MECHANICAL INTEGRATORS DERIVED FROM A DISCRETE VARIATIONAL PRINCIPLE

Many numerical integrators for mechanical system simulation are create d by using discrete algorithms to approximate the continuous equations of motion. In this paper, we present a procedure to construct time-st epping algorithms that approximate the flow of continuous ODEs for mec hanical systems by discretizing Hamilton's principle rather than the e quations of motion. The discrete equations share similarities to the c ontinuous equations by preserving invariants, including the symplectic form and the momentum map. We first present a formulation of discrete mechanics along with a discrete variational principle. We then show t hat the resulting equations of motion preserve the symplectic form and that this formulation of mechanics leads to conservation laws from a discrete version of Noether's theorem. We then use the discrete mechan ics formulation to develop a procedure for constructing symplectic-mom entum mechanical integrators for Lagrangian systems with holonomic con straints. We apply the construction procedure to the rigid body and th e double spherical pendulum to demonstrate numerical properties of the integrators.