Intrinsic equations for a relaxed elastic line of second kind in Minkowski 3-space
Ergi̇n Bayram, Emi̇n Kasap · Filomat · 2015
Let ? be an arc on a connected oriented surface S in Minkowski 3-space, parameterized by arc length s, with torsion ? and length l. The total square torsion H of ? is defined by H = ?10 ?2ds. The arc ? is called a relaxed elastic line of second kind if it is an extremal for the variational problem of minimizing the value of H within the family of all arcs of length l on S having the same initial point and initial direction as ?. In this study, we obtain the differential equation and boundary conditions for a relaxed elastic line of second kind on an oriented surface in Minkowski 3-space. This formulation should give a more direct and more geometric approach to questions concerning relaxed elastic lines of second kind on a surface.