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Mathematical Methods of Classical Mechanics (title of the original in Russian: Математические методы классической механики) 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.cite-ref-1[1] It is aimed at graduate students.

• Contents

• Russian original and translations

• Reviews

• See also

• References

• Bibliography

• 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 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.

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."cite-ref-2[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."cite-ref-3[3]

• List of textbooks in classical and quantum mechanics

cite-note-11. ↑ Mathematical Lives: Protagonists of the Twentieth Century From Hilbert to Wiles. Springer Science & Business Media. 2010. p. 211. ISBN 9783642136061.

cite-note-22. ↑ citerefsneddon1980Sneddon, Ian N. (March 1980). "Book Review of Mathematical methods of classical mechanics and A course in mathematical physics, vol. 1: Classical dynamical systems". Bulletin of the American Mathematical Society. 2 (2): 346–352. doi:10.1090/S0273-0979-1980-14755-2 – via Project Euclid.

cite-note-33. ↑ citerefbroucke1982Broucke, R (1982). "Book-Review - Mathematical Methods of Classical Mechanics". Celestial Mechanics. 28: 345. Bibcode:1982CeMec..28..345A. doi:10.1007/bf01243742. S2CID 189830621 – via SAO/NASA ADS.

• citerefarnold1989Arnold, Vladimir I. (16 May 1989) [First published in 1974]. . 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.