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Mathematical Methods of Classical Mechanics

  • Textbook
  • © 1989

Overview

Authors:
  1. V. I. Arnold

    1. Department of Mathematics Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

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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 N3-xvi
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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 301-519
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Keywords

About this book

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.

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 Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

    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/10.1007/978-1-4757-2063-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York 1989

  • Hardcover ISBN: 978-0-387-96890-2Published: 16 May 1989

  • Softcover ISBN: 978-1-4419-3087-3Published: 01 December 2010

  • eBook ISBN: 978-1-4757-2063-1Published: 09 April 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: XVI, 520

  • Additional Information: Originally published by Nauka, Moscow, 1974

  • Topics: Analysis, Theoretical, Mathematical and Computational Physics

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