= Solution
Parametrize the regular curve by arclength $s$. Its unit tangent is $T=\gamma'$, and its <curvature> is $\kappa=|T'|$. Where $\kappa>0$, define the principal normal $N=T'/\kappa$ and binormal $B=T\times N$. The <torsion of a space curve> is $\tau=-B'\cdot N$. Orthonormality and differentiation give the <Frenet-Serret formulas>
$$
\boxed{T'=\kappa N,\qquad N'=-\kappa T+\tau B,\qquad B'=-\tau N.}
$$
For a general parameter, $\kappa=|\dot\gamma\times\ddot\gamma|/|\dot\gamma|^3$ and $\tau=\det(\dot\gamma,\ddot\gamma,\dddot\gamma)/|\dot\gamma\times\ddot\gamma|^2$. The normal and torsion formulas require nonzero <curvature>; at zero-<curvature> points this particular Frenet frame need not be defined.
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