A new perspective on symplectic integration of constrained mechanical systems via discretization maps
Numerical Analysis
2024-12-10 v2 Numerical Analysis
Mathematical Physics
math.MP
Abstract
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the discretization rule rather than viceversa. As a result, the constraint submanifold is exactly preserved by the symplectic discrete flow and the extension of these methods to the case of non-linear configuration spaces is doable.
Keywords
Cite
@article{arxiv.2306.06786,
title = {A new perspective on symplectic integration of constrained mechanical systems via discretization maps},
author = {María Barbero Liñán and David Martín de Diego and Rodrigo T. Sato Martín de Almagro},
journal= {arXiv preprint arXiv:2306.06786},
year = {2024}
}