Different Models of Friction in Double-Spherical Tippe-Top Dynamics

  • A. A. Zobova
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 30)


Dynamics of a two-spherical tippe-top on a rough horizontal plane is considered. The tippe-top is bounded by a non-convex surface that consists of two-spheres and a cylinder; the axis of cylinder coincides with the common spheres’ axes of symmetry. Being fast spun around its axis of symmetry the tippe-top overturns from the bottom (the big sphere) to the leg (that is modeled by a small sphere) and some time it returns back to stable equilibrium position. Different models of friction are examined analytically and numerically. Numerical investigation is done in assumption that supporting plane is slightly deformable, that allows one to describe rolling and impacts by the same system of dynamical equations. Results of numerical investigation coincide with analytical conclusions.


Friction Force Friction Model Coulomb Friction Friction Torque Rigid Body Dynamic 
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  1. 1.
    Contensou, P.: Couplage entre frottement de glissement et frottement de pivotement dans la theorie de la toupee. In: Kreiselprobleme. Gyrodym. Symp., pp. 210–216 (1963)Google Scholar
  2. 2.
    Karapetyan, A.V.: Invariant Sets of Mechanical Systems. In: Modern Methods of Analytical Dynamics and their Applications. Springer, Wien-NY (1998)Google Scholar
  3. 3.
    Karapetyan, A.V.: Global qualitative analysis of tippe top dynamics. Mechanics of Solids 43(3), 342–348 (2008)CrossRefGoogle Scholar
  4. 4.
    Karapetyan, A.V.: A two-parameter friction model. J. Appl. Math. Mech. 73(4), 367–370 (2009)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Leine, R.I., Gloker, C.: A set-valued force law for spatial Coulomb – Contensou friction. Europ. J. Mech. A/Solids. 22(2), 193–216 (2003)zbMATHCrossRefGoogle Scholar
  6. 6.
    Routh, E.J.: The advanced part of a treatise on the dynamics of a system of rigid bodies. MacMillan, London (1884)Google Scholar
  7. 7.
    Zhuravlev, V.F.: A model of dry friction in the problem of the rolling of solids. J. Appl. Math. Mech. 62(5), 762–767 (1998)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Zobova, A.A., Karapetyan, A.: Analysis of the steady motions of the tippe top. J. Appl. Math. Mech. 73(6), 623–630 (2009)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Dordrecht Heidelberg London New York 2011

Authors and Affiliations

  • A. A. Zobova
    • 1
  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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