  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.
