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Regular and Chaotic Dynamics, 2024, Volume 29, Issue 5, Pages 728–750
DOI: https://doi.org/10.1134/S1560354724530017 (Mi rcd1278) 		 
Special Issue: Proceedings of RCD Conference 2023

Nonlinear Dynamics of a Roller Bicycle

Ivan A. Bizyaeva, Ivan S. Mamaevb

a Ural Mathematical Center, Udmurt State University, ul. Universitetskaya 1, 426034 Izhevsk, Russia
b Kalashnikov Izhevsk State Technical University, ul. Studencheskaya 7, 426069 Izhevsk, Russia
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DOI: https://doi.org/10.1134/S1560354724530017
Abstract: In this paper we consider the dynamics of a roller bicycle on a horizontal plane. For this bicycle we derive a nonlinear system of equations of motion in a form that allows us to take into account the symmetry of the system in a natural form. We analyze in detail the stability of straight-line motion depending on the parameters of the bicycle. We find numerical evidence that, in addition to stable straight-line motion, the roller bicycle can exhibit other, more complex, trajectories for which the bicycle does not fall.
Keywords: roller bicycle, nonholonomic system, stability, quasi-velocities, Poincaré map
Funding agency Grant number
Russian Science Foundation 21-71-10039
Ministry of Science and Higher Education of the Russian Federation FZZN-2020-0011
The work of I. A. Bizyaev (Sections 2 and 4) was supported by the Russian Science Foundation (No. 21-71-10039). The work of I. S. Mamaev (Sections 3 and 5) was carried out within the framework of the state assignment of the Ministry of Science and Higher Education of Russia (FZZN-2020-0011).
Received: 12.03.2024
Accepted: 29.04.2024
Document Type: Article
MSC: 37J60, 34A34
Language: English
Citation: Ivan A. Bizyaev, Ivan S. Mamaev, “Nonlinear Dynamics of a Roller Bicycle”, Regul. Chaotic Dyn., 29:5 (2024), 728–750
Citation in format AMSBIB
\Bibitem{BizMam24}
\by Ivan A. Bizyaev, Ivan S. Mamaev
\paper Nonlinear Dynamics of a Roller Bicycle
\jour Regul. Chaotic Dyn.
\yr 2024
\vol 29
\issue 5
\pages 728--750
\mathnet{http://mi.mathnet.ru/rcd1278}
\crossref{https://doi.org/10.1134/S1560354724530017}
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