Variational order for forced Lagrangian systems II: Euler-Poincar\'e equations with forcing

Autor:	de Diego, David Martín, de Almagro, Rodrigo T. Sato Martín
Rok vydání:	2019
Předmět:	Mathematical Physics Mathematics - Differential Geometry Mathematics - Numerical Analysis Mathematics - Symplectic Geometry 17B66 22A22 70G45 70Hxx
Druh dokumentu:	Working Paper
DOI:	10.1088/1361-6544/ab8bb1
Popis:	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. Comment: 34 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1906.09819 Zobrazit plný text záznamu View this record from Arxiv