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Nelin. Dinam., 2019, Volume 15, Number 4, Pages 409–414 (Mi nd670)  

Hidden Maxwell Stratum in Euler's Elastic Problem

A. A. Ardentov

Ailamazyan Program Systems Institute of RAS, Pereslavl-Zalessky, Yaroslavl Region, 152020 Russia

Abstract: This investigation continues the study of the classical problem of stationary configurations of an elastic rod on a plane. The length of the rod, the ends of the rod and the directions at the ends are fixed. The problem was first studied by Leonard Euler in 1744 and the optimal synthesis problem is still an open problem. Euler described a family of geodesics containing the solutions, which are called Euler elasticae. It is known that sufficiently small pieces of Euler elasticae are optimal, i.e., they have a minimum of the potential energy. In theory, the point where an optimal curve loses its optimality is called a cut point. Usually several optimal curves arrive at such points, so the points have multiplicity more than 1 and are called Maxwell points. The aim of this work is to describe numerically Maxwell points where two nonsymmetric elasticae come with the same length and energy value.

Keywords: Euler elastica, Maxwell strata, optimal control

Funding Agency Grant Number
Russian Science Foundation 17-11-01387
This research was performed at the Ailamazyan Program Systems Institute of the Russian Academy of Sciences under the financial support from the Russian Science Foundation (project no. 17-11-01387).


DOI: https://doi.org/10.20537/nd190402

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MSC: 93C10, 93C15
Received: 04.05.2019
Accepted:03.10.2019

Citation: A. A. Ardentov, “Hidden Maxwell Stratum in Euler's Elastic Problem”, Nelin. Dinam., 15:4 (2019), 409–414

Citation in format AMSBIB
\Bibitem{Ard19}
\by A. A. Ardentov
\paper Hidden Maxwell Stratum in Euler's Elastic Problem
\jour Nelin. Dinam.
\yr 2019
\vol 15
\issue 4
\pages 409--414
\mathnet{http://mi.mathnet.ru/nd670}
\crossref{https://doi.org/10.20537/nd190402}


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