Implementation of Linear Multistep Methods for Solving Constrained Equations of Motion

A class of multistep methods for numerical integration of the equations of motion of constrained mechanical systems is considered. They are based on different local parametrizations of the differentiable manifold defined by the kinematic constraints. During integration, the kinematic constraints are preserved at all levels: position, velocity, and acceleration. The numerical implementations described in the paper require only one symmetric matrix factorization at each integration step.