 6, and 8. Chapter 1 is devoted to the basic mathematical models of classical - chanics that are usually used for describing the motion of real mechanical systems. Special attention is given to the study of motion with constraints and to the problems of realization of constraints in dynamics. In Chapter 3 we discuss symmetry groups of mechanical systems and the corresponding conservation laws. We also expound various aspects of ord- reduction theory for systems with symmetries, which is often used in appli- tions. Chapter 4 is devoted to variational principles and methods of classical mechanics. They allow one, in particular, to obtain non-trivial results on the existence of periodic trajectories. Special attention is given to the case where the region of possible motion has a non-empty boundary. Applications of the variational methods to the theory of stability of motion are indicated.

Keywords

celestial mechanics classical mechanics classsical mechanics integrability nonintegrability perturbation theory

Authors and affiliations

  • Vladimir I. Arnold
    • 1
    • 2
  • Valery V. Kozlov
    • 3
    • 4
  • Anatoly I. Neishtadt
    • 5
    • 6
  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.CEREMADEUniversité Paris 9 - DauphineFrance
  3. 3.Steklov Mathematical InstituteMoscowRussia
  4. 4.Department of Mathematics and MechanicsLomonosov Moscow State UniversityMoscowRussia
  5. 5.Space Research InstituteMoscowRussia
  6. 6.Department of Mathematics and MechanicsLomonosov Moscow State UniversityMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-48926-9
  • Copyright Information Springer 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-28246-4
  • Online ISBN 978-3-540-48926-9
  • Series Print ISSN 0938-0396
  • About this book