Jacobi structure for dissipative mechanical systems on Lie Algebroids

We extend the Jacobi structure from $TQ\times \mathbb{R}$ and $T^{\ast }Q\times \mathbb{R}$ to $A\times \mathbb{R}$ and $A^{\ast }\times \mathbb{R}$, respectively, where $A$ is a Lie algebroid and $A^{\ast }$ carries the associated Poisson structure. We see that $A^{\ast }\times \mathbb{R}$ possesses a natural Jacobi structure from where we are able to model dissipative mechanical systems, generalizing previous models on $TQ\times \mathbb{R}$ and $\mathfrak{g}\times \mathbb{R}$.