凸体在平面上滚动而不滑动的非整体性问题的仿射概括

arXiv - MATH - Mathematical Physics Pub Date : 2024-09-12 DOI:arxiv-2409.08072

M. Costa Villegas, L. C. García-Naranjo

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摘要

我们介绍了一类例子，这些例子提供了凸体在平面上滚动而不滑动的非整体问题的仿射一般化。我们研究了系统的动力学方面，如第一积分的存在性、光滑不变度量和可积分性，并特别关注了凸体是动态平衡球或旋转体的情况。

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Affine generalizations of the nonholonomic problem of a convex body rolling without slipping on the plane

We introduce a class of examples which provide an affine generalization of the nonholonomic problem of a convex body rolling without slipping on the plane. We investigate dynamical aspects of the system such as existence of first integrals, smooth invariant measure and integrability, giving special attention to the cases in which the convex body is a dynamically balanced sphere or a body of revolution.

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arXiv - MATH - Mathematical Physics

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