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Dynamics of a rolling and sliding disk in a plane. Asymptotic solutions, stability and numerical simulations

机译:平面中滚动和滑动磁盘的动力学。渐近解,稳定性和数值模拟

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摘要

We present a qualitative analysis of the dynamics of a rolling and sliding disk in a horizontal plane. It is based on using three classes of asymptotic solutions: straight-line rolling, spinning about a vertical diameter and tumbling solutions. Their linear stability analysis is given and it is complemented with computer simulations of solutions starting in the vicinity of the asymptotic solutions. The results on asymptotic solutions and their linear stability apply also to an annulus and to a hoop
机译:我们提出了在水平面上的滚动和滑动磁盘动力学的定性分析。它基于使用三类渐近解:直线滚动,绕垂直直径旋转和翻滚解。给出了它们的线性稳定性分析,并辅以从渐近解开始的解的计算机模拟。渐近解及其线性稳定性的结果也适用于环面和箍

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