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This article is cited in 43 scientific papers (total in 43 papers)
The Dynamics of Nonholonomic Systems Consisting of a
Spherical Shell with a Moving Rigid Body Inside
Ivan A. Bizyaeva, Alexey V. Borisovbcd, Ivan S. Mamaeva a Udmurt State University,
ul. Universitetskaya 1, Izhevsk, 426034 Russia
b Moscow Institute of Physics and Technology,
Institutskii per. 9, Dolgoprudny, Moscow Region, 141700 Russia
c A. A.Blagonravov Mechanical Engineering Research Institute of RAS,
ul. Bardina 4, Moscow, 117334 Russia
d National Research Nuclear University “MEPhI”,
Kashirskoe sh. 31, Moscow, 115409 Russia
Abstract:
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.
Keywords:
nonholonomic constraint, tensor invariants, isomorphism, nonholonomic hinge.
Received: 04.09.2013 Accepted: 31.10.2013
Citation:
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
Linking options:
https://www.mathnet.ru/eng/rcd126 https://www.mathnet.ru/eng/rcd/v19/i2/p198
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Abstract page: | 254 | References: | 68 |
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