RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Avtomat. i Telemekh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Avtomat. i Telemekh., 2018, Issue 7, Pages 22–40 (Mi at14881)  

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

Nonlinear Systems

Multiple solutions in Euler's elastic problem

A. A. Ardentov

Ailamazyan Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalessky, Russia

Abstract: The paper is devoted to multiple solutions of the classical problem on stationary configurations of an elastic rod on a plane; we describe boundary values for which there are more than two optimal configurations of a rod (optimal elasticae). We define sets of points where three or four optimal elasticae come together with the same value of elastic energy. We study all configurations that can be translated into each other by symmetries, i.e., reflections at the center of the elastica chord and reflections at the middle perpendicular to the elastica chord. For the first symmetry, the ends of the rod are directed in opposite directions, and the corresponding boundary values lie on a disk. For the second symmetry, the boundary values lie on a Möbius strip. As a result, we study both sets numerically and in some cases analytically; in each case, we find sets of points with several optimal configurations of the rod. These points form the currently known part of the reachability set where elasticae lose global optimality.

Keywords: Eulerís elastica, optimal control, Maxwell stratum, symmetries, elasticity theory, elliptic integral.

Funding Agency Grant Number
Russian Science Foundation 17-11-01387
This work was supported by the Russian Science Foundation, project no. 17-11-01387, at the A. K. Ailamazyan Institute of Software Systems of the RAS.


Full text: PDF file (1723 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Automation and Remote Control, 2018, 79:7, 1191–1206

Bibliographic databases:

Document Type: Article
Presented by the member of Editorial Board: A. G. Kushner

Received: 25.09.2017

Citation: A. A. Ardentov, “Multiple solutions in Euler's elastic problem”, Avtomat. i Telemekh., 2018, no. 7, 22–40; Autom. Remote Control, 79:7 (2018), 1191–1206

Citation in format AMSBIB
\Bibitem{Ard18}
\by A.~A.~Ardentov
\paper Multiple solutions in Euler's elastic problem
\jour Avtomat. i Telemekh.
\yr 2018
\issue 7
\pages 22--40
\mathnet{http://mi.mathnet.ru/at14881}
\elib{http://elibrary.ru/item.asp?id=35754481}
\transl
\jour Autom. Remote Control
\yr 2018
\vol 79
\issue 7
\pages 1191--1206
\crossref{https://doi.org/10.1134/S0005117918070020}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000438654700002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85050002995}


Linking options:
  • http://mi.mathnet.ru/eng/at14881
  • http://mi.mathnet.ru/eng/at/y2018/i7/p22

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Cazzolli A., Dal Corso F., “Snapping of Elastic Strips With Controlled Ends”, Int. J. Solids Struct., 162 (2019), 285–303  crossref  isi  scopus
  • Avtomatika i Telemekhanika
    Number of views:
    This page:90
    References:11
    First page:16

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019