Abstract—

The simplest model of a tippe-top is a nonhomogeneous dynamically symmetric ball whose center of mass lies on the axis of dynamic symmetry, but does not coincide with the geometric center. Local analysis of this model is presented in [1, 2] and global qualitative analysis is presented in [3–5]. Numerical studies for multicomponent dry friction were carried out in [6]. A comparative analysis of various models was carried out in [7]. A method of generalized Smale diagrams [9, 10] regarding the problem of the motion of a tippe-top top on a viscoelastic plane is presented in [8].

In this paper, approximate equations that describe the dynamics of the top and allow us to supplement the qualitative analysis with quantitative estimates for multicomponent models of dry and viscous friction under a certain class of initial conditions have been presented.

中文翻译：

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Tippe-Top动力学中的过渡过程

摘要-

翻斗顶部的最简单模型是不均匀的动态对称球，其质心位于动态对称轴上，但与几何中心不重合。该模型的局部分析在[1，2]中进行，整体定性分析在[3-5]中进行。在[6]中进行了多组分干摩擦的数值研究。在[7]中对各种模型进行了比较分析。在[8]中提出了一种关于毛尖顶在粘弹性平面上运动问题的广义Smale图的方法[9，10]。

在本文中，提出了近似方程式，该方程式描述了顶部的动力学特性，并允许我们使用定量估计来补充定性分析，该定量估计是针对特定类别的初始条件下的干摩擦和粘滞摩擦的多分量模型。