Variational order for forced Lagrangian systems II: Euler-Poincar\'e equations with forcing
Mathematical Physics
2020-08-26 v1 Numerical Analysis
Differential Geometry
math.MP
Numerical Analysis
Symplectic Geometry
Abstract
In this paper we provide a variational derivation of the Euler-Poincar\'e equations for systems subjected to external forces using an adaptation of the techniques introduced by Galley and others. Moreover, we study in detail the underlying geometry which is related to the notion of Poisson groupoid. Finally, we apply the previous construction to the formal derivation of the variational error for numerical integrators of forced Euler-Poincar\'e equations and the application of this theory to the derivation of geometric integrators for forced systems.
Cite
@article{arxiv.1906.09819,
title = {Variational order for forced Lagrangian systems II: Euler-Poincar\'e equations with forcing},
author = {David Martín de Diego and Rodrigo T. Sato Martín de Almagro},
journal= {arXiv preprint arXiv:1906.09819},
year = {2020}
}
Comments
34 pages, 5 figures