Tip-top dynamics in viscous friction

The simplest model of a tippe-top is an nonhomogeneous dynamically symmetric ball, the center of mass of which lies on the axis of dynamic symmetry, but does not coincide with the geometric center. In the present work, approximate equations that describe the dynamics of a tip-top under a certain class of initial conditions for a model of viscous friction are obtained. Qualitative analysis is supplemented by quantitative estimates.