UBC Mathematics Department
In this talk we shall give several results on the interplay between the dynamics and control of mechanical systems. One of the systems of interest is that of an autonomous underwater vehicle. We shall use the energy-momentum method to study stability of its relative equilibria and the associated Lie-Poisson theory. We also discuss a stabilization technique that can be applied to systems such as rigid bodies with rotors spinning about their middle axes. This will be related to a general Kaluza-Klein construction for feedback controls.