|
This article is cited in 13 scientific papers (total in 13 papers)
Dynamics of the Chaplygin Sleigh on a Cylinder
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, 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:
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Dynamics of the Chaplygin Sleigh on a Cylinder”, Regul. Chaotic Dyn., 21:1 (2016), 136–146
Linking options:
https://www.mathnet.ru/eng/rcd58 https://www.mathnet.ru/eng/rcd/v21/i1/p136
|
Statistics & downloads: |
Abstract page: | 282 | References: | 60 |
|