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Transition Processes in Tippe-Top Dynamics

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Abstract—

The simplest model of a tippe-top is a nonhomogeneous dynamically symmetric ball whose center of mass lies on the axis of dynamic symmetry, but does not coincide with the geometric center. Local analysis of this model is presented in [1, 2] and global qualitative analysis is presented in [3–5]. Numerical studies for multicomponent dry friction were carried out in [6]. A comparative analysis of various models was carried out in [7]. A method of generalized Smale diagrams [9, 10] regarding the problem of the motion of a tippe-top top on a viscoelastic plane is presented in [8].

In this paper, approximate equations that describe the dynamics of the top and allow us to supplement the qualitative analysis with quantitative estimates for multicomponent models of dry and viscous friction under a certain class of initial conditions have been presented.

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Funding

The work was supported by the Russian Foundation for Basic Research, project nos. 19-01-00140 and 18-01-00335, and the program of basic research in priority areas determined by the Presidium of the Russian Academy of Sciences, no. 7 “New developments in promising areas of energy, mechanics, and robotics”.

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  1. Moscow Institute of Physics and Technology, Dolgoprudny, Russia

    M. A. Munitsyna

  2. Trapeznikov Institute of Control Sciences RAS, Moscow, Russia

    M. A. Munitsyna

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  1. M. A. Munitsyna
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Correspondence to M. A. Munitsyna.

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Translated by N. Petrov

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Munitsyna, M.A. Transition Processes in Tippe-Top Dynamics. Mech. Solids 55, 1178–1184 (2020). https://doi.org/10.3103/S0025654420080178

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