Regularization of the amended potential and the bifurcation of relative equilibria

Hernandez, A. and J. E. Marsden

J. of Nonlinear Sci. 15, 93-132

Abstract:

In the context of simple mechanical systems with symmetry, we give a method based on blowing up the amended potential for obtaining symmetry-breaking branches of relative equilibria bifurcating from a given set of symmetric relative equilibria. The general method is illustrated with two concrete mechanical examples, the double spherical pendulum and the symmetric coupled rigid bodies.