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Help with the Euler-Lagrange formula for a geodesic

  1. Oct 20, 2009 #1
    1. The problem statement, all variables and given/known data

    The metric is:

    ds[tex]^{2}[/tex] = y[tex]^{2}[/tex](dx[tex]^{2}[/tex] + dy[tex]^{2}[/tex])

    I have to find the equation relating x and y along a geodesic.

    3. The attempt at a solution

    ds = [tex]\sqrt{ydx^{2} + ydy^{2}}[/tex] - is this right?

    ds = [tex]\sqrt{y + yy'^{2}}[/tex] dx

    F = [tex]\sqrt{y + yy'^{2}}[/tex]

    So then I apply the Euler-Lagrange equation

    dF/dy - d/dx[dF/dy'] = 0

    Now I'm stuck, please help.
  2. jcsd
  3. Oct 20, 2009 #2


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    It's a y^2 inside the square root, isn't it? Not a y.
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