Аннотация:
In this paper we investigate two systems consisting of a spherical shell rolling without slipping on a plane and a moving rigid body fixed inside the shell by means of two different mechanisms. In the former case the rigid body is attached to the center of the ball on a spherical hinge. We show an isomorphism between the equations of motion for the inner body with those for the ball moving on a smooth plane. In the latter case the rigid body is fixed by means of a nonholonomic hinge. Equations of motion for this system have been obtained and new integrable cases found. A special feature of the set of tensor invariants of this system is that it leads to the Euler–Jacobi–Lie theorem, which is a new integration mechanism in nonholonomic mechanics. We also consider the problem of free motion of a bundle of two bodies connected by means of a nonholonomic hinge. For this system, integrable cases and various tensor invariants are found.
The work of A. V.Borisov was carried out within the framework of the state assignment to
the Udmurt State University “Regular and Chaotic Dynamics”. The work of I.S.Mamaev was
supported by the RFBR grants 13-01-12462-ofi m. The work of I. A.Bizyaev was supported by the
Grant of the President of the Russian Federation for Support of Young Doctors of Science MD-
2324.2013.1, and by the Grant of the President of the Russian Federation for Support of Leading
Scientific Schools NSh-2964.2014.1.
Поступила в редакцию: 04.09.2013 Принята в печать: 31.10.2013
Образец цитирования:
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of Nonholonomic Systems Consisting of a
Spherical Shell with a Moving Rigid Body Inside”, Regul. Chaotic Dyn., 19:2 (2014), 198–213
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\by Ivan~A.~Bizyaev, Alexey~V.~Borisov, Ivan~S.~Mamaev
\paper The Dynamics of Nonholonomic Systems Consisting of a
Spherical Shell with a Moving Rigid Body Inside
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 2
\pages 198--213
\mathnet{http://mi.mathnet.ru/rcd126}
\crossref{https://doi.org/10.1134/S156035471402004X}
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Цитирование в формате AMSBIB
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