Dual spherical elastica-Reference-Cited by-同舟云学术

Dual spherical elastica

Published:2023 Issue:8 Volume:37 Page:2483-2493
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Yücesan Ahmet¹,Özkan Tükel²

Affiliation:

1. Süleyman Demirel University, Türkiye

2. Isparta University of Applied Sciences, Türkiye

Abstract

The solutions of the dual bending energy functional on the dual unit sphere S2 ? D3 are investigated. Dual spherical elastica is characterized by the dual Euler-Lagrange equation by using techniques of calculus of variation. The real and dual parts of the dual Euler-Lagrange differential equation are solved by different methods. Dual spherical elastica is shown to correspond to the elastic strip constituted by planar elastica in R3.

Publisher

National Library of Serbia

Subject

General Mathematics

Reference14 articles.

1. G. Brunnett, P. E. Crouch, Elastic curves on the sphere, Advances in Computational Mathematics. 2(1994), 1, 23 − 40.

2. P. F. Byrd, M. D. Friedman, Table of integrals of Jacobian elliptic functions, In Handbook of Elliptic Integrals for Engineers and Scientists (pp. 191 − 222). Springer, Berlin, Heidelberg, 1971.

3. D. Chubelaschwili, U. Pinkall, Elastic strips, Manuscripta Mathematica. 133(2010), 3 − 4, 307 − 326.

4. H. W. Guggenheimer, Differential geometry, McGraw-Hill, New York, 1963.

5. J. Guven, M. V. Dulce, P. Vázquez-Montejo, Environmental bias and elastic curves on surfaces, Journal of Physics A: Mathematical and Theoretical. 47(2014), 35, 355201, 29p.

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