Stabilization of relative equilibria

This paper discusses the problem of obtaining feedback laws to asymptotical ly stabilize relative equilibria of mechanical systems with symmetry We sho w how to stabilize an internally unstable relative equilibrium using intern al actuators. The methodology is that of potential shaping, but the system is allowed to be underactuated, i,e,, have fewer actuators than the dimensi on of the shape space. The theory is illustrated with the problem of stabil ization of the cowboy relative equilibrium of the double spherical pendulum .