Frenet apparatus

1. Feb 7, 2005

Sneaksuit

I need to calculate the Frenet apparatus for the space curve defined by

$$\overrightarrow{r} (t) = \langle t - cos (t), sin(t), t \rangle$$

so for T I did
$$\overrightarrow{r} \prime (t) = \langle 1 + sin(t), cos(t), 1 \rangle$$
then I got |r'(t)| = $$\sqrt{2sin(t) + 3$$
which i'm pretty sure is either wrong or not simplified. Anyone care to look at my problem?

Last edited: Feb 7, 2005
2. Feb 7, 2005

Lose the spaces in the tex tags...$$and the same for the closure. Daniel. 3. Feb 7, 2005 krab I fixed the LaTeX, and other problems... Last edited: Feb 7, 2005 4. Feb 7, 2005 Sneaksuit Thanx for the latex help. Now, do u see a problem with the math? 5. Feb 7, 2005 dextercioby Everything is okay with your exercise. Daniel. 6. Feb 8, 2005 Sneaksuit Ok, but then that gives me [tex] T(t) = \frac{(1 + sin(t))i + (cos(t))j + k} {\sqrt{2sin(t) + 3}}$$
Now for T'(t) I don't ever remember taking derivatives of vectors this complicated. Do I use the quotient rule?

7. Feb 8, 2005

dextercioby

Okay,that's r' vector which is indeed the tangent vector.Now why would you need another derivative wrt to "t"...?Curvature,torsion...?

Daniel.

8. Feb 8, 2005

Sneaksuit

Yes, I need the entire Frenet apparatus....tangent, normal, binormal, curvature, and torsion.