regular smooth curve - Penn Math

Proof of the fundamental theorem
of the local theory of curves in R 3 .
We are given smooth functions �(s) > 0 and �(s) , for s � I ,
and must find a regular curve �: I � R 3 parametrized by arc
length, with curvature �(s) and torsion �(s) .
Let's begin by writing the Frenet equations for the Frenet frame.
T'(s) = �(s) N(s)
N'(s) = — �(s) T(s) + �(s) B(s)
B'(s) = — �(s) N(s) .
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