论文标题
滚动电阻模型对Tippe顶部反演的影响
The influence of the rolling resistance model on tippe top inversion
论文作者
论文摘要
在本文中，我们分析了摩擦模型对Tippe顶部反转的效果，在此情况下，所有耗散力的作用不仅是通过在接触点上施加的力来描述的，而且还通过额外的滚动电阻扭矩来描述。我们表明，根据所使用的摩擦模型，系统接收不同的第一积分。特别是，我们提供了摩擦模型的示例，其中保留了耶利特积分，拉格朗日积分或区域积分。 我们详细介绍了所有耗散力的作用均简化为水平滚动抗性扭矩。在这种情况下，我们发现系统的永久旋转并分析其线性稳定性。另外，我们表明，对于这种摩擦模型，未观察到倒置。
In this paper, we analyze the effect which the choice of a friction model has on tippe top inversion in the case where the resulting action of all dissipative forces is described not only by the force applied at the contact point, but also by the additional rolling resistance torque. We show that, depending on the friction model used, the system admits different first integrals. In particular, we give examples of friction models where the Jellett integral, the Lagrange integral or the area integral is preserved. We examine in detail the case where the action of all dissipative forces reduces to the horizontal rolling resistance torque. For this case we find permanent rotations of the system and analyze their linear stability. Also, we show that for this friction model no inversion is observed.
