Tulczyjew triple on the Atiyah algebroid with connection
Mathematical Physics
2024-01-04 v1 Differential Geometry
math.MP
Abstract
The Tulczyjew triple on a principal bundle with connection is constructed in a convenient trivialisation. A reduction by the structure group is performed leading to the triple on the trivialised Atiyah algebroid and a presentation of this algebroid via a double vector bundle morphism. The dynamics of physical systems with configuration manifolds having the structure of a principal bundle with connection or the Atiyah algebroid is discussed and applied to the example of an axially symmetric body confined to a sphere.
Keywords
Cite
@article{arxiv.2401.01700,
title = {Tulczyjew triple on the Atiyah algebroid with connection},
author = {Katarzyna Grabowska and Paweł Korzeb and Kuba Krawczyk},
journal= {arXiv preprint arXiv:2401.01700},
year = {2024}
}