A Study on a Generalized Relaxed Curvature Energy Action

Authors : Gözde ÖZKAN TÜKEL, Ahmet YÜCESAN

Pages : 541-546

View : 16 | Download : 14

Publication Date : 2018-10-05

Article Type : Research Paper

Abstract :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.
Keywords : Generalized relaxed elastic line, Euler Lagrange equations, Variational calculus