Frénet formulas

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:

$${\tau }_x^{\prime }=k_1\nu ,$$

$${\nu }_s^{\prime }=-k_1\tau -k_2\beta ,$$

$${\beta }_s^{\prime }=k_2\nu .$$

They were obtained by F. Frénet (1847).

Comments[edit]

References[edit]