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arXiv · 2408.06892

Symmetry reduction and reconstruction in contact geometry and Lagrange-Poincar\'e-Herglotz equations

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

In this paper, we investigate the reduction process of a contact Lagrangian system whose Lagrangian is invariant under a group of symmetries. We give explicit coordinate expressions of the resulting reduced differential equations, the so-called Lagrange-Poincare-Herglotz equations. Our framework relied on the associated Herglotz vector field and its projected vector field, and the use of well-chosen quasi-velocities. Some examples are also discussed.

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Alexandre Anahory Simoes, Leonardo Colombo, Manuel de Leon, Modesto Salgado, Silvia Souto. 2024-08-13. Symmetry reduction and reconstruction in contact geometry and Lagrange-Poincar\'e-Herglotz equations. https://arxiv.org/abs/2408.06892

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