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.
Updated version of a classic text (first published 1974 in Russian, and 1978 in English translation) by a man who for several decades has been universally acknowledged to stand at the forefront of the effort to clarify the deep mathematical problems to which classical mechanics gives rise, and who himself discovered or inspired the discovery of many of the new insights which have necessitated the update. Everything by V.I. Arnold is treasured by serious students of the fields, every such person will want to have a copy of this volume within easy reach. Written in a style calculated to engage the experience and imagination of physicists, the book is deeply mathematical but not off-puttingly so. Beautifully produced. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)