Stability of relative equilibria with singular momentum values in simple mechanical systems

A method for testing $G_{\mu }$-stability of relative equilibria in Hamiltonian systems of the form “kinetic + potential energy” is presented. This method extends the Reduced Energy-Momentum Method of Simo et al. to the case of non-free group actions and singular momentum values. A normal form for the symplectic matrix at a relative equilibrium is also obtained.