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Uspekhi Mat. Nauk, 2012, Volume 67, Issue 2(404), Pages 93–108 (Mi umn9473)  

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

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

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


DOI: https://doi.org/10.4213/rm9473

Full text: PDF file (511 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2012, 67:2, 281–296

Bibliographic databases:

UDC: 517.984
MSC: Primary 49-02; Secondary 37N10, 37N20, 49K15, 74K10, 76B47, 76M30
Received: 14.06.2011

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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    This publication is cited in the following articles:
    1. J. J. Brown, R. C. Mettler, O. D. Supekar, V. M. Bright, “Nonlinear mechanics of interlocking cantilevers”, J. Appl. Mech. Trans. ASME, 84:12 (2017), 121012  crossref  isi  scopus
  • Успехи математических наук Russian Mathematical Surveys
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