A NEW APPROACH TO BENDING ENERGY OF ELASTICA FOR SPACE CURVES IN DE-SITTER SPACE

Abstract

In this paper, we firstly introduce kinematics properties of a moving particle lying in De-Sitter space S-1(3). We assume that the particle corresponds to a different type of space curves such that they are characterized by using the Frenet vector field in De-Sitter spacetime. Based on this assumption, we present geometrical understanding of energy on the particle in each Frenet vector fields depending on being a spacelike or timelike curve in S-1(3).Then, we also determine the bending elastic energy functional for the same particle in 3 S-1(3) by assuming the particle has a bending feature of elastica. Finally, we prove that bending energy formula can be represented by the energy on the particle in each Frenet vector field. We conclude our results by providing energy variation sketches with respect to time for different cases.