... thecurve, and g1is tangential to C at any point.Hencedsdξ=√g11(2.47)and the total length of C,ifξ varies monotonically from 0 to 1, isL =10√g11dξ. (2.48)A unit tangent vector to ... plane with increasing s. If the osculating plane does notrotate, then b is a constant vector, the torsion is zero at every point, and the curvemust lie in a plane. To evaluate dn/ds, we can ... perpendicular to g2and g3, which are tangential to the co-ordinatecurves on which x2and x3, respectively, vary, implies that g1must be perpendicular to the plane which contains these tangential...