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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, Volume 32, Issue 4, Pages 615–629
DOI: https://doi.org/10.35634/vm220408 (Mi vuu829) 		 
MECHANICS

Investigation of the orbital stability of rectilinear motions of roller-racer on a vibrating plane

E. M. Artemovaa, A. A. Kilina, Yu. V. Korobeinikovab

a Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia
b Kalashnikov Izhevsk State Technical University, ul. Studencheskaya, 7, Izhevsk, 426069, Russia
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DOI: https://doi.org/10.35634/vm220408
Abstract: This paper addresses the problem of a roller-racer rolling on an oscillating plane. Equations of motion of the roller-racer in the form of a system of four nonautonomous differential equations are obtained. Two families of particular solutions are found which correspond to rectilinear motions of the roller-racer along and perpendicular to the plane's oscillations. Numerical estimates are given for the multipliers of solutions corresponding to the motion of the robot along the oscillations. Also, a special case is presented in which it is possible to obtain analytic expressions of the multipliers. In this case, it is shown that the motion along oscillations of a “folded” roller-racer is linearly orbitally stable as it moves with its joint ahead, and that all other motions are unstable. It is shown that, in a linear approximation, the family corresponding to the motion of the robot is perpendicular to the plane's oscillations, that is, it is unstable.
Keywords: roller-racer, nonholonomic constraints, vibrating plane, monodromy matrix, orbital stability.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2022-889
FEWS–2020–0009
FZZN–2020–0011
The work of A.A. Kilin (§1) was performed at the Ural Mathematical Center (Agreement No. 075-02-2022-889). The work of E.M. Artemova (§2.1) was supported by the framework of the state assignment or the Ministry of Science and Higher Education (No. FEWS-2020-0009). The work of Yu.V. Korobeinikova (§2.2) was supported by the framework of the state assignment or the Ministry of Science and Higher Education (No. FZZN-2020-0011).
Received: 17.10.2022
Accepted: 09.12.2022
Bibliographic databases:
Document Type: Article
UDC: 517.933, 517.938
MSC: 37J60, 34D20
Language: Russian
Citation: E. M. Artemova, A. A. Kilin, Yu. V. Korobeinikova, “Investigation of the orbital stability of rectilinear motions of roller-racer on a vibrating plane”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 32:4 (2022), 615–629
Citation in format AMSBIB
\Bibitem{ArtKilKor22}
\by E.~M.~Artemova, A.~A.~Kilin, Yu.~V.~Korobeinikova
\paper Investigation of the orbital stability of rectilinear motions of roller-racer on a vibrating plane
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2022
\vol 32
\issue 4
\pages 615--629
\mathnet{http://mi.mathnet.ru/vuu829}
\crossref{https://doi.org/10.35634/vm220408}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4534874}
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    		Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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