On Determining the Equation of a Salkowski Curve Satisfying tau/kappa=1/s

Abstract

In this paper, we determine the equation of a Salkowski curve whose ratio of torsion to curvature is given by 1/s, where s is the arc length of the curve. The Frenet-Serret equations provide the third-order vector differential equation for the unit tangent vector T(s) and the general (series) solution was obtained. In the end, the series solution is entirely determined by the given initial conditions.