In these ve lectures, I cover selected items from the following topics:
1. Reduction theory for mechanical systems with symmetry,
2. Stability, bifurcation and underwater vehicle dynamics,
3. Systems with rolling constraints and locomotion,
4. Optimal control and stabilization of balance systems,
5. Variational integrators.
Each topic itself could be expanded into several lectures, but I limited myself to what I
could reasonably explain in the allotted time. The hope is that the overview is informative
enough so that the reader can understand the fundamental ideas and can intelligently choose
from the literature for additional details on topics of interest.
Compatible with the theme of the PCI graduate school, I assume that the readers are
familiar with the elements of geometric mechanics, including the basics of symplectic and
Poisson geometry. The reader can find the needed background in, for example, Marsden
and Ratiu [1998]
