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Regul. Chaotic Dyn., 2016, Volume 21, Issue 4, Pages 455–476 (Mi rcd88)  

This article is cited in 7 scientific papers (total in 7 papers)

Historical and Critical Review of the Development of Nonholonomic Mechanics: the Classical Period

Alexey V. Borisova, Ivan S. Mamaevb, Ivan A. Bizyaevc

a Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700 Russia
b Izhevsk State Technical University Studencheskaya 7, Izhevsk, 426069 Russia
c Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia

Abstract: In this historical review we describe in detail the main stages of the development of nonholonomic mechanics starting from the work of Earnshaw and Ferrers to the monograph of Yu.I. Neimark and N.A. Fufaev. In the appendix to this review we discuss the d’Alembert–Lagrange principle in nonholonomic mechanics and permutation relations.

Keywords: nonholonomic mechanics, nonholonomic constraint, d’Alembert–Lagrange principle, permutation relations

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation
Russian Foundation for Basic Research 15-08-09261-a
15-38-20879 mol a ved
Russian Science Foundation 14-19-01303
The work of A.V.Borisov (Introduction and Sections 3, 4) was carried out within the framework of the state assignment for institutions of higher education and supported by the RFBR grant No. 15-08-09261-a. Appendix was prepared by I. S. Mamaev under the RSF grant No. 14-19-01303. Sections 1 and 2 were written by I.A.Bizyaev within the framework of the state assignment for institutions of higher education and supported by the RFBR grant No. 15-38-20879 mol a ved.


DOI: https://doi.org/10.1134/S1560354716040055

References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 37J60, 01A05
Language: English

Citation: Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “Historical and Critical Review of the Development of Nonholonomic Mechanics: the Classical Period”, Regul. Chaotic Dyn., 21:4 (2016), 455–476

Citation in format AMSBIB
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\by Alexey~V.~Borisov, Ivan~S.~Mamaev, Ivan~A.~Bizyaev
\paper Historical and Critical Review of the Development of Nonholonomic Mechanics: the Classical Period
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 4
\pages 455--476
\mathnet{http://mi.mathnet.ru/rcd88}
\crossref{https://doi.org/10.1134/S1560354716040055}
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    Citing articles on Google Scholar: Russian citations, English citations
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    Translation

    This publication is cited in the following articles:
    1. Alexey V. Borisov, Sergey P. Kuznetsov, “Regular and Chaotic Motions of a Chaplygin Sleigh under Periodic Pulsed Torque Impacts”, Regul. Chaotic Dyn., 21:7-8 (2016), 792–803  mathnet  crossref
    2. Alexander P. Ivanov, “On Final Motions of a Chaplygin Ball on a Rough Plane”, Regul. Chaotic Dyn., 21:7-8 (2016), 804–810  mathnet  crossref
    3. Alexey V. Borisov, Alexey O. Kazakov, Elena N. Pivovarova, “Regular and Chaotic Dynamics in the Rubber Model of a Chaplygin Top”, Regul. Chaotic Dyn., 21:7-8 (2016), 885–901  mathnet  crossref
    4. Alexey V. Borisov, Alexey O. Kazakov, Igor R. Sataev, “Spiral Chaos in the Nonholonomic Model of a Chaplygin Top”, Regul. Chaotic Dyn., 21:7-8 (2016), 939–954  mathnet  crossref
    5. 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
    6. I. A. Bizyaev, A. V. Borisov, S. P. Kuznetsov, “Chaplygin sleigh with periodically oscillating internal mass”, EPL, 119:6 (2017), 60008  crossref  isi
    7. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Hamilton'S Principle and the Rolling Motion of a Symmetric Ball”, Dokl. Phys., 62:6 (2017), 314–317  mathnet  crossref  mathscinet  isi  scopus
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