This article is cited in 18 scientific papers (total in 18 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"
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.
non-integrable constraints, vakonomic mechanics, optimal control theory, sub-Riemannian geometry, non-holonomic mechanics, invariant measure.
|Ministry of Education and Science of the Russian Federation
|Russian Foundation for Basic Research
|National Research University Higher School of Economics
|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).
* Author to whom correspondence should be addressed
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Russian Mathematical Surveys, 2017, 72:5, 783–840
MSC: Primary 70Exx, 70F25, 70G45, 70H03, 70H05; Secondary 37J60
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
\by A.~V.~Borisov, I.~S.~Mamaev, I.~A.~Bizyaev
\paper Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics
\jour Uspekhi Mat. Nauk
\jour Russian Math. Surveys
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