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.[1]

Mathematical Methods of Classical Mechanics
First English edition
AuthorVladimir I. Arnol'd
Original titleMatematicheskie metody klassicheskoi mekhaniki
CountryRussia
LanguageRussian
SubjectsMathematical physics
Classical mechanics
GenreNon-fiction
Published1974
Published in English
1978
ISBN0387968903

Contents
  • Part I: Newtonian Mechanics
    • Chapter 1: Experimental Facts
    • Chapter 2: Investigation of the Equations of Motion
  • Part II: Lagrangian Mechanics
  • 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."[2]

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."[3]

gollark: F-strings bad.
gollark: It is [DATA EXPUNGED].
gollark: Or ${new Date().getFullYear()} if you like.
gollark: Yes, it is $CURRENT_YEAR.
gollark: gnu-nobody is also somewhat bees.

References
  1. Mathematical Lives: Protagonists of the Twentieth Century From Hilbert to Wiles. Springer Science & Business Media. 2010. p. 211. ISBN 9783642136061.
  2. Sneddon, Ian N. (March 1980). "Book Review of Mathematical methods of classical mechanis and A course in mathematical physics, vol. 1: Classical dynamical systems". Bulletin of the American Mathematical Society. 2, Number 2: 346–352 – via Project Euclid.
  3. Broucke, R (1982). "Book-Review - Mathematical Methods of Classical Mechanics". Celestial Mechanics. 28: 345. doi:10.1007/bf01243742 – via SAO/NASA ADS.

See also
  • List of textbooks in classical and quantum mechanics
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