Reduction of Hamiltonian Systems with Involutory Functions

Trajectory optimization through indirect methods yields a finite-dimensional boundary-valued problem whose dynamical motion is governed by a Hamiltonian system. Such Hamiltonian systems possessing constants-of-motion may be reduced to an equivalent, but lower dimensional problem. In the case of involutory constants-of-motion under the Poisson bracket induced by the symplectic form, we give a general procedure for deriving the lower dimensional boundary-valued problem.