Given a curvature $\kappa$ and torsion $\tau$, find a regular curve with such (Solving Frenet Serret equations)

Asked Jan 29 '19 at 02:44

Active Jan 29 '19 at 02:44

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$T'=\kappa N$

$N'=-\kappa T + \tau B$

$B' = -\kappa N$

How do I find the curve given the Frenet-serret equations, $\tau$ and $\kappa$? Is this purely a differential equations question at this point? If so, could somebody walk me through it? My knowledge on the subject is extremely limited. Thanks!

asked Jan 29 '19 at 02:44

Do you have some example in mind? – feynhat Jan 29 '19 at 03:38
This is a non-trivial problem! – Robert Lewis Jan 29 '19 at 03:45
Are $\kappa>0$ and $\tau$ constant in this case? If so, this is covered in e.g. https://math.stackexchange.com/q/1469521/169085. – Alp Uzman Jan 28 '22 at 04:13

Given a curvature $\kappa$ and torsion $\tau$, find a regular curve with such (Solving Frenet Serret equations)

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