On the Control of Mechanical Systems from One Equilibrium Location to Another

In this paper we prove a general theorem concerning the controlled motion of a mechanical system, such as a (simple or multiple) pendulum, from an equilibrium in one location to an equilibrium in another location. The dynamics of such mechanical systems are described by non-linear ordinary differential equations with controls; what we prove is a non-local controllability result. The proof rests on an open mapping theorem and a compactness argument.