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Lancret Equation

The Lancret equation relates the normal, tangent, and binormal line elements of a space curve. Let a space curve have line elements ds_N, ds_T, and ds_B along the normal, tangent, and binormal vectors respectively, then

ds_N^2=ds_T^2+ds_B^2,
(1)

where

ds_N^2=(kappa^2+tau^2)ds^2
(2)
ds_T^2=kappa^2ds^2
(3)
ds_B^2=tau^2ds^2,
(4)

and kappa and tau are the curvature and torsion, respectively.

See also

Curvature, Torsion, Total Curvature

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References

Kreyszig, E. Differential Geometry. New York: Dover, p. 47, 1991.

Referenced on Wolfram|Alpha

Lancret Equation

Cite this as:

Weisstein, Eric W. "Lancret Equation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LancretEquation.html

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