English

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}
}