Some remarks about the role of isotropy in the dynamics of relative equilibria for Hamiltonian and mechanical systems

When?

Friday 13 March 2009, 4:00pm

Where?

Room 22AA04

Open to:

Staff, Students

Speaker:

Miguel Rodríguez-Olmos (University of Manchester)

We will use the bundle equations of Roberts et al for symmetric Hamiltonian systems in order to study some aspects of the stability and bifurcations of relative equilibria. It will be shown how the existence of continuous isotropy groups for the symmetry action can affect these properties with respect to the free case. Notably, we will discuss how these isotropy groups can induce bifurcations from a formally stable branch of relative equilibria, and will clarify the notion of orthogonal velocities that appears in the literature. Finally, we will show how to particularize these results to the case of mechanical systems of the form kinetic + potential energy and study some examples.