An Alternative Method for Determination of the Position Vector of a Slant Helix

Abstract

In this paper, we provide an alternative method to determine the position vector of a slant helix with the help of an alternative moving frame. We then construct a vector differential equation in terms of the principal normal vector of a slant helix using an alternative moving frame. By solving this vector differential equation, we determine the position vector of the slant helix. Afterward, we obtain parametric representations of some examples of slant helices for chosen curvature and torsion functions as an application of the proposed method. Finally, we discuss the method and whether further research should be conducted or not.