Mathematical Methods of Classical Mechanics

Mathematical Methods of Classical Mechanics is a classic graduate textbook by 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
Author Vladimir I. Arnol'd
Country Russia
Language Russian
Genre Mathematics/Classical Mechanics
Published 1974
ISBN 0387968903

Contents

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

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]

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 – via SAO/NASA ADS.
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