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Regular and Chaotic Dynamics, 2016, Volume 21, Issue 7-8, Pages 832–839
DOI: https://doi.org/10.1134/S1560354716070066 (Mi rcd229) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Relation Between Euler’s Elasticae and Sub-Riemannian Geodesics on $SE(2)$

Alexey Mashtakov, Andrei Ardentov, Yuri L. Sachkov

Program Systems Institute of RAS, Pereslavl-Zalessky, Yaroslavl Region, 152020 Russia
Citations (2)
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DOI: https://doi.org/10.1134/S1560354716070066
Abstract: In this note we describe a relation between Euler’s elasticae and sub-Riemannian geodesics on $SE(2)$. Analyzing the Hamiltonian system of the Pontryagin maximum principle, we show that these two curves coincide only in the case when they are segments of a straight line.
Keywords: elastica, sub-Riemannian geodesic, group of rototranslations.
Funding agency Grant number
Russian Foundation for Basic Research 16-31-60083 mol_a_dk
The reported study was funded by RFBR, research project No. 16-31-60083 mol_a_dk.
Received: 09.09.2016
Accepted: 02.11.2016
Bibliographic databases:
Document Type: Article
MSC: 58E10
Language: English
Citation: Alexey Mashtakov, Andrei Ardentov, Yuri L. Sachkov, “Relation Between Euler’s Elasticae and Sub-Riemannian Geodesics on $SE(2)$”, Regul. Chaotic Dyn., 21:7-8 (2016), 832–839
Citation in format AMSBIB
\Bibitem{MasArdSac16}
\by Alexey Mashtakov, Andrei Ardentov, Yuri L. Sachkov
\paper Relation Between Euler’s Elasticae and Sub-Riemannian Geodesics on $SE(2)$
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 7-8
\pages 832--839
\mathnet{http://mi.mathnet.ru/rcd229}
\crossref{https://doi.org/10.1134/S1560354716070066}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85016015437}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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