Mathematical Methods of Classical Mechanics 2nd ed. 1989

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 copyright Book News, Inc. Portland, Or.
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.
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.