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!

Curvature forumula of a planar trajectory

  1. Sep 11, 2008 #1
    1. The problem statement, all variables and given/known data

    [​IMG]

    If the image doesn't load (and it might not, although I'm not sure why), it can be found at:

    http://steam.cs.ohio.edu/~cmourning/problem1.jpg

    2. Relevant equations

    Part of the problem is I'm not entirely sure what all the relevant equations are. This is a planar trajectory so the torsion is 0, so I've just included the first two Frenet-Serret equations at:

    http://steam.cs.ohio.edu/~cmourning/eqautions1.pdf


    3. The attempt at a solution

    It is rather complicated equationally, so I felt more comfortable typing it in something other than this, you can find the work at:

    http://steam.cs.ohio.edu/~cmourning/physics1.pdf

    If I should put this somewhere else on the forums let me know, this is my first time.
     
  2. jcsd
  3. Sep 11, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Just call the curve parameter s=x. Then the curve is (x,y(x)). The tangent vector is (1,y'(x)). That makes the normalized tangent T=(1,y'(x))/(1+y'(x)^2)^(1/2). Now kappa=|dT/dx|. You have that in your solution. You have to find the vector that is dT/dx and find it's magnitude. Start differentiating.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Curvature forumula of a planar trajectory
  1. Elliptical trajectory (Replies: 2)

Loading...