Classical mechanics has always been a source of interesting dynamics problems.
Many ideas in dynamical systems theory (and the rest of mathematics, for that matter) were first
developed in an attempt to understand the Newtonian n-body problem or the motion of a rigid body.
I will try to present the theory in a modern style and illustrate it with concrete
examples. Topics will include as many of the following as time permits:
| Newtonian and Lagrangian mechanics, calculus of variations |
| Hamiltonian mechanics, symplectic structures, Liouville's theorem |
| Symmetry, Noether's theorem, reduction |
| Integrable systems |
| Equilibrium points, Birkhoff normal form |
| KAM theorem |
| Nonintegrability and chaos |
| Variational methods |
Mathematical Methods of Classical Mechanics (2nd edition)
, by V.I. Arnold. This is one of the two classic mathematics texts
in the subject, the other being "Foundations of Mechanics", by Abraham and Marsden.
Which one you prefer can be viewed as a test of your mathematical tastes --- intuitive or
formal. They actually complement one another nicely. In any case Arnold's book is a
source of inspiration for anyone interested in mechanics. I will try to maintain its spirit.