main text: V. I. Arnold: "Mathematical Methods of Classical Mechanics", second edition, Springer, (1989) isbn 0-387-96890-3, second isbn: 3-540-96890-3
The choice of a textbook for this course is a hard one. On the one hand are books that rework the Lagrangian and Hamiltonian methods taught in undergraduate courses at a somewhat more general level. On the other hand are books that aim to gain the deepest possible insight into issues like conservation laws, symmetries, integrability and adiabatic invariants. Our chosen textbook is in the latter category. Its author V. I. Arnold is one of the giants of twentieth-century Russian physics. Arnold aims to account for classical motion insofar as possible in geometric terms. His aim at depth carries a cost: it is a difficult book. Partly it is difficult because it forces us to view familiar subjects in unfamiliar, geometric terms. We must understand concepts of differential geometry normally encountered in general relativity. By choosing this book, I hope to expose you to the state of the art in understanding this fundamental aspect of physics.
supplementary text: L. D. Landau and E. M. Lifshitz, "mechanics", third edition, Pergamon Press, Oxford, 1976, ISBN 0-08-021020-8
supplementary text: Herbert Goldstein, Charles Poole, John Safko,
"Classical Mechanics" third edition, Addison Wesley, New York, (2002) ISBN 0-201-65702-3