  In this paper, we consider a geometric formalism for optimal control of
underactuated mechanical systems. Our techniques are an adaptation of the
classical Skinner and Rusk approach for the case of Lagrangian dynamics with
higher-order constraints. We study a regular case where it is possible to
establish a symplectic framework and, as a consequence, to obtain a unique
vector field determining the dynamics of the optimal control problem. These
developments will allow us to develop a new class of geometric integrators
based on discrete variational calculus.
