Configuration Controllability of Simple Mechanical Control Systems

In this paper we present a definition of "configuration controllability" for mechanical systems whose Lagrangian is kinetic energy with respect to a Riemannian metric minus potential energy. A computable test for this new version of controllability is also derived. This condition involves a new object which we call the {\em symmetric product}. Of particular interest is a definition of "equilibrium controllability" for which we are able to derive computable sufficient conditions. Examples illustrate the theory.