This book is written with the belief that classical mechanics, as a
theoretical discipline, possesses an inherent beauty, depth, and
richness that far transcends its immediate applications in
mechanical systems. These properties are manifested, by and large,
through the coherence and elegance of the mathematical structure
underlying the discipline, and are eminently worthy of being
communicated to physics students at the earliest stage possible.
This volume is therefore addressed mainly to advanced undergraduate
and beginning graduate physics students who are interested in the
application of modern mathematical methods in classical mechanics,
in particular, those derived from the fields of topology and
differential geometry, and also to the occasional mathematics
student who is interested in important physics applications of
these areas of mathematics. Its main purpose is to offer an
introductory and broad glimpse of the majestic edifice of the
mathematical theory of classical dynamics, not only in the
time-honored analytical tradition of Newton, Laplace, Lagrange,
Hamilton, Jacobi, and Whittaker, but also the more
topological/geometrical one established by Poincare, and enriched
by Birkhoff, Lyapunov, Smale, Siegel, Kolmogorov, Arnold, and Moser
(as well as many others).
General
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