Discrete Mechanics - A General Treatment

Abstract

A new numerical method for use in the solution of classical equations of motion is described, accurate to third-order in the coordinates and second-order in the velocities. The method has the unique property of preserving the energy and total linear and angular momenta at their initial values in the computation. This "discrete mechanics " is derived from general symmetry properties of the equations of motion and is compared in several numerical examples with conventional predictor-corrector methods. The theory is applied to derive a general expression for the impulsive limit of motion due to a potential.