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Nelin. Dinam., 2016, Volume 12, Number 1, Pages 145–163 (Mi nd517)  

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

Translated papers

On the Hadamard–Hamel problem and the dynamics of wheeled vehicles

A. V. Borisova, A. A. Kilinb, I. S. Mamaeva

a Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700 Russia
b Udmurt State University, Universitetskaya 1, Izhevsk, 426034 Russia

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
Russian Foundation for Basic Research 15-38-20879 ́îë_à_âåä
15-08-09261-à


Full text: PDF file (445 kB)
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English version:
Regul. Chaotic Dyn., 2015, 20:6, 752–766

Document Type: Article
UDC: 531.3
MSC: 37J60, 37N05
Received: 12.10.2015
Revised: 09.11.2015

Citation: A. V. Borisov, A. A. Kilin, I. S. Mamaev, “On the Hadamard–Hamel problem and the dynamics of wheeled vehicles”, Nelin. Dinam., 12:1 (2016), 145–163; Regul. Chaotic Dyn., 20:6 (2015), 752–766

Citation in format AMSBIB
\Bibitem{BorKilMam16}
\by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev
\paper On the Hadamard–Hamel problem and the dynamics of wheeled vehicles
\jour Nelin. Dinam.
\yr 2016
\vol 12
\issue 1
\pages 145--163
\mathnet{http://mi.mathnet.ru/nd517}
\transl
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 6
\pages 752--766
\crossref{https://doi.org/10.1134/S1560354715060106}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84948952940}


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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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