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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. 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.