Formulas that express the derivatives of the unit vectors of the tangent $\tau$, the normal $\nu$ and the binormal $\beta$ to a regular curve with respect to the natural parameter $s$ in terms of these same vectors and the values of the curvature $k_1$ and torsion $k_2$ of the curve:
They were obtained by F. Frénet (1847).
|[a1]||C.C. Hsiung, "A first course in differential geometry" , Wiley (1981) pp. Chapt. 3, Sect. 4|
Frénet formulas. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Fr%C3%A9net_formulas&oldid=32754