1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Frenet frame
Loading...