A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Historical and critical review of the development of nonholonomic mechanics: the classical period”, Nelin. Dinam., 12:3 (2016), 385–411; Regular and Chaotic Dynamics, 21:4 (2016), 455

Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Rus. J. Nonlin. Dyn.:
Year:
Volume:
Issue:
Page:
	Find

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

Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2016, Volume 12, Number 3, Pages 385–411
DOI: https://doi.org/10.20537/nd1603007 (Mi nd534)

This article is cited in 22 scientific papers (total in 22 papers)

Translated papers

Historical and critical review of the development of nonholonomic mechanics: the classical period

A. V. Borisov^a, I. S. Mamaev^bc, I. A. Bizyaev^c

^a Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudny, Moscow, 141700, Russia
^b Institute of Mathematics and Mechanics of the Ural Branch of RAS, ul. S.Kovalevskoi 16, Ekaterinburg, 620990, Russia
^c Udmurt State University, Universitetskaya 1, Izhevsk, 426034, Russia

Full-text PDF (1944 kB) Citations (22)

References:

PDF

HTML

DOI: https://doi.org/10.20537/nd1603007

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
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Russian Foundation for Basic Research	15-08-09261-а 15-38-20879 мол_а_вед

Received: 05.05.2016
Accepted: 22.06.2016

English version:
Regular and Chaotic Dynamics, 2016, Volume 21, Issue 4, Pages 455–476
DOI: https://doi.org/10.1134/S1560354716040055

Bibliographic databases:

Document Type: Article

UDC: 517.925

MSC: 37J60, 01A05

Language: Russian

Citation: A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Historical and critical review of the development of nonholonomic mechanics: the classical period”, Nelin. Dinam., 12:3 (2016), 385–411; Regular and Chaotic Dynamics, 21:4 (2016), 455–476

Citation in format AMSBIB

\Bibitem{BorMamBiz16}

\by A.~V.~Borisov, I.~S.~Mamaev, I.~A.~Bizyaev

\paper Historical and critical review of the development of nonholonomic mechanics: the classical period

\jour Nelin. Dinam.

\yr 2016

\vol 12

\issue 3

\pages 385--411

\mathnet{http://mi.mathnet.ru/nd534}

\crossref{https://doi.org/10.20537/nd1603007}

\zmath{https://zbmath.org/?q=an:1352.37172}

\elib{https://elibrary.ru/item.asp?id=27328721}

\transl

\jour Regular and Chaotic Dynamics

\yr 2016

\vol 21

\issue 4

\pages 455--476

\crossref{https://doi.org/10.1134/S1560354716040055}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84980398123}

Linking options:

https://www.mathnet.ru/eng/nd534

https://www.mathnet.ru/eng/nd/v12/i3/p385

Translation

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

This publication is cited in the following 22 articles:

Víctor M. Jiménez, Manuel de León, “The nonholonomic bracket on contact mechanical systems”, Journal of Geometry and Physics, 213 (2025), 105484
Nivaldo A. Lemos, “Complete inequivalence of nonholonomic and vakonomic mechanics”, Acta Mech, 233:1 (2022), 47
Alfredo Delgado-Spindola, Victor Santibanez, Eusebio Bugarin, Juan Antonio Rojas-Quintero, 2021 9th International Conference on Systems and Control (ICSC), 2021, 178
Francisco Jesús Arjonilla García, Yuichi Kobayashi, “Supervised learning of mapping from sensor space to chained form for unknown non-holonomic driftless systems”, IR, 48:5 (2021), 710
Ivan A. Bizyaev, Ivan S. Mamaev, “Separatrix splitting and nonintegrability in the nonholonomic rolling of a generalized Chaplygin sphere”, International Journal of Non-Linear Mechanics, 126 (2020), 103550
Vaughn Gzenda, Vakhtang Putkaradze, “Integrability and Chaos in Figure Skating”, J Nonlinear Sci, 30:3 (2020), 831
Elizaveta M. Artemova, Alexander A. Kilin, 2020 International Conference Nonlinearity, Information and Robotics (NIR), 2020, 1
Ivan S. Mamaev, Evgeny V. Vetchanin, “Dynamics of Rubber Chaplygin Sphere under Periodic Control”, Regul. Chaotic Dyn., 25:2 (2020), 215–236
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Comment on “Confining rigid balls by mimicking quadrupole ion trapping” [Am. J. Phys. 85, 821 (2017)]”, American Journal of Physics, 87:11 (2019), 935
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Different Models of Rolling for a Robot Ball on a Plane as a Generalization of the Chaplygin Ball Problem”, Regul. Chaotic Dyn., 24:5 (2019), 560–582
Ivan A. Bizyaev, Alexey V. Borisov, Sergey P. Kuznetsov, “The Chaplygin sleigh with friction moving due to periodic oscillations of an internal mass”, Nonlinear Dyn, 95:1 (2019), 699
Yi Zhang, Xue Tian, “Conservation laws of nonconservative nonholonomic system based on Herglotz variational problem”, Physics Letters A, 383:8 (2019), 691
Vakhtang Putkaradze, Stuart Rogers, “On the dynamics of a rolling ball actuated by internal point masses”, Meccanica, 53:15 (2018), 3839
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
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
A. V. Borisov, A. A. Kilin, I. S. Mamaev, “The Hamilton principle and the rolling motion of a symmetric ball”, Dokl. Math., 62:6 (2017), 314–317
Ivan A. Bizyaev, Alexey V. Borisov, Sergey P. Kuznetsov, “Chaplygin sleigh with periodically oscillating internal mass”, EPL, 119:6 (2017), 60008–7
A.V. BORISOV, A.A. Kilin, I. S. Mamaev, “PRINTsIP GAMILTONA I KAChENIE SIMMETRIChNOGO ShARA, “Doklady Akademii nauk””, Doklady Akademii Nauk, 2017, no. 5, 558
Alexey V. Borisov, Sergey P. Kuznetsov, “Regular and Chaotic Motions of a Chaplygin Sleigh under Periodic Pulsed Torque Impacts”, Regul. Chaotic Dyn., 21:7 (2016), 792–803
Alexander P. Ivanov, “On Final Motions of a Chaplygin Ball on a Rough Plane”, Regul. Chaotic Dyn., 21:7 (2016), 804–810

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

Statistics & downloads:
Abstract page:	500
Full-text PDF :	143
References:	74

Что такое QR-код?

Registration to the website

Logotypes