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arXiv · 2306.07028

Reduction by symmetries of contact mechanical systems on Lie groups

Alexandre Anahory Simoes·Leonardo Colombo·Manuel de León·Juan Carlos Marrero·David Martín de Diego·Edith Padrón
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Abstract

We study the dynamics of contact mechanical systems on Lie groups that are invariant under a Lie group action. Analogously to standard mechanical systems on Lie groups, existing symmetries allow for reducing the number of equations. Thus, we obtain Euler-Poincar\'e-Herglotz equations on the extended reduced phase space $\mathfrak{g}\times \R$ associated with the extended phase space $TG\times \R$, where the configuration manifold $G$ is a Lie group and $\mathfrak{g}$ its Lie algebra. Furthermore, we obtain the Hamiltonian counterpart of these equations by studying the underlying Jacobi structure. Finally, we extend the reduction process to the case of symmetry-breaking systems which are invariant under a Lie subgroup of symmetries.

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Alexandre Anahory Simoes, Leonardo Colombo, Manuel de León, Juan Carlos Marrero, David Martín de Diego, Edith Padrón. 2023-06-12. Reduction by symmetries of contact mechanical systems on Lie groups. https://arxiv.org/abs/2306.07028

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