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...
| Autores: | , , , , |
|---|---|
| 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 |
| 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. |
|---|