RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uspekhi Mat. Nauk, 2017, Volume 72, Issue 5(437), Pages 3–62 (Mi umn9783)  

This article is cited in 8 scientific papers (total in 8 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"

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).


DOI: https://doi.org/10.4213/rm9783

Full text: PDF file (1224 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2017, 72:5, 783–840

Bibliographic databases:

Document Type: Article
MSC: Primary 70Exx, 70F25, 70G45, 70H03, 70H05; Secondary 37J60
Received: 09.06.2017

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
\Bibitem{BorMamBiz17}
\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
\yr 2017
\vol 72
\issue 5(437)
\pages 3--62
\mathnet{http://mi.mathnet.ru/umn9783}
\crossref{https://doi.org/10.4213/rm9783}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3716512}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2017RuMaS..72..783B}
\elib{http://elibrary.ru/item.asp?id=30512320}
\transl
\jour Russian Math. Surveys
\yr 2017
\vol 72
\issue 5
\pages 783--840
\crossref{https://doi.org/10.1070/RM9783}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000422922900001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85041125460}


Linking options:
  • http://mi.mathnet.ru/eng/umn9783
  • https://doi.org/10.4213/rm9783
  • http://mi.mathnet.ru/eng/umn/v72/i5/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. A. Bizyaev, “Invariantnaya mera v zadache o kachenii diska po ploskosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:4 (2017), 576–582  mathnet  crossref  elib
    2. Alexey P. Mashtakov, Anton Yu. Popov, “Extremal Controls in the Sub-Riemannian Problem on the Group of Motions of Euclidean Space”, Regul. Chaotic Dyn., 22:8 (2017), 949–954  mathnet  crossref  mathscinet  zmath  isi  scopus
    3. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration”, Regul. Chaotic Dyn., 22:8 (2017), 955–975  mathnet  crossref
    4. Alexey V. Borisov, Ivan S. Mamaev, Eugeny V. Vetchanin, “Dynamics of a Smooth Profile in a Medium with Friction in the Presence of Parametric Excitation”, Regul. Chaotic Dyn., 23:4 (2018), 480–502  mathnet  crossref  mathscinet
    5. O. N. Kirillov, “Locating the sets of exceptional points in dissipative systems and the self-stability of bicycles”, Entropy, 20:7 (2018), 502, 16 pp.  crossref  isi  scopus
    6. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “An invariant measure and the probability of a fall in the problem of an inhomogeneous disk rolling on a plane”, Regul. Chaotic Dyn., 23:6 (2018), 665–684  mathnet  crossref  mathscinet  isi  scopus
    7. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dynamics of the Chaplygin ball on a rotating plane”, Russ. J. Math. Phys., 25:4 (2018), 423–433  crossref  mathscinet  zmath  isi
    8. A. P. Mashtakov, “O mnozhestve razreza na dvukhstupennykh svobodnykh gruppakh Karno”, Programmnye sistemy: teoriya i prilozheniya, 9:4 (2018), 319–360  mathnet  crossref
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:336
    References:26
    First page:35

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019