Stabilization of relative equilibria for systems on Riemannian manifolds

Describes a systematic procedure to exponentially stabilize relative equilibria of mechanical systems. We review the notion of relative equilibria and their stability in a Riemannian geometry context. Potential shaping and dissipation are employed to obtain full exponential stabilization to the desired trajectory. Two necessary conditions are that the effective potential be positive definite over a specified subspace and that the system be linearly controllable.