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This article is cited in 3 scientific papers (total in 3 papers) The Rolling Motion of a Truncated Ball Without Slipping and Spinning on a Plane Alexander A. Kilinab, Elena N. Pivovarovab a Institute of Mathematics and Mechanics of the Ural Branch of RAS, ul. S. Kovalevskoi 16, Ekaterinburg, 620990 Russia b Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia Abstract: This paper is concerned with the dynamics of a top in the form of a truncated ball as it moves without slipping and spinning on a horizontal plane about a vertical. Such a system is described by differential equations with a discontinuous right-hand side. Equations describing the system dynamics are obtained and a reduction to quadratures is performed. A bifurcation analysis of the system is made and all possible types of the top’s motion depending on the system parameters and initial conditions are defined. The system dynamics in absolute space is examined. It is shown that, except for some special cases, the trajectories of motion are bounded. Keywords: integrable system, system with discontinuity, nonholonomic constraint, bifurcation diagram, absolute dynamics
DOI: https://doi.org/10.1134/S156035471703008X   References:
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Bibliographic databases:    Document Type: Article MSC: 70E15, 70E18, 70E40, 37Jxx Received: 03.04.2017 Language: English Citation: Alexander A. Kilin, Elena N. Pivovarova, “The Rolling Motion of a Truncated Ball Without Slipping and Spinning on a Plane”, Regul. Chaotic Dyn., 22:3 (2017), 
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Citing articles on Google Scholar: Russian citations, English citations Related articles on Google Scholar: Russian articles, English articles This publication is cited in the following articles:
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