Article Contents
Article Contents

# Bifurcations of relative equilibria near zero momentum in Hamiltonian systems with spherical symmetry

• For Hamiltonian systems with spherical symmetry there is a marked difference between zero and non-zero momentum values, and amongst all relative equilibria with zero momentum there is a marked difference between those of zero and those of non-zero angular velocity. We use techniques from singularity theory to study the family of relative equilibria that arise as a symmetric Hamiltonian which has a group orbit of equilibria with zero momentum is perturbed so that the zero-momentum relative equilibrium are no longer equilibria. We also analyze the stability of these perturbed relative equilibria, and consider an application to satellites controlled by means of rotors.
Mathematics Subject Classification: 70H33, 58F14, 37J20.

 Citation:

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