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. Essentially, we prove that when a discretization of contact order of the Lagrangian and force are used, the integrator has the same contact order. Our analysis is performed first for discrete forced mechanical systems defined over , where we study the existence of flows, the construction and properties of discrete exact systems and the contact order of the flows (variational integrators) 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 .
Cite
@article{arxiv.2103.11060,
title = {Error analysis of forced discrete mechanical systems},
author = {Javier Fernández and Sebastián Elías Graiff Zurita and Sergio Grillo},
journal= {arXiv preprint arXiv:2103.11060},
year = {2021}
}
Comments
Minor revision: slight modification of Definition 3.1 to accept more general examples. All results remain unchanged