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Nelin. Dinam., 2016, Volume 12, Number 4, Pages 675–687 (Mi nd546)  

This article is cited in 1 scientific paper (total in 1 paper)

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

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation


DOI: https://doi.org/10.20537/nd1604010

Full text: PDF file (331 kB)
References: PDF file   HTML file

English version:
Regular and Chaotic Dynamics, 2016, 21:1, 136–146

Bibliographic databases:

Document Type: Article
UDC: 531.38
MSC: 37J60, 37C10
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

Citation in format AMSBIB
\Bibitem{BizBorMam16}
\by I.~A.~Bizyaev, A.~V.~Borisov, I.~S.~Mamaev
\paper Dynamics of the Chaplygin sleigh on a cylinder
\jour Nelin. Dinam.
\yr 2016
\vol 12
\issue 4
\pages 675--687
\mathnet{http://mi.mathnet.ru/nd546}
\crossref{https://doi.org/10.20537/nd1604010}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3453983}
\zmath{https://zbmath.org/?q=an:1346.70006}
\elib{http://elibrary.ru/item.asp?id=27715771}
\transl
\jour Regular and Chaotic Dynamics
\yr 2016
\vol 21
\issue 1
\pages 136--146
\crossref{https://doi.org/10.1134/S1560354716010081}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84957548917}


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    Translation

    This publication is cited in the following articles:
    1. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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