Error analysis of forced discrete mechanical systems

Abstract

The purpose of this paper is to perform an error analysis of the variational integrators of mechanical systems subject to external forcing. Es- sentially, we prove that when a discretization of contact order r of the La- grangian and force are used, the integrator has the same contact order. Our analysis is performed first for discrete forced mechanical systems defined over TQ, where we study the existence of ows, the construction and properties of discrete exact systems and the contact order of the ows (variational integra- tors) in terms of the contact order of the original systems. Then we use those results to derive the corresponding analysis for the analogous forced systems defined over Q x Q.