Stability of Hamiltonian relative equilibria

We generalize a sufficient condition for the stability of relative equilibr ia in symmetric Hamiltonian systems, due to Patrick (1992 Relative equilibr ia in Hamiltonian systems: the dynamic interpretation of nonlinear stabilit y on a reduced phase space J. Gee. Phys. 9 111-19), to the case in which th ese relative equilibria have non-trivial symmetry. We also describe a block diagonalization that facilitates the use of this result in particular exam ples and shows the relation between the stability of the relative equilibri um and the Lyapunov stability of the associated singular reduced equilibriu m.