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This article is cited in 7 scientific papers (total in 7 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
| Funding Agency |
Grant Number |
Russian Foundation for Basic Research  |
15-08-09093-a
15-38-20879 mol_a_ved |
| Russian Science Foundation |
15-12-20035 |
| The work of A.A. Kilin (Sections 1, 2, and 4) is supported by the RFBR grants 15-08-09093-a and 15-38-20879 mol_a_ved. The work of E.N. Pivovarova (Section 3) is carried out within the framework of the RSF grant no. 15-12-20035. |
DOI:
https://doi.org/10.1134/S156035471703008X
 References:
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Bibliographic databases:
  
MSC: 70E15, 70E18, 70E40, 37Jxx
Received: 03.04.2017
Accepted:12.05.2017
Language:
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), 298–317
Citation in format AMSBIB
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\by Alexander A. Kilin, Elena N. Pivovarova
\paper The Rolling Motion of a Truncated Ball Without Slipping and Spinning on a Plane
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 3
\pages 298--317
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\crossref{https://doi.org/10.1134/S156035471703008X}
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Linking options:
http://mi.mathnet.ru/eng/rcd258 http://mi.mathnet.ru/eng/rcd/v22/i3/p298
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Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “An Invariant Measure and the Probability of a Fall in the Problem of an Inhomogeneous Disk Rolling on a Plane”, Regul. Chaotic Dyn., 23:6 (2018), 665–684
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A. V. Borisov, A. V. Tsyganov, “Vliyanie effektov Barnetta-Londona i Einshteina-de Gaaza na dvizhenie negolonomnoi sfery Rausa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:4 (2019), 583–598
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Ivan S. Mamaev, Evgeny V. Vetchanin, “Dynamics of Rubber Chaplygin Sphere under Periodic Control”, Regul. Chaotic Dyn., 25:2 (2020), 215–236
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Elizaveta M. Artemova, Yury L. Karavaev, Ivan S. Mamaev, Evgeny V. Vetchanin, “Dynamics of a Spherical Robot with Variable Moments of Inertia and a Displaced Center of Mass”, Regul. Chaotic Dyn., 25:6 (2020), 689–706
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