Avtomat. i Telemekh., 2018, Issue 7, Pages 22–40
This article is cited in 1 scientific paper (total in 1 paper)
Multiple solutions in Euler's elastic problem
A. A. Ardentov
Ailamazyan Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalessky, Russia
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.
Eulerís elastica, optimal control, Maxwell stratum, symmetries, elasticity theory, elliptic integral.
|Russian Science Foundation
|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.
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Automation and Remote Control, 2018, 79:7, 1191–1206
Presented by the member of Editorial Board: A. G. Kushner
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
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\paper Multiple solutions in Euler's elastic problem
\jour Avtomat. i Telemekh.
\jour Autom. Remote Control
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Cazzolli A., Dal Corso F., “Snapping of Elastic Strips With Controlled Ends”, Int. J. Solids Struct., 162 (2019), 285–303
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