Journal of Applied Mathematics / 2012 / Article / Fig 15

Research Article

Towards a Prototype of a Spherical Tippe Top

Figure 15

Periodic motion around intermediate state (IS) in frame, , , and . Solution (i) is the pure rolling case for , , and , (ii) is the pure slipping case for and (iii) is for , and (iv) for , the first s. The data is chosen for a stable at , and the initial condition for (ii), (iii), and (iv) is a point on the solution curve of (i). For (i) a periodic motion is obtained, and for (ii) a quasiperiodic motion is observed as it is sketched in the frame. For the trajectories spiral inwards towards the IS. For large friction, this motion is very slow (only the first 100 s is depicted). Also the speed at the contact point, , is given. In case (iii) this speed is large when far from the IS, and for (iv) this speed is very small corresponding to the very slow spiraling motion. Note that at , as it is expected.

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