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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Volume 278, Pages 227–241 (Mi tm3409)  
This article is cited in 18 scientific papers (total in 18 papers)

Closed Euler elasticae

Yu. L. Sachkov

Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalessky, Russia
Full-text PDF (275 kB) Citations (18)
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Abstract: Euler's classical problem on stationary configurations of an elastic rod in a plane is studied as an optimal control problem on the group of motions of a plane. We show complete integrability of the Hamiltonian system of the Pontryagin maximum principle. We prove that a closed elastica is either a circle or a figure-of-eight elastica, wrapped around itself several times. Finally, we study local and global optimality of closed elasticae: the figure-of-eight elastica is optimal only locally, while the circle is optimal globally.
Received in February 2011
English version:
Proceedings of the Steklov Institute of Mathematics, 2012, Volume 278, Pages 218–232
DOI: https://doi.org/10.1134/S0081543812060211
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: English
Citation: Yu. L. Sachkov, “Closed Euler elasticae”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 278, MAIK Nauka/Interperiodica, Moscow, 2012, 227–241; Proc. Steklov Inst. Math., 278 (2012), 218–232
Citation in format AMSBIB
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    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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