  The tippedisk is a mathematical-mechanical archetype for a peculiar
friction-induced instability phenomenon leading to the inversion of an
unbalanced spinning disk, being reminiscent to (but different from) the
well-known inversion of the tippetop. A reduced model of the tippedisk, in the
form of a three-dimensional ordinary differential equation, has been derived
recently, followed by a preliminary local stability analysis of stationary
spinning solutions. In the current paper, a global analysis of the reduced
system is pursued using the framework of singular perturbation theory. It is
shown how the presence of friction leads to slow-fast dynamics and the creation
of a two-dimensional slow manifold. Furthermore, it is revealed that a
bifurcation scenario involving a homoclinic bifurcation and a Hopf bifurcation
leads to an explanation of the inversion phenomenon. In particular, a
closed-form condition for the critical spinning speed for the inversion
phenomenon is derived. Hence, the tippedisk forms an excellent
mathematical-mechanical problem for the analysis of global bifurcations in
singularly perturbed dynamics.
