接触几何和拉格朗日-平卡雷-赫格洛茨方程中的对称性还原和重构

Alexandre Anahory Simoes, Leonardo Colombo, Manuel de Leon, Modesto Salgado, Silvia Souto
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引用次数: 0

摘要

本文研究了一个接触拉格朗日系统的还原过程,该系统的拉格朗日在一组对称性下是不变的。我们给出了所得到的还原微分方程,即所谓的拉格朗日-庞加莱-赫格洛兹方程的明确坐标表达式。我们的框架依赖于相关的赫格洛茨矢量场及其投影矢量场,以及使用精心选择的准位移。我们还讨论了一些例子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Symmetry reduction and reconstruction in contact geometry and Lagrange-Poincaré-Herglotz equations
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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