Mathematical Methods of Classical Mechanics

Short description: Mathematics book first published in Russian in 1974

Mathematical Methods of Classical Mechanics is a classic graduate textbook by the mathematician 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

First English edition

Author| Vladimir I. Arnol'd
Original title| Matematicheskie metody klassicheskoi mekhaniki
Country| Russia
Language| Russian
Subjects| Mathematical physics
Classical mechanics
Genre| Non-fiction
Published| 1974

Published in English

| 1978
ISBN| ISBN:0387968903

## Contents

* 1 Contents
* 2 Russian Original and Translations
* 3 Reviews
* 4 See also
* 5 References
* 6 Bibliography
* 7 External links

## 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 one was published in 1979, and a third - in 1989.
* The first French translation, Les Méthodes mathématiques de la mécanique classique, was published in 1976.
* The first Bulgarian translation, Математически методи на класическата механика, was published in 1978. А second translation of the second Russian edition appeared in 1985.
* The first Japanese translation, 古典力学の数学的方法, was published in 1980. А second translation was published in 2003
* The first Romanian translation, Metodele matematice ale mecanicii clasice, was published in 1980.
* The first Polish translation, "Metody matematyczne mechaniki klasycznej", was published in 1981.
* The first Spanish translation, Mecánica clásica. Métodos matemáticos, was published in 1983.
* The first Hungarian translation, A mechanika matematikai módszerei, was published in 1985. А second translation appeared in 2013.
* The first Portuguese translation, Métodos matemáticos da mecânica clássica, was published in 1987.
* The first German translation, Mathematische Methoden der klassischen Mechanik, was published in 1988.
* The first Italian translation, Metodi matematici della meccanica classica, was published in 1992.
* The first Chinese translation, 经典力学的数学方法, was published in 1992.

## 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

* List of textbooks in classical and quantum mechanics

## References

1. ↑ Mathematical Lives: Protagonists of the Twentieth Century From Hilbert to Wiles. Springer Science & Business Media. 2010. pp. 211. ISBN 9783642136061. https://books.google.com/books?id=J4nk1U3qjh0C.
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 (2): 346–352. doi:10.1090/S0273-0979-1980-14755-2. https://projecteuclid.org/download/pdf_1/euclid.bams/1183546243.
3. ↑ Broucke, R (1982). "Book-Review - Mathematical Methods of Classical Mechanics". Celestial Mechanics 28: 345. doi:10.1007/bf01243742. Bibcode: 1982CeMec..28..345A. http://adsabs.harvard.edu/full/1982CeMec..28..345A.

## Bibliography

* Template:Arnold Mathematical Methods of Classical Mechanics 1989

## External links

* pdf version

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