Notes on the bienergy and biangle of a moving particle lying in a surface of euclidean space

Abstract

In this study, we research bienergy and biangles of moving particles lying in the surface of Euclidean space by using their energy and angle values. We present a geometrical understanding of a bienergy of a particle in Darboux vector fields depending on surface. We also give a relation between bienergy of the curve corresponding to a moving particle in space and bienergy of the elastica assuming the curve that has the elastic feature. We conclude our results by providing an bienergy-curve graphics for different cases.