- #1
martinhiggs
- 24
- 0
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'] = 0Now I'm stuck, please help.