Mathematical Methods of Classical Mechanics

• 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

• 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.

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]

• List of textbooks in classical and quantum mechanics

• Arnold, Vladimir I. (16 May 1989) [First published in 1974]. Mathematical Methods of Classical Mechanics Математические методы классической механики. Graduate Texts in Mathematics. 60. Translated by Vogtmann, Karen; Weinstein, Alan D. (2nd ed.). New York: Springer-Verlag. ISBN 978-0-387-96890-2. OCLC 18681352.CS1 maint: date and year (link)

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