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Homework Help: Frenet frame

  1. Nov 7, 2012 #1
    1. The problem statement, all variables and given/known data

    calculate the frenet frame for the vector:
    [itex]\vec{r}(t)=(2t cost,2tsint,5t)[/itex]

    calculate the acceleration in frenet frame.

    2. Relevant equations
    [itex]\hat{T}=\frac{dr}{ds}=\frac{\dot{r}}{|\dot{r}|}[/itex]
    [itex]\hat{N}=\frac{\frac{dT}{ds}}{|\frac{dT}{ds}|}[/itex]
    [itex]\hat{B}=\hat{T}\times \hat{N}[/itex]


    3. The attempt at a solution

    I'm not too sure how to get to [itex]\vec{r}(s)[/itex]
    what I tried is : [itex]s=2t \ \ \Rightarrow \vec{r}(s)= s(\cos \frac{s}{2},\sin \frac{s}{2},2.5)[/itex]
    [itex]T=\frac{dr}{ds}=s(-\sin \frac{s}{2},\cos \frac{s}{2},0)+(\cos \frac{s}{2},\sin \frac{s}{2},2.5)[/itex]

    which is NOT a unit vector.
    if I try use t as the variable it's just becomes a gigantic answer.
     
  2. jcsd
  3. Nov 7, 2012 #2
    There are two ways to solve this problem:

    • The first way is to put r into arclength parametrization. You should have seen several formulas in your course that show how to make r into a curve with unit speed. These formulas use integrals, so are not always handy or solvable, however.
    • The second way is to use formulas for the Frenet frame which do not require the curve to have unit speed. These formulas are a bit more complicated than the usual formulas.

    So, look in your course for these things and see if you can do something with it.
     
  4. Nov 8, 2012 #3
    Thanks.
    I know the second way,and I did it like that.
    About the first way, can you recommend on a book that show how to do it?
    in our course it was only when z=0...

    edit: nvm googled it...
    I feel ashamed. Thanks!
     
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