Frenet-Serret formulas

(redirected from Frenet formula)

Frenet-Serret formulas

[fre′nā sə′rā ‚fōr·myə·ləz]
(mathematics)
Formulas in the theory of space curves, which give the directional derivatives of the unit vectors along the tangent, principal normal and binormal of a space curve in the direction tangent to the curve. Also known as Serret-Frenet formulas.
Mentioned in ?
References in periodicals archive ?
2] are the natural curvature and torsion of [alpha] (t), respectively, then for [alpha] the Frenet formulas are given by
2] are the torsions of base curves of M and M*, then from the Frenet formulas we have [k*.
Finally, Chapter 7 is dedicated to various aspects of extrinsic geometry, such as Frenet formulas for curves, ruled and developable surfaces, the shape operator, principal curvatures and curvature lines, etc.
We confine ourselves to the case n = 4, but it is obvious that similar Frenet formulas hold for every dimension n.
We study the Frenet frames and Frenet formulas in the Minkovski spacetime [E.
It represents the Frenet formulas for a versor field if the functions [[xi].
The Frenet formulas for non-unit speed curves in [E.
It is clear to show that there exists a function [tau](s)on D such that the Frenet formulas hold.
For their derivatives the following Frenet formulas hold [9]
Differentiating both sides of the equation (9) with respect to s and use the Frenet formulas, we obtain
Differentiating both sides of equation (12) with respect to s and using Frenet formulas, we have following equation