Help with the Euler-Lagrange formula for a geodesic

  • #1

Homework Statement



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.


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.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,260
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It's a y^2 inside the square root, isn't it? Not a y.
 

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