V. I. Arnold - Mathematical Metods of Classical Mechanics

Description

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.
This book is an example of great scientific writing style. Not all the epsilon and deltas are spelled out, and yet the the proofs are nowhere short of rigorous. Besides, they convey insight and intuition: the opposite of Gallavotti's "the element of mechanics" (a very competent book, but obsessed with details). As all the great mathematicians, Arnold separates what's essential from what is not, what is interesting from what is pedantic. The result is a challenging, wonderful book.



V.I Arnold is professor of Mathematics at the Russian Academy of Sciences. His research in the theory of differential equations (dynamical systems, stability theory, celestial and classical mechanics) has brought him world wide recognition as an outstanding mathematician and scientist. He was awarded the Lenin Prize for his work on stability theory with Kolmogorov.


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