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Dynamics of the tippe top via Routhian reduction

Abstract

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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Correspondence to M. C. Ciocci.

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Ciocci, M.C., Langerock, B. Dynamics of the tippe top via Routhian reduction. Regul. Chaot. Dyn. 12, 602–614 (2007). https://doi.org/10.1134/S1560354707060032

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  • DOI: https://doi.org/10.1134/S1560354707060032

MSC2000 numbers

  • 37J15
  • 37J25
  • 70E18
  • 70H03
  • 70H33

Key words

  • tippe top
  • eccentric sphere
  • Lagrangian equations
  • symmetries
  • Routhian reduction
  • relative equilibria
  • (linear) stability
  • bifurcation