The Tippedisk: A Minimal Model For Friction-Induced Inversion

Abstract

The tippedisk is a new mechanical-mathematical archetype for friction induced insta-bility phenomena, showing an inversion similar to the inversion of the tippetop. Un-like the tippetop, the tippedisk has no rotational symmetry, which greatly complicates its analysis. Since the system cannot be reduced to a planar one, one has to consider the full three-dimensional kinematics, being intrinsically nonlinear. In this work a new minimal model is derived that contains the main relevant physical effects so that the inversion phenomenon can be described qualitatively. The in-depth analysis leads to slow-fast systems with homoclinic connections and global bifurcations.