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Let $\gamma\colon \mathbb{R}\to\mathbb{R}^3$ be a unit-speed curve, and let $t(s),n(s),b(s)$ be the corresponding Frenet frame.

  1. What is the rotation vector $w$ for the Frenet frame? (better if expressed as a linear combination of $t$, $n$, and $b$）
  2. Show that $\dot{t} \times \ddot{t} = \kappa^2w$
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Do you perchance have any partial work to show? – Henning Makholm Sep 22 '11 at 19:12
Have you seen this? – J. M. Sep 22 '11 at 19:14
Are you talking about the Darboux / angular momentum vector? How is that vector defined in your text? (I'm not familiar with it.) I assume you know the Frenet-Serret formulas? – anon Sep 22 '11 at 19:14

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