Contact formalism for dissipative mechanical systems on Lie algebroids

In this paper, we introduce a geometric description of contact Lagrangian and Hamiltonian systems on Lie algebroids in the framework of contact geometry, using the theory of prolongations. We discuss the relation between Lagrangian and Hamiltonian settings through a convenient notion of Legendre tra...

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Bibliographic Details
Authors: Anahory Simoes, Alexandre, Colombo, Leonardo, de León, Manuel, Salgado, Modesto, Souto, Silvia
Format: article
Status:Published version
Publication Date:2025
Country:España
Institution:Consejo Superior de Investigaciones Científicas (CSIC)
Repository:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/419158
Online Access:http://hdl.handle.net/10261/419158
Access Level:Open access
Keyword:Contact geometry
Dissipative systems
Lie algebroids
Herglotz equations
Description
Summary:In this paper, we introduce a geometric description of contact Lagrangian and Hamiltonian systems on Lie algebroids in the framework of contact geometry, using the theory of prolongations. We discuss the relation between Lagrangian and Hamiltonian settings through a convenient notion of Legendre transformation. We also discuss the Hamilton-Jacobi problem in this framework and introduce the notion of a Legendrian Lie subalgebroid of a contact Lie algebroid.

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