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Regul. Chaotic Dyn., 2016, Volume 21, Issue 7-8, Pages 832–839 (Mi rcd229)  

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

Relation Between Eulerís 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

Abstract: In this note we describe a relation between Eulerís 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.


DOI: https://doi.org/10.1134/S1560354716070066

References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 58E10
Received: 09.09.2016
Accepted:02.11.2016
Language: English

Citation: Alexey Mashtakov, Andrei Ardentov, Yuri L. Sachkov, “Relation Between Eulerís 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 Eulerís 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}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000403091800006}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85016015437}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Ardentov, A. V. Smirnov, “Upravlenie mobilnym robotom vdol elastik Eilera”, Programmnye sistemy: teoriya i prilozheniya, 8:4 (2017), 163–178  mathnet  crossref
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