FRENET-FRAME CONTINUITY AND EXISTENCE OF THE SERRET-FRENET EQUATIONS AT ZERO-CURVATURE POINTS

The continuity of the Frenet frame and existence of the Serret-Frenet equations at zero-curvature points are established for a general three-dimensional curve with arbitrary parameterization. To this end, the Frenet-Euler angles, referred to for brevity as Frenet angles, are used. Definition of the Frenet bank angle is used to prove existence of the curve normal vector at the zero curvature points.