A NEW APPROACH ON THE CURVATURE DEPENDENT ENERGY FOR ELASTIC CURVES IN A LIE GROUP

Abstract

Elastica is known as classical curve that is a solution of variational problem, which minimize a thin inextensible wire's bending energy. Studies on elastica has been conducted in Euclidean space firstly, then it has been extended to Riemannian manifold by giving different characterizations. In this paper, we focus on energy of the elastic curve in a Lie group. We attepmt to compute its energy by using geometric description of the curvature and the torsion of the trajectory of the elastic curve of the trajectory of the moving particle in the Lie group. Finally, we also investigate the relation between energy of the elastic curve and energy of the same curve in Frenet vector fields in the Lie group.