Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If $t(t),n(t),b(t)$ are rotating, right-handed frame of orthogonal unit vectors. Show that there exists a vector $w(t)$ (the rotation vector) such that $\dot{t} = w \times t$, $\dot{n} = w \times n$, and $\dot{b} = w \times b$

So I'm thinking this is related to Frenet-Serret Equations and that the matrix of coefficient for $\dot{t}, \dot{n}, \dot{b}$ with respect to $t,n,b$ is skew-symmetric.


share|cite|improve this question
up vote 4 down vote accepted

You have sufficient information to compute it yourself! :)

Suppose that $w=aT+bN+cB$, with $a$, $b$ and $c$ some functions. Then you want, for example, that $$\kappa N = T' = w\times T = (aT+bN+cB)\times T=b N\times T+cB\times T=-bB+cN.$$ Since $\{T,N,B\}$ is an basis, this gives you some information about the coefficients. Can you finish?

share|cite|improve this answer
@ Mariano: I'm not very familiar with linear algebra. What does basis have to do with the coefficients? – Lindsay Duran Sep 23 '11 at 19:01
@LindsayDuran, you should really familiarize yourself with linear algebra: explaining this is a bit outside of the scope of comments! – Mariano Suárez-Alvarez Sep 23 '11 at 19:02
@Mariano: I got $\omega$ in terms of $\tau$ and $\kappa$, but the problem didnt specify a curve. How should I deal with this? – ninja Sep 23 '11 at 20:00
@ninja: That's fine, as both curvature and torsion should indeed be involved. What else were you expecting? – J. M. Sep 24 '11 at 3:04

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.