A Study on a Generalized Relaxed Curvature Energy Action

• Main Authors: Gözde ÖZKAN TÜKEL, Ahmet YÜCESAN
• Format: Article
• Language: English
• Published: Suleyman Demirel University 2018-09-01
• Series: Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi
• Subjects: Generalized relaxed elastic line; Euler-Lagrange equations; Variational calculus
• Online Access: http://dergipark.ulakbim.gov.tr/sdufenbed/article/view/5000214866

<p>We investigate the variational problem of the generalized relaxed elastic line defined as the problem of finding critical points of the functional obtained by adding the twisting energy to the bending energy functional, on a non-degenerate surface in Minkowski 3-space. There arise two different situations for the curve $\alpha $ given on any non-degenerate surface S in Minkowski 3-space according to the absolute value expression in the curvature and torsion formulas. We study the problem for both cases and as a result we characterize the generalized relaxed elastic line with an Euler-Lagrange equation and 3 boundary conditions in both cases. Finally, we search special solutions for the differential equation system obtained with regard to the geodesic curvature, geodesic torsion and normal curvature of the curve.</p>