  The optimal control of a mechanical system is of crucial importance in many
realms. Typical examples are the determination of a time-minimal path in
vehicle dynamics, a minimal energy trajectory in space mission design, or
optimal motion sequences in robotics and biomechanics. In most cases, some sort
of discretization of the original, infinite-dimensional optimization problem
has to be performed in order to make the problem amenable to computations. The
approach proposed in this paper is to directly discretize the variational
description of the system's motion. The resulting optimization algorithm lets
the discrete solution directly inherit characteristic structural properties
from the continuous one like symmetries and integrals of the motion. We show
that the DMOC approach is equivalent to a finite difference discretization of
Hamilton's equations by a symplectic partitioned Runge-Kutta scheme and employ
this fact in order to give a proof of convergence.
  The numerical performance of DMOC and its relationship to other existing
optimal control methods are investigated.
