• Source: Mathematical Methods of Classical Mechanics
    • Mathematical Methods of Classical Mechanics is a textbook by mathematician Vladimir I. Arnold. It was originally written in Russian, and later translated into English by A. Weinstein and K. Vogtmann. It is aimed at graduate students.


      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 edition was published in 1979, and a third in 1989. The book has since been translated into a number of other languages, including French, German, Japanese and Mandarin.


      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


      References




      Bibliography


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

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