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Mathematical Methods of Classical Mechanics: 60 (Graduate Texts in Mathematics, 60) - Hardcover

Book 124 of 180: Graduate Texts in Mathematics

Arnol'd, V.I.

 
9780387968902: Mathematical Methods of Classical Mechanics: 60 (Graduate Texts in Mathematics, 60)
Hardcover
ISBN 10: 0387968903 ISBN 13: 9780387968902
Publisher: Springer, 1989

Synopsis

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.

"synopsis" may belong to another edition of this title.

Review

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

Synopsis

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.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
1989
Language
English
ISBN 10 
0387968903
ISBN 13 
9780387968902
Binding
Hardcover
Edition number
2
Number of pages
536