The aim of this paper is to introduce the tippedisk to the theoretical mechanics community as a new mechanical-mathematical archetype for friction induced instability phenomena. We discuss the modeling and simulation of the tippedisk, which is an inhomogeneous disk showing an inversion phenomenon similar but more complicated than the tippetop. In particular, several models with different levels of abstraction, parameterizations and force laws are introduced. Moreover, the numerical simulations are compared qualitatively with recordings from a high-speed camera. Unlike the tippetop, the tippedisk has no rotational symmetry, which greatly complicates the three-dimensional nonlinear kinematics. The governing differential equations, which are presented here in full detail, describe all relevant physical effects and serve as a starting point for further research.

本文的目的是介绍小提琴作为一种新的力学-数学原型来解决摩擦引起的不稳定性现象，这给理论力学界带来了新的希望。我们讨论了tippisk的建模和仿真，tippisk是一个不均匀的磁盘，显示出与tippetop相似但更复杂的反转现象。特别是，引入了几种具有不同抽象度，参数化和力定律的模型。此外，数值模拟与高速相机的记录进行了定性比较。与尖端不同，尖齿不具有旋转对称性，这使三维非线性运动学大大复杂化。在这里详细介绍的控制微分方程描述了所有相关的物理效应，并作为进一步研究的起点。