A Complete Stability Chart for the Tippedisk

The tippedisk is a mathematical–mechanical archetype, showing a non-intuitive inversion behavior, if the disk is spun fast enough. By introducing a full 3D mechanical model and assuming set-valued force laws to account for normal and frictional contact forces, the dynamics of the tippedisk can be studied numerically. In addition, the model dimension can be reduced through model reduction techniques, yielding a lower dimensional model, being perfectly suited for the closed-form analysis of the qualitative dynamics. The previous work of the authors has shown that the bifurcation scenario contains a heteroclinic bifurcation, followed by a subcritical Hopf bifurcation. In this chapter, we derive a complete stability chart that characterizes various bifurcation scenarios in closed-form, which allows us to understand the qualitative dynamics of the tippedisk.