Mechanical Hamiltonian systems with respect to linear Poisson structures and Jacobi-Reeb dynamics

In this paper, we present a relation between Jacobi-Reeb dynamics and the dynamics associated with a mechanical Hamiltonian system with respect to a linear Poisson structure on a vector bundle. For this purpose, we will use the so-called Jacobi bundle metrics induced by the mechanical Hamiltonian sy...

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Bibliographic Details
Published in:arXiv.org 2022-12
Main Authors: D Iglesias Ponte, Marrero, J C, Padrón, E
Format: Article
Language:English
Subjects:
Hamiltonian functions
Online Access:Get full text
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Summary:In this paper, we present a relation between Jacobi-Reeb dynamics and the dynamics associated with a mechanical Hamiltonian system with respect to a linear Poisson structure on a vector bundle. For this purpose, we will use the so-called Jacobi bundle metrics induced by the mechanical Hamiltonian system. These constructions extend classical results on the relation between standard mechanical Hamiltonian systems on cotangent bundles and Reeb dynamics.
ISSN:2331-8422
DOI:10.48550/arxiv.2204.13523