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arXiv · 2305.18735

Jacobi structure for dissipative mechanical systems on Lie Algebroids

Alexandre Anahory Simoes·Leonardo Colombo·Manuel de Leon·Modesto Salgado·Silvia Souto
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Abstract

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

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Alexandre Anahory Simoes, Leonardo Colombo, Manuel de Leon, Modesto Salgado, Silvia Souto. 2023-05-30. Jacobi structure for dissipative mechanical systems on Lie Algebroids. https://arxiv.org/abs/2305.18735

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