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 × R and T ∗ Q × R to A × R and A ∗ × R , respectively, where A is a Lie algebroid and A ∗ carries the associated Poisson structure. We see that A ∗ × R possesses a natural Jac...

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Bibliographic Details
Published in:Analysis and mathematical physics 2024-02, Vol.14 (1), Article 3
Main Authors: Anahory Simoes, Alexandre, Colombo, Leonardo, de León, Manuel, Salgado, Modesto, Souto, Silvia
Format: Article
Language:English
Subjects:
Analysis
Lie groups
Mathematical Methods in Physics
Mathematical models
Mathematics
Mathematics and Statistics
Mechanical systems
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Summary:We introduce Euler–Lagrange–Herglotz equations on Lie algebroids. The methodology is to extend the Jacobi structure from T Q × R and T ∗ Q × R to A × R and A ∗ × R , respectively, where A is a Lie algebroid and A ∗ carries the associated Poisson structure. We see that A ∗ × 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 × R and introducing new ones as for instance for reduced systems on Lie algebras, semidirect products (action Lie algebroids) and Atiyah bundles.
ISSN:1664-2368
1664-235X
DOI:10.1007/s13324-023-00859-x