250099 VO Dynamical Systems in Mechanics (2013S)

The mathematical study of mechanical systems (such as driven or coupled pendula, the
Earth revolving around the Sun) is in terms of ordinary differential equations, which may
be too complicated to solve explicitly, but there are various other techniques and methods,
which are at the heart of a field called Dynamical Systems. However, differential geometry
and ergodic theory play a role in this area too.

Topics to be covered include
- Basic example from Newtownian mechanics.
- Periodic motion quasi-periodic motion and resonance.
- Preserved quantities (first integrals of motion).
- Hamiltonian formalism.
- Symmetries and Noether's Theorem.