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CMFD, 2011, Volume 42, Pages 158–165 (Mi cmfd198)  

This article is cited in 1 scientific paper (total in 1 paper)

Asymptotics of extremal curves in the ball rolling problem on the plane

A. P. Mashtakov

The Program Systems Institute of RAS, Pereslavl-Zalessky, Russia

Abstract: In the present paper, we study an optimal sphere rolling problem on the plane (without slew and slip) with predefined boundary-value conditions. To solve it, we use methods from the optimal control theory. The controlled system for sphere orientation is represented via the rotation quaternion. Asymptotics of extremal paths on a sphere rolling along small-amplitude sine waves is found.

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English version:
Journal of Mathematical Sciences, 2014, 199:6, 687–694

Bibliographic databases:

Document Type: Article
UDC: 517.977

Citation: A. P. Mashtakov, “Asymptotics of extremal curves in the ball rolling problem on the plane”, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), CMFD, 42, PFUR, M., 2011, 158–165; Journal of Mathematical Sciences, 199:6 (2014), 687–694

Citation in format AMSBIB
\Bibitem{Mas11}
\by A.~P.~Mashtakov
\paper Asymptotics of extremal curves in the ball rolling problem on the plane
\inbook Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3--7, 2009)
\serial CMFD
\yr 2011
\vol 42
\pages 158--165
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd198}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3013836}
\transl
\jour Journal of Mathematical Sciences
\yr 2014
\vol 199
\issue 6
\pages 687--694
\crossref{https://doi.org/10.1007/s10958-014-1894-z}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902835303}


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    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. 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
  • Современная математика. Фундаментальные направления
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