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

Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]

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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2016, Volume 12, Number 4, Pages 675–687
DOI: https://doi.org/10.20537/nd1604010 (Mi nd546)

This article is cited in 12 scientific papers (total in 12 papers)

Translated papers

Dynamics of the Chaplygin sleigh on a cylinder

I. A. Bizyaev^a, A. V. Borisov^bc, I. S. Mamaev^a

^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

Full-text PDF (331 kB) Citations (12)

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

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

Received: 16.10.2015
Accepted: 28.12.2015

English version:
Regular and Chaotic Dynamics, 2016, Volume 21, Issue 1, Pages 136–146
DOI: https://doi.org/10.1134/S1560354716010081

Bibliographic databases:

Document Type: Article

UDC: 531.38

MSC: 37J60, 37C10

Language: Russian

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

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\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://mathscinet.ams.org/mathscinet-getitem?mr=3453983}

\zmath{https://zbmath.org/?q=an:1346.70006}

\elib{https://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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84957548917}

Linking options:

https://www.mathnet.ru/eng/nd546

https://www.mathnet.ru/eng/nd/v12/i4/p675

Translation

Dynamics of the Chaplygin Sleigh on a Cylinder
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev
Regul. Chaotic Dyn., 2016, 21:1, 136–146

This publication is cited in the following 12 articles:

Ali Ahmadi, Mahdi Gorji, Ahmad Peymaei, Kimia Khosravi Soofi, Ali Kamali, “Autonomous swimming on limit cycles with disturbance rejection capability for a fish-inspired robot”, Nonlinear Dyn, 2024
Alexander Kilin, Yuriy Karavaev, Kirill Yefremov, Lecture Notes in Networks and Systems, 324, Robotics for Sustainable Future, 2022, 428
Elizaveta M. Artemova, Alexander A. Kilin, 2020 International Conference Nonlinearity, Information and Robotics (NIR), 2020, 1
Kirill S. Yefremov, Tatiana B. Ivanova, Alexander A. Kilin, Yury L. Karavaev, 2020 International Conference Nonlinearity, Information and Robotics (NIR), 2020, 1
I. A. Bizyaev, A. V. Borisov, V. V. Kozlov, I. S. Mamaev, “Fermi-like acceleration and power-law energy growth in nonholonomic systems”, Nonlinearity, 32:9 (2019), 3209–3233
Borislav Gajić, Božidar Jovanović, “Nonholonomic connections, time reparametrizations, and integrability of the rolling ball over a sphere”, Nonlinearity, 32:5 (2019), 1675
Vitaliy Fedonyuk, Phanindra Tallapragada, “Sinusoidal control and limit cycle analysis of the dissipative Chaplygin sleigh”, Nonlinear Dyn, 93:2 (2018), 835
A. P. Ivanov, “On singular points of equations of mechanics”, Dokl. Math., 97:2 (2018), 167–169
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
A. A. Oshemkov, P. E. Ryabov, S. V. Sokolov, “Explicit determination of certain periodic motions of a generalized two-field gyrostat”, Russ. J. Math. Phys., 24:4 (2017), 517
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration”, Regul. Chaotic Dyn., 22:8 (2017), 955–975
I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “The Hess–Appelrot system and its nonholonomic analogs”, Proc. Steklov Inst. Math., 294 (2016), 252–275

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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