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The Tippedisk: a Tippetop Without Rotational Symmetry

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Abstract

The aim of this paper is to introduce the tippedisk to the theoretical mechanics community as a new mechanical-mathematical archetype for friction induced instability phenomena. We discuss the modeling and simulation of the tippedisk, which is an inhomogeneous disk showing an inversion phenomenon similar but more complicated than the tippetop. In particular, several models with different levels of abstraction, parameterizations and force laws are introduced. Moreover, the numerical simulations are compared qualitatively with recordings from a high-speed camera. Unlike the tippetop, the tippedisk has no rotational symmetry, which greatly complicates the three-dimensional nonlinear kinematics. The governing differential equations, which are presented here in full detail, describe all relevant physical effects and serve as a starting point for further research.

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Notes

  1. http://www.thephitop.com/

  2. Youtube: Orbit Spinning Tops (Youtube: Orbit Spinning Tops)

  3. Youtube: Spinning Disk Trick (Youtube: Spinning Disk Trick)

  4. Youtube: Spinning Disk Trick Solution (Youtube: Spinning Disk Trick Solution)

  5. https://rotations.berkeley.edu/a-tumbling-t-handle-in-space/

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Authors and Affiliations

  1. Institute for Nonlinear Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569, Stuttgart, Germany

    Simon Sailer, Simon R. Eugster & Remco I. Leine

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  1. Simon Sailer
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  2. Simon R. Eugster
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  3. Remco I. Leine
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Correspondence to Simon Sailer, Simon R. Eugster or Remco I. Leine.

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MSC2010

70E18, 70K20, 70E50

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Sailer, S., Eugster, S.R. & Leine, R.I. The Tippedisk: a Tippetop Without Rotational Symmetry. Regul. Chaot. Dyn. 25, 553–580 (2020). https://doi.org/10.1134/S1560354720060052

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