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Russian Mathematical Surveys, 2012, Volume 67, Issue 2, Pages 281–296
DOI: https://doi.org/10.1070/RM2012v067n02ABEH004787 (Mi rm9473) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Theory and applications of the problem of Euler elastica

M. I. Zelikinab

a Moscow State University
b Steklov Mathematical Institute of the Russian Academy of Sciences
English version PDF (399 kB) Citations (3)
References:
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DOI: https://doi.org/10.1070/RM2012v067n02ABEH004787
Abstract: The paper is devoted to the theory of extremal problems on Euler elastica. The Riccati equation method is used to study sufficient optimality conditions for the associated problem of minimization of the energy of a physical pendulum. Numerous applications are described for the problem of Euler elastica, and its connections with the theory of completely integrable Hamiltonian systems are discussed.
Bibliography: 10 titles.
Keywords: Pontryagin maximum principle, Riccati equation, elliptic functions, non-linear Schrödinger equation.
Funding agency Grant number
Russian Foundation for Basic Research 10-01-00293-а
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Received: 14.06.2011
Russian version:
Uspekhi Matematicheskikh Nauk, 2012, Volume 67, Issue 2(404), Pages 93–108
DOI: https://doi.org/10.4213/rm9473
Bibliographic databases:
Document Type: Article
UDC: 517.984
MSC: Primary 49-02; Secondary 37N10, 37N20, 49K15, 74K10, 76B47, 76M30
Language: English
Original paper language: Russian
Citation: M. I. Zelikin, “Theory and applications of the problem of Euler elastica”, Uspekhi Mat. Nauk, 67:2(404) (2012), 93–108; Russian Math. Surveys, 67:2 (2012), 281–296
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/rm/v67/i2/p93
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Успехи математических наук Russian Mathematical Surveys
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    Abstract page:785
    Russian version PDF:348
    English version PDF:58
    References:100
    First page:38
     
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