RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb., 2011, Volume 202, Number 9, Pages 97–120 (Mi msb7762)  

This article is cited in 6 scientific papers (total in 6 papers)

Extremal trajectories and the asymptotics of the Maxwell time in the problem of the optimal rolling of a sphere on a plane

A. P. Mashtakov, Yu. L. Sachkov

Program Systems Institute of RAS

Abstract: The problem of a sphere rolling on a plane without twisting or slipping is considered. It is required to roll the sphere from one contact configuration to another so that the length of the curve described by the contact point is minimal. A parametrization of extremal trajectories is obtained. The asymptotics of extremal trajectories and the behaviour of the Maxwell time for the rolling of a sphere over sinusoids of small amplitude are studied; for such trajectories estimates for the so-called cut time are obtained.
Bibliography: 21 titles.

Keywords: optimal control, geometric methods, symmetries of the exponential map, rolling of surfaces, Euler elastics.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm7762

Full text: PDF file (691 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2011, 202:9, 1347–1371

Bibliographic databases:

UDC: 517.977
MSC: Primary 49K15; Secondary 70B10, 93B27
Received: 24.06.2010

Citation: A. P. Mashtakov, Yu. L. Sachkov, “Extremal trajectories and the asymptotics of the Maxwell time in the problem of the optimal rolling of a sphere on a plane”, Mat. Sb., 202:9 (2011), 97–120; Sb. Math., 202:9 (2011), 1347–1371

Citation in format AMSBIB
\Bibitem{MasSac11}
\by A.~P.~Mashtakov, Yu.~L.~Sachkov
\paper Extremal trajectories and the asymptotics of the Maxwell time in the problem of the optimal rolling of a~sphere on a~plane
\jour Mat. Sb.
\yr 2011
\vol 202
\issue 9
\pages 97--120
\mathnet{http://mi.mathnet.ru/msb7762}
\crossref{https://doi.org/10.4213/sm7762}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2884366}
\zmath{https://zbmath.org/?q=an:1252.49056}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2011SbMat.202.1347M}
\elib{http://elibrary.ru/item.asp?id=19066306}
\transl
\jour Sb. Math.
\yr 2011
\vol 202
\issue 9
\pages 1347--1371
\crossref{https://doi.org/10.1070/SM2011v202n09ABEH004190}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000296920400005}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-81255188439}


Linking options:
  • http://mi.mathnet.ru/eng/msb7762
  • https://doi.org/10.4213/sm7762
  • http://mi.mathnet.ru/eng/msb/v202/i9/p97

    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. A. P. Mashtakov, “Algoritmicheskoe i programmnoe obespechenie resheniya konstruktivnoi zadachi upravleniya negolonomnymi pyatimernymi sistemami”, Programmnye sistemy: teoriya i prilozheniya, 3:1 (2012), 3–29  mathnet
    2. Proc. Steklov Inst. Math., 278 (2012), 218–232  mathnet  crossref  mathscinet  isi  elib  elib
    3. I. Yu. Beschatnyi, “The optimal rolling of a sphere, with twisting but without slipping”, Sb. Math., 205:2 (2014), 157–191  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Yu. L. Sachkov, E. F. Sachkova, “Exponential mapping in Euler's elastic problem”, J. Dyn. Control Syst., 20:4 (2014), 443–464  crossref  mathscinet  zmath  isi  scopus
    5. Lazureanu C., Binzar T., “Symmetries and Properties of the Energy-Casimir Mapping in the Ball-Plate Problem”, Adv. Math. Phys., 2017, 5164602  crossref  mathscinet  isi  scopus
    6. A. P. Mashtakov, “O mnozhestve razreza na dvukhstupennykh svobodnykh gruppakh Karno”, Programmnye sistemy: teoriya i prilozheniya, 9:4 (2018), 319–360  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:373
    Full text:93
    References:47
    First page:14

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