Towards a Prototype of a Spherical Tippe Top

Figure 12

Trajectories of the system (3.15)-(3.16) projected onto the subspace of variables (𝛼,𝜃,𝑛) for an eccentric ball of Group IIb with friction 𝜇=0.04. The bold-solid curve is that of intermediate states (5.4), (5.5), and (5.10); the line 𝑆 in the (𝛼,𝑛)-plane represents the initial condition 𝛼=(1/2𝐴)(𝐶𝑛+𝐶²𝑛²+4𝐴𝑚𝑔𝜖). For 𝑛>𝑛₋, fixed points on 𝜃=0 are unstable. Trajectories are then attracted to a stable intermediate state (a point on the solid curve) for 𝑛₋<𝑛<𝑛_∗ or to a point on the plane 𝜃=𝜋 (i.e., flipping occurs) for 𝑛>𝑛_∗. The two insets are details at the starting position, one for the stable case and one for the unstable case. The parameters are chosen as 𝑚=𝑔=1, 𝜖/𝑅=0.3, and 𝐴/𝐶=0.92.