ERROR ANALYSIS OF FORCED DISCRETE MECHANICAL SYSTEMS

JAVIER FERNÁNDEZ; SEBASTIAN GRAIFF ZURITA; SERGIO GRILLO

Journal of Geometric Mechanics

AIMS

Año: 2021

1941-4889

The purpose of this paper is to perform an error analysis of thevariational 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. Ouranalysis is performed first for discrete forced mechanical systems defined overTQ, where we study the existence of flows, the construction and properties ofdiscrete exact systems and the contact order of the flows (variational integra-tors) in terms of the contact order of the original systems. Then we use thoseresults to derive the corresponding analysis for the analogous forced systemsdefined over QxQ.