Abstract

A relative equilibrium for a mechanical system with continuous symmetry is a solution of the equations of motion that is also an orbit of the symmetry group. Similarly to equilibria for non-symmetric systems, relative equilibria lie at the core of the qualitative analysis of the phase space.
We apply geometric methods, and in particular the Reduced Energy-Momentum method, to the analysis of stability of planar rotationally invariant relative equilibria of point mass systems. We analyze two examples in detail: equilateral relative equilibria for the three body problem, and isosceles triatomic molecules. We discuss some open problems to which the method is applicable, including roto-translational motion in the full three-body problem.

This is joint work with Tanya Schmah (Univ. of Toronto)