Mathematical Methods of Classical Mechanics

Mathematical Methods of Classical Mechanics is a classic graduate textbook by the eminent mathematician Vladimir I. Arnold. It was originally written in Russian, but was translated into English by A. Weinstein and K. Vogtmann.

Mathematical Methods of Classical Mechanics

First English edition
Author	Vladimir I. Arnol'd
Original title	Matematicheskie metody klassicheskoi mekhaniki
Language	Russian
Subjects	Mathematical physics Classical mechanics
Genre	Non-fiction
Published	1974
Publication place	Russia
Published in English	1978
ISBN	0387968903

Contents

• Part I: Newtonian Mechanics
  • Chapter 1: Experimental Facts
  • Chapter 2: Investigation of the Equations of Motion
• Part II: Lagrangian Mechanics
  • Chapter 3: Variational Principles
  • Chapter 4: Lagrangian Mechanics on Manifolds
  • Chapter 5: Oscillations
  • Chapter 6: Rigid Bodies
• Part III: Hamiltonian Mechanics
  • Chapter 7: Differential forms
  • Chapter 8: Symplectic Manifolds
  • Chapter 9: Canonical Formalism
  • Chapter 10: Introduction to Perturbation Theory
• Appendices
  • Riemannian curvature
  • Geodesics of left-invariant metrics on Lie groups and the hydrodynamics of ideal fluids
  • Symplectic structures on algebraic manifolds
  • Contact structures
  • Dynamical systems with symmetries
  • Normal forms of quadratic Hamiltonians
  • Normal forms of Hamiltonian systems near stationary points and closed trajectories
  • Theory of perturbations of conditionally period motion and Kolmogorov's theorem
  • Poincaré's geometric theorem, its generalizations and applications
  • Multiplicities of characteristic frequencies, and ellipsoids depending on parameters
  • Short wave asymptotics
  • Lagrangian singularities
  • The Kortweg-de Vries equation
  • Poisson structures
  • On elliptic coordinates
  • Singularities of ray systems

Russian Original and Translations

• The original Russian first edition Математические методы классической механики was published in 1974 by Наука, a second one was published in 1979, and a third - in 1989.
• The first French translation, Les Méthodes mathématiques de la mécanique classique, was published in 1976.
• The first Bulgarian translation, Математически методи на класическата механика, was published in 1978. А second translation of the second Russian edition appeared in 1985.
• The first Japanese translation, 古典力学の数学的方法, was published in 1980. А second translation was published in 2003
• The first Romanian translation, Metodele matematice ale mecanicii clasice, was published in 1980.
• The first Polish translation, "Metody matematyczne mechaniki klasycznej", was published in 1981.
• The first Spanish translation, Mecánica clásica. Métodos matemáticos, was published in 1983.
• The first Hungarian translation, A mechanika matematikai módszerei, was published in 1985. А second translation appeared in 2013.
• The first Portuguese translation, Métodos matemáticos da mecânica clássica, was published in 1987.
• The first German translation, Mathematische Methoden der klassischen Mechanik, was published in 1988.
• The first Italian translation, Metodi matematici della meccanica classica, was published in 1992.
• The first Chinese translation, 经典力学的数学方法, was published in 1992.

Reviews

The Bulletin of the American Mathematical Society said, "The [book] under review [...] written by a distinguished mathematician [...is one of] the first textbooks [to] successfully to present to students of mathematics and physics, [sic] classical mechanics in a modern setting."

A book review in the journal Celestial Mechanics said, "In summary, the author has succeeded in producing a mathematical synthesis of the science of dynamics. The book is well presented and beautifully translated [...] Arnold's book is pure poetry; one does not simply read it, one enjoys it."

See also

• List of textbooks in classical and quantum mechanics

External links

• pdf version