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Russian Mathematical Surveys, 2017, Volume 72, Issue 5, Pages 783–840
DOI: https://doi.org/10.1070/RM9783 (Mi rm9783) 		 
This article is cited in 25 scientific papers (total in 25 papers)

Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics

A. V. Borisova, I. S. Mamaevb, I. A. Bizyaevc

a Udmurtian State University
b Izhevsk State Technical University
c National Research University "Higher School of Economics"
English version PDF (1131 kB) Citations (25)
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DOI: https://doi.org/10.1070/RM9783
Abstract: This is a survey of the main forms of equations of dynamical systems with non-integrable constraints, divided into two large groups. The first group contains systems arising in vakonomic mechanics and optimal control theory, with the equations of motion obtained from the variational principle, and the second contains systems in classical non-holonomic mechanics, when the constraints are ideal and therefore the D'Alembert–Lagrange principle holds.
Bibliography: 134 titles.
Keywords: non-integrable constraints, vakonomic mechanics, optimal control theory, sub-Riemannian geometry, non-holonomic mechanics, invariant measure.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.2404.2017/4.6
1.2405.2017/4.6
Russian Foundation for Basic Research 15-08-09093-а
16-51-10005 КО-а
National Research University Higher School of Economics 90
A. V. Borisov's research (§§ 1 and 2) was carried out in the framework of the State Assignment no. 1.2404.2017/4.6 of the Ministry of Education and Science of the Russian Federation. Sections 3 and 4 were prepared by I. S. Mamaev in the framework of the State Assignment no. 1.2405.2017/4.6 of the Ministry of Education and Science of the Russian Federation. I. A. Bizyaev's research (§§ 5 and 6) was supported by the Programme of Fundamental Research of the National Research University “Higher School of Economics”, project no. 90, in 2017. The research was also supported by the Russian Foundation for Basic Research (grant nos. 15-08-09093-a and 16-51-10005 KO-a).
Received: 09.06.2017
Russian version:
Uspekhi Matematicheskikh Nauk, 2017, Volume 72, Issue 5(437), Pages 3–62
DOI: https://doi.org/10.4213/rm9783
Bibliographic databases:
Document Type: Article
MSC: Primary 70Exx, 70F25, 70G45, 70H03, 70H05; Secondary 37J60
Language: English
Original paper language: Russian
Citation: A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Uspekhi Mat. Nauk, 72:5(437) (2017), 3–62; Russian Math. Surveys, 72:5 (2017), 783–840
Citation in format AMSBIB
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    • This publication is cited in the following 25 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:1109
    Russian version PDF:324
    English version PDF:60
    References:88
    First page:49
     
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