Author:
Anahory Simoes Alexandre,Colombo Leonardo,de León Manuel,Salgado Modesto,Souto Silvia
Abstract
AbstractWe introduce Euler–Lagrange–Herglotz equations on Lie algebroids. The methodology is to extend the Jacobi structure from $$TQ\times \mathbb {R}$$
T
Q
×
R
and $$T^{*}Q \times \mathbb {R}$$
T
∗
Q
×
R
to $$A\times \mathbb {R}$$
A
×
R
and $$A^{*}\times \mathbb {R}$$
A
∗
×
R
, respectively, where A is a Lie algebroid and $$A^{*}$$
A
∗
carries the associated Poisson structure. We see that $$A^*\times \mathbb {R}$$
A
∗
×
R
possesses a natural Jacobi structure from where we are able to model dissipative mechanical systems on Lie algebroids, generalizing previous models on $$TQ\times \mathbb {R}$$
T
Q
×
R
and introducing new ones as for instance for reduced systems on Lie algebras, semidirect products (action Lie algebroids) and Atiyah bundles.
Funder
Consejo Superior de Investigaciones Cientificas
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Algebra and Number Theory,Analysis