Regular and Chaotic Dynamics

, Volume 12, Issue 6, pp 602–614 | Cite as

Dynamics of the tippe top via Routhian reduction

Articles

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.

Key words

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

MSC2000 numbers

37J15 37J25 70E18 70H03 70H33 

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Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  1. 1.Department of MathematicsImperial College LondonLondonUK
  2. 2.Department of ArchitectureSint-Lucas Institute for Higher Education in the Sciences and the ArtsGhentBelgium

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