Controllability of Hamiltonian systems with drift: action-angle variables and ergodic partition

Control of Hamiltonian systems with drift is investigated for the case when the drift is integrable. Transformation of the system to action-angle coordinates is used to describe the ergodic partition of the drift. This is in turn used to obtain conditions for controllability of such systems. The key idea is that control must be capable of moving the system transverse to any set in the ergodic partition of the drift Hamiltonian vector field. Using this, additional results on controllability of more general systems are obtained.