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 x R and T*Q x R to A x R and A* x R, respectively, where A is a Lie algebroid and A* carries the associated Poisson structure. We see that A* x R possesses a natural Jacobi structure from where we are able to model dissipative mechanical systems on Lie algebroids, generalizing previous models on TQ x R and introducing new ones as for instance for reduced systems on Lie algebras, semidirect products (action Lie algebroids) and Atiyah bundles.