Constrained motion of Hamiltonian systems

This paper considers dynamical systems described by Hamilton's equations. It deals with the development of the explicit equations of motion for such systems when constraints are imposed on them. Such explicit equations do not appear to have been obtained hereto. The holonomic and/or nonholonomic constraints imposed can be nonlinear functions of the canonical momenta, the coordinates, and time, and they can be functionally dependent. These explicit equations of motion for constrained systems are obtained through the development of the connection between the Lagrangian concept of virtual displacements and Hamiltonian dynamics. A simple three-step approach for obtaining the explicit equations of motion of constrained Hamiltonian systems is presented. Four examples are provided illustrating the ease and simplicity with which these equations can be obtained by using the proposed three-step approach