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Regular and Chaotic Dynamics, 2015, Volume 20, Issue 6, Pages 752–766
DOI: https://doi.org/10.1134/S1560354715060106 (Mi rcd34) 		 
This article is cited in 37 scientific papers (total in 37 papers)

On the Hadamard–Hamel Problem and the Dynamics of Wheeled Vehicles

Alexey V. Borisova, Alexander A. Kilinb, Ivan S. Mamaevc

a Moscow Institute of Physics and Technology, Dolgoprudnyi, 141700, Russia
b Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia
c Steklov Mathematical Institute, ul. Gubkina 8, Moscow, 119991, Russia
Citations (37)
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DOI: https://doi.org/10.1134/S1560354715060106
Abstract: In this paper, we develop the results obtained by J.Hadamard and G.Hamel concerning the possibility of substituting nonholonomic constraints into the Lagrangian of the system without changing the form of the equations of motion. We formulate the conditions for correctness of such a substitution for a particular case of nonholonomic systems in the simplest and universal form. These conditions are presented in terms of both generalized velocities and quasi-velocities. We also discuss the derivation and reduction of the equations of motion of an arbitrary wheeled vehicle. In particular, we prove the equivalence (up to additional quadratures) of problems of an arbitrary wheeled vehicle and an analogous vehicle whose wheels have been replaced with skates. As examples, we consider the problems of a one-wheeled vehicle and a wheeled vehicle with two rotating wheel pairs.
Keywords: nonholonomic constraint, wheeled vehicle, reduction, equations of motion.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation
Russian Foundation for Basic Research 15-38-20879 mol_a_ved
13-01-12462-ofi_m
The work of A.V.Borisov was carried out within the framework of the state assignment for institutions of higher education. The work of A.A.Kilin was supported by the RFBR grant no. 15-38-20879 mol_a_ved. The work of I.S.Mamaev was supported by the RFBR grant no. 13-01-12462-ofi_m.
Received: 12.10.2015
Accepted: 09.11.2015
Bibliographic databases:
Document Type: Article
MSC: 37J60, 37N05
Language: English
Citation: Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “On the Hadamard–Hamel Problem and the Dynamics of Wheeled Vehicles”, Regul. Chaotic Dyn., 20:6 (2015), 752–766
Citation in format AMSBIB
\Bibitem{BorKilMam15}
\by Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev
\paper On the Hadamard--Hamel Problem and the Dynamics of Wheeled Vehicles
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 6
\pages 752--766
\mathnet{http://mi.mathnet.ru/rcd34}
\crossref{https://doi.org/10.1134/S1560354715060106}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3431189}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2015RCD....20..752B}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84948952940}
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    This publication is cited in the following 37 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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