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arXiv · 2401.01700

Tulczyjew triple on the Atiyah algebroid with connection

Katarzyna Grabowska·Paweł Korzeb·Kuba Krawczyk
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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.

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Katarzyna Grabowska, Paweł Korzeb, Kuba Krawczyk. 2024-01-03. Tulczyjew triple on the Atiyah algebroid with connection. https://arxiv.org/abs/2401.01700

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