Variational integrators for mechanical systems with configuration dependent inertia

Abstract

This paper develops discrete Euler-Lagrange equations for finite-dimensional, conservative, mechanical systems with configuration-dependent inertia. The configuration dependence of the inertia makes the Hamiltonian of such a system non-separable. We apply a discrete version of Routh reduction when there is a cyclic generalized coordinate, reflecting a symmetry. These discrete Euler-Lagrange and reduced Lagrange-Routh equations provide variational integration algorithms with good long-term numerical properties. They conserve the conjugate momentum corresponding to the cyclic coordinate, and error in the computed total energy remains bounded. These properties are illustrated through simulations of the free planar dynamics of an elastic dumbbell body in an inverse square central gravity field.