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

Arnol'd, V.I.

Hardcover

ISBN 10: 0387968903 ISBN 13: 9780387968902

Verlag: Springer, 1989

<P>THIS BOOK CONSTRUCTS THE MATHEMATICAL APPARATUS OF CLASSICAL MECHANICS FROM THE BEGINNING, EXAMINING BASIC PROBLEMS IN DYNAMICS LIKE THE THEORY OF OSCILLATIONS AND THE HAMILTONIAN FORMALISM. THE AUTHOR EMPHASIZES GEOMETRICAL CONSIDERATIONS AND INCLUDES PHASE SPACES AND FLOWS, VECTOR FIELDS, AND LIE GROUPS. DISCUSSION INCLUDES QUALITATIVE METHODS OF THE THEORY OF DYNAMICAL SYSTEMS AND OF ASYMPTOTIC METHODS LIKE AVERAGING AND ADIABATIC INVARIANCE.</P>

Críticas:

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

Reseña del editor:

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.