Dynamics of the Tippe Top via Routhian Reduction

Details Dynamics of the Tippe Top via Routhian Reduction Dynamics of the Tippe Top via Routhian Reduction

2007-04-10

arxiv.org/abs/0704.1221v3

Regul. Chaotic Dyn. 12 (2007) pp602--614

Mathematics

Dynamical Systems

16 pages, 7 figures, added reference. Typos corrected and a forgotten term in de linearized system is added

Scientific paper

10.1134/S1560354707060032

We consider a tippe top modeled as an eccentric sphere, spinning on a horizontal table and subject to a sliding friction. Ignoring translational effects, we show that the system is reducible using a Routhian reduction technique. The reduced system is a two dimensional system of second order differential equations, that allows an elegant and compact way to retrieve the classification of tippe tops in six groups as proposed in [1] according to the existence and stability type of the steady states.

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