English

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}
}