  In symmetric Hamiltonian systems, relative equilibria usually arise in
continuous families. The geometry of these families in the setting of free
actions of the symmetry group is well-understood. Here we consider the question
for non-free actions. Some results are already known in this direction, and we
use the so called bundle equations to provide a systematic treatment of this
question which both consolidates the known results, extending the scope of the
results to deal with non-compact symmetry groups, as well as producing new
results. Specifically we address questions about the stability, persistence and
bifurcations of these relative equilibria.
