Generalized relaxed elastic line on an oriented surface
We study the relaxed elastic line in a more general case on an oriented surface. In particular, we obtain a differential equation with three boundary conditions for the generalized relaxed elastic line. Then we analyze the results in a plane, on a sphere, on a cylinder, and on the geodesics of these surfaces.
English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 8, pp 1277-1289.
Citation Example: Özkan G., Yücesan A. Generalized relaxed elastic line on an oriented surface // Ukr. Mat. Zh. - 2012. - 64, № 8. - pp. 1121-1131.