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Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2024, Volume 11, Issue 2, Pages 347–353
DOI: https://doi.org/10.21638/spbu01.2024.208
(Mi vspua301)
 

MECHANICS

Integrability by quadratures of the problem of rolling motion of a heavy homogeneous ball on a surface of revolution of the second order

A. S. Kuleshov, A. A. Shishkov

Lomonosov Moscow State University, 1, Leninskie Gory, Moscow, 119991, Russian Federation
Abstract: In this paper, we consider the problem of rolling of a heavy homogeneous ball on a perfectly rough surface of revolution. Usually, when considering this problem, it is convenient to specify explicitly the surface along which the center of the ball moves during rolling, instead of the surface along which the ball rolls. The surface on which the center of the ball moves is equidistant to the surface on which the ball is rolling. It is well known, that the considered problem is reduced to the integration the second order linear homogeneous differential equation. In this paper we assume, that the surface along which the center of the ball moves is a non - degenerate surface of revolution of the second order. Using the Kovacic algorithm we prove that the general solution of the corresponding linear differential equation can be found explicitly. This means, that in this case the problem of rolling of a ball on a surface of revolution can be integrated by quadratures.
Keywords: rolling without sliding, homogeneous ball, surface of revolution of the 2nd order, integrability by quadratures.
Funding agency Grant number
Russian Science Foundation RAI-RSF-2490
This work is supported by Russian Science Foundation (project no. RAI-RSF-2490).
Received: 09.08.2023
Revised: 06.11.2023
Accepted: 09.11.2023
Document Type: Article
UDC: 517.926+531.384
MSC: 70E18, 70F25, 34A30
Language: Russian
Citation: A. S. Kuleshov, A. A. Shishkov, “Integrability by quadratures of the problem of rolling motion of a heavy homogeneous ball on a surface of revolution of the second order”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 11:2 (2024), 347–353
Citation in format AMSBIB
\Bibitem{KulShi24}
\by A.~S.~Kuleshov, A.~A.~Shishkov
\paper Integrability by quadratures of the problem of rolling motion of a heavy homogeneous ball on a surface of revolution of the second order
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2024
\vol 11
\issue 2
\pages 347--353
\mathnet{http://mi.mathnet.ru/vspua301}
\crossref{https://doi.org/10.21638/spbu01.2024.208}
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