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VOL. 9 | 2008 Explicit Parameterization of Euler’s Elastica
Peter A. Djondjorov, Mariana Ts. Hadzhilazova, Ivaïlo M. Mladenov, Vassil M. Vassilev

Editor(s) Ivaïlo M. Mladenov

Abstract

The consideration of some non-standard parametric Lagrangian leads to a fictitious dynamical system which turns out to be equivalent to the Euler problem for finding out all possible shapes of the lamina. Integrating the respective differential equations one arrives at novel explicit parameterizations of the Euler’s elastica curves. The geometry of the inflexional elastica and especially that of the figure “eight” shape is studied in some detail and the close relationship between the elastica problem and mathematical pendulum is outlined.

Information

Published: 1 January 2008
First available in Project Euclid: 13 July 2015

zbMATH: 1196.53004
MathSciNet: MR2436270

Digital Object Identifier: 10.7546/giq-9-2008-175-186

Rights: Copyright © 2008 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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