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.
 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 |
| Pages | xvi + 516 |
| ISBN | 0387968903 |
Contents edit
- 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 edit
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 edit
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 edit
References edit
- ^ Mathematical Lives: Protagonists of the Twentieth Century From Hilbert to Wiles. Springer Science & Business Media. 2010. p. 211. ISBN 9783642136061.
- ^ 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 – via Project Euclid.
- ^ Broucke, 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.
Bibliography edit
- 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.