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Homework Help: Curvature forumula of a planar trajectory

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

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

    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.
     
    Last edited by a moderator: Apr 23, 2017
  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.
     
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