Nonlinear oscillations in the rolling motion of Euler’s disk

The fixed points of the dynamical system describing the rolling motion of a uniform disk or a uniform circular hoop on a rough horizontal plane without dissipation are analyzed. All fixed points of the system are stated to be steady motion states which are either saddle points or centers. The spectral analysis of the sound amplitude time series emitted by a toy of the rolling disk shows that the similar nonlinear oscillations are expected in the motion with dissipation. If under adiabatic approximation a finite-time singularity occurs, the bifurcation in the disk motion can appear.