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 i-x
  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 301-464

About this book

Introduction

Many different mathematical methods and concepts are used in classical mechanics: differential equations and phase ftows, smooth mappings and manifolds, Lie groups and Lie algebras, symplectic geometry and ergodic theory. Many modern mathematical theories arose from problems in mechanics and only later acquired that axiomatic-abstract form which makes them so hard to study. In this book we construct the mathematical apparatus of classical mechanics from the very beginning; thus, the reader is not assumed to have any previous knowledge beyond standard courses in analysis (differential and integral calculus, differential equations), geometry (vector spaces, vectors) and linear algebra (linear operators, quadratic forms). With the help of this apparatus, we examine all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the hamiltonian formalism. The author has tried to show the geometric, qualitative aspect of phenomena. In this respect the book is closer to courses in theoretical mechanics for theoretical physicists than to traditional courses in theoretical mechanics as taught by mathematicians.

Keywords

Hamiltonian Lie Mathematica Newtonian mechanics algebra calculus classical mechanics differential equation dynamical systems dynamics equation invariant manifold mechanics oscillation

Authors and affiliations

  • V. I. Arnold
    • 1
  1. 1.Department of MathematicsUniversity of MoscowMoscowUSSR

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-1693-1
  • Copyright Information Springer-Verlag New York 1978
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-1695-5
  • Online ISBN 978-1-4757-1693-1
  • Series Print ISSN 0072-5285
  • About this book