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This article is cited in 12 scientific papers (total in 12 papers)
Translated papers
Dynamics of the Chaplygin sleigh on a cylinder
I. A. Bizyaeva, A. V. Borisovbc, I. S. Mamaeva a Udmurt State University,
ul. Universitetskaya 1, Izhevsk, 426034, Russia
b Moscow Institute of Physics and Technology,
Institutskiy per. 9, Dolgoprudny, Moscow, 141700, Russia
c National Research Nuclear University “MEPhI”,
Kashirskoe sh. 31, Moscow, 115409, Russia
Abstract:
This paper is concerned with the motion of the Chaplygin sleigh on the surface of a circular cylinder. In the case of inertial motion, the problem reduces to the study of the dynamical system on a (two-dimensional) torus and to the classification of singular points. Particular cases in which the system admits an invariant measure are found. In the case of a balanced and dynamically symmetric Chaplygin sleigh moving in a gravitational field it is shown that on the average the system has no drift along the vertical.
Keywords:
Chaplygin sleigh, invariant measure, nonholonomic mechanics.
Received: 16.10.2015 Accepted: 28.12.2015
Citation:
I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dynamics of the Chaplygin sleigh on a cylinder”, Nelin. Dinam., 12:4 (2016), 675–687; Regular and Chaotic Dynamics, 21:1 (2016), 136–146
Linking options:
https://www.mathnet.ru/eng/nd546 https://www.mathnet.ru/eng/nd/v12/i4/p675
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