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 |
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Original title | Matematicheskie metody klassicheskoi mekhaniki |
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Country | Russia |
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Language | Russian |
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Subjects | Mathematical physics Classical mechanics |
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Genre | Non-fiction |
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Published | 1974 |
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Published in English | 1978 |
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ISBN | ISBN:0387968903 |
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Contents
- Part I: Newtonian Mechanics
- Chapter 1: Experimental Facts
- Chapter 2: Investigation of the Equations of Motion
- Part II: Lagrangian Mechanics
- 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
Bibliography
External links
| Original source: https://en.wikipedia.org/wiki/Mathematical Methods of Classical Mechanics. Read more |