Frenet apparatus

  • Thread starter Sneaksuit
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  • #1
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I need to calculate the Frenet apparatus for the space curve defined by

[tex] \overrightarrow{r} (t) = \langle t - cos (t), sin(t), t \rangle [/tex]

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

Answers and Replies

  • #2
dextercioby
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Lose the spaces in the tex tags...[tex] and the same for the closure.


Daniel.
 
  • #3
krab
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Sneaksuit said:
I need to calculate the Frenet apparatus for the space curve defined by

[tex] \overrightarrow{r} (t) = \langle t - \cos (t), \sin(t), t \rangle [/tex]

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

hmmm...i can't seem to get Latex to work properly
I fixed the LaTeX, and other problems...
 
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  • #4
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Thanx for the latex help. Now, do u see a problem with the math?
 
  • #5
dextercioby
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Everything is okay with your exercise.


Daniel.
 
  • #6
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Ok, but then that gives me
[tex] T(t) = \frac{(1 + sin(t))i + (cos(t))j + k} {\sqrt{2sin(t) + 3}} [/tex]
Now for T'(t) I don't ever remember taking derivatives of vectors this complicated. Do I use the quotient rule?
 
  • #7
dextercioby
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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
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Yes, I need the entire Frenet apparatus....tangent, normal, binormal, curvature, and torsion.
 

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