Dynamics of the Tippe Top via Routhian Reduction

    2007, Volume 12, Number 6, pp.  602-614

    Author(s): Ciocci M., Langerock B.

    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 CBJB according to the existence and stability type of the steady states.
    Keywords: tippe top, eccentric sphere, Lagrangian equations, symmetries, Routhian reduction, relative equilibria, (linear) stability, bifurcation
    Citation: Ciocci M., Langerock B., Dynamics of the Tippe Top via Routhian Reduction, Regular and Chaotic Dynamics, 2007, Volume 12, Number 6, pp. 602-614

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