From retraction maps to symplectic-momentum numerical integrators

Retraction maps have been generalized to discretization maps in (Barbero Liñán and and Mart\'ın de Diego, 2022). Discretization maps are used to systematically derive numerical integrators that preserve the symplectic structure, as well as the discrete momemtum map under the assumption of symme...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-01
Main Authors: Barbero-Liñán, María, Marrero, Juan Carlos, Martín de Diego, David
Format: Article
Language:English
Subjects:
Discretization
Integrators
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Retraction maps have been generalized to discretization maps in (Barbero Liñán and and Mart\'ın de Diego, 2022). Discretization maps are used to systematically derive numerical integrators that preserve the symplectic structure, as well as the discrete momemtum map under the assumption of symmetric preservation for the discretization map. The procedure described here gives a geometrical construction that can be easily adapted to discretize dynamics on more general structures and open the door to reduction processes.
ISSN:2331-8422