  In this paper we consider an intrinsic point of view to describe the
equations of motion for higher-order variational problems with constraints on
higher-order trivial principal bundles. Our techniques are an adaptation of the
classical Skinner-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. As an interesting application we deduce
the equations of motion for optimal control of underactuated mechanical systems
defined on principal bundles.
