Mathematical Methods of Classical Mechanics

  • V. I. Arnold

Part of the Graduate Texts in Mathematics book series (GTM, volume 60)

Table of contents

  1. Front Matter
    Pages N3-xvi
  2. Newtonian Mechanics

    1. Front Matter
      Pages 1-1
    2. V. I. Arnold
      Pages 3-14
    3. V. I. Arnold
      Pages 15-52
  3. Lagrangian Mechanics

    1. Front Matter
      Pages 53-53
    2. V. I. Arnold
      Pages 55-74
    3. V. I. Arnold
      Pages 75-97
    4. V. I. Arnold
      Pages 98-122
    5. V. I. Arnold
      Pages 123-159
  4. Hamiltonian Mechanics

    1. Front Matter
      Pages 161-161
    2. V. I. Arnold
      Pages 163-200
    3. V. I. Arnold
      Pages 201-232
    4. V. I. Arnold
      Pages 233-270
    5. V. I. Arnold
      Pages 271-300
  5. Back Matter
    Pages 301-519

About this book

Introduction

In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.

Keywords

Lagrangian mechanics Mathematische Physik Mechanik Rigid body Vector field classical mechanics differential equation

Authors and affiliations

  • V. I. Arnold
    • 1
  1. 1.Department of Mathematics Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-2063-1
  • Copyright Information Springer-Verlag New York 1989
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3087-3
  • Online ISBN 978-1-4757-2063-1
  • Series Print ISSN 0072-5285
  • About this book