Anahory Simoes, A., Colombo, L., de León, M., Salgado, M., & Souto, S. (2024). Euler–Lagrange–Herglotz equations on Lie algebroids. Analysis and Mathematical Physics, 14(1), 3.

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

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Authors from IE Research Datalab

Alexandre Anahory

Assistant Professor

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