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Contemporary Mathematics. Fundamental Directions, 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
Full-text PDF (162 kB) Citations (1)
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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.
English version:
Journal of Mathematical Sciences, 2014, Volume 199, Issue 6, Pages 687–694
DOI: https://doi.org/10.1007/s10958-014-1894-z
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
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://mathscinet.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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902835303}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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