Dynamics near relative equilibria: Nongeneric momenta at a 1 : 1 group-reduced resonance

An interesting situation occurs when the linearized dynamics of the shape o f a formally stable Hamiltonian relative equilibrium at nongeneric momentum 1 : 1 resonates with a frequency of the relative equilibrium's generator. In this case some of the shape variables couple to the group variables to f irst order in the momentum perturbation, and the first order perturbation t heory implies that the relative equilibrium slowly changes orientation in t he same way that a charged particle with magnetic moment moves on a sphere under the influence of a radial magnetic monopole. In the course of showing this a normal form is constructed for linearizations of relative equilibri a and for Hamiltonians near group orbits of relative equilibria.