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Mathematical Methods of Classical Mechanics

  • Textbook
  • © 1978

Overview

Authors:
  1. V. I. Arnold

    1. Department of Mathematics, University of Moscow, Moscow, USSR

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-x
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  2. Newtonian Mechanics

    1. Front Matter

      Pages 1-1
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    2. Experimental facts

      • V. I. Arnold
      Pages 3-14

    3. Investigation of the equations of motion

      • V. I. Arnold
      Pages 15-52

  3. Lagrangian Mechanics

    1. Front Matter

      Pages 53-53
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    2. Variational principles

      • V. I. Arnold
      Pages 55-74

    3. Lagrangian mechanics on manifolds

      • V. I. Arnold
      Pages 75-97

    4. Oscillations

      • V. I. Arnold
      Pages 98-122

    5. Rigid bodies

      • V. I. Arnold
      Pages 123-159

  4. Hamiltonian Mechanics

    1. Front Matter

      Pages 161-161
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    2. Differential forms

      • V. I. Arnold
      Pages 163-200

    3. Symplectic manifolds

      • V. I. Arnold
      Pages 201-232

    4. Canonical formalism

      • V. I. Arnold
      Pages 233-270

    5. Introduction to perturbation theory

      • V. I. Arnold
      Pages 271-300

  5. Back Matter

    Pages 301-464
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Keywords

About this book

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.

Reviews

Second Edition

V.I. Arnol’d

Mathematical Methods of Classical Mechanics

"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

Authors and Affiliations

  • Department of Mathematics, University of Moscow, Moscow, USSR

    V. I. Arnold

Bibliographic Information

  • Book Title: Mathematical Methods of Classical Mechanics

  • Authors: V. I. Arnold

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-1693-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1978

  • eBook ISBN: 978-1-4757-1693-1Published: 11 November 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: X, 464

  • Additional Information: Title of the original Russian edition: Matematiceskie metody klassiceskoj mechaniki

  • Topics: Mathematics, general

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