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- About this Textbook
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In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
- Reviews
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Second Edition
V.I. Arnol’d
Mathematical Methods of Classical Mechanics
"The book's goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising . . . The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview."
—AMERICAN MATHEMATICAL MONTHLY
- Table of contents (10 chapters)
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Experimental facts
Pages 3-14
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Investigation of the equations of motion
Pages 15-52
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Variational principles
Pages 55-74
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Lagrangian mechanics on manifolds
Pages 75-97
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Oscillations
Pages 98-122
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Table of contents (10 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Mathematical Methods of Classical Mechanics
- Authors
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- V.I. Arnol'd
- Translated by
- Vogtmann, K., Weinstein, A.
- Series Title
- Graduate Texts in Mathematics
- Series Volume
- 60
- Copyright
- 1989
- Publisher
- Springer-Verlag New York
- Copyright Holder
- Springer-Verlag New York
- eBook ISBN
- 978-1-4757-2063-1
- DOI
- 10.1007/978-1-4757-2063-1
- Hardcover ISBN
- 978-0-387-96890-2
- Softcover ISBN
- 978-1-4419-3087-3
- Series ISSN
- 0072-5285
- Edition Number
- 2
- Number of Pages
- XVI, 520
- Additional Information
- Originally published by Nauka, Moscow, 1974
- Topics
