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Frenet apparatus

  1. Feb 7, 2005 #1
    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: Feb 7, 2005
  2. jcsd
  3. Feb 7, 2005 #2

    dextercioby

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    Lose the spaces in the tex tags...[tex] and the same for the closure.


    Daniel.
     
  4. Feb 7, 2005 #3

    krab

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    I fixed the LaTeX, and other problems...
     
    Last edited: Feb 7, 2005
  5. Feb 7, 2005 #4
    Thanx for the latex help. Now, do u see a problem with the math?
     
  6. Feb 7, 2005 #5

    dextercioby

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    Everything is okay with your exercise.


    Daniel.
     
  7. Feb 8, 2005 #6
    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?
     
  8. Feb 8, 2005 #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.
     
  9. Feb 8, 2005 #8
    Yes, I need the entire Frenet apparatus....tangent, normal, binormal, curvature, and torsion.
     
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