Euler–Lagrange–Herglotz equations on Lie algebroids

We introduce Euler–Lagrange–Herglotz equations on Lie algebroids. The methodology is to extend the Jacobi structure from TQ× R and T∗Q× R to A× R and A∗× R , respectively, where A is a Lie algebroid and A∗ carries the associated Poisson structure. We see that A∗× R possesses a natural Jacobi structu...

Descripción completa

Detalles Bibliográficos
Autores: Anahory Simoes, Alexandre, Colombo, Leonardo, León, Manuel de, Salgado, Modesto, Souto, Silvia
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/380920
Acceso en línea:http://hdl.handle.net/10261/380920
https://api.elsevier.com/content/abstract/scopus_id/85180177780
Access Level:acceso abierto
Palabra clave:Contact systems
Dissipative mechanical systems
Jacobi structures
Lie algebroids
Descripción
Sumario:We introduce Euler–Lagrange–Herglotz equations on Lie algebroids. The methodology is to extend the Jacobi structure from TQ× R and T∗Q× R to A× R and A∗× R , respectively, where A is a Lie algebroid and A∗ carries the associated Poisson structure. We see that A∗× R possesses a natural Jacobi structure from where we are able to model dissipative mechanical systems on Lie algebroids, generalizing previous models on TQ× R and introducing new ones as for instance for reduced systems on Lie algebras, semidirect products (action Lie algebroids) and Atiyah bundles.