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Mathematical Methods of Classical Mechanics

Mathematical physics book by V.I. Arnold From Wikipedia, the free encyclopedia

Mathematical Methods of Classical Mechanics
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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.[1] It is aimed at graduate students.

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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
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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."[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]

See also

References

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Bibliography

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