Frenet-Serret formulas


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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.
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Hence, we have a pseudo-orthonormal frame field {[alpha](s), t(s), n(s), e(s)} of [R.sup.4.sub.1] along [alpha] and the following Frenet-Serret formulas:
Depending on the causal character of the curve [alpha], we have the following Frenet-Serret formulas.