- #1
cpsinkule
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Homework Statement
Calculate the geodesic for euclidean polar coordinates given ds[itex]^{2}[/itex]=dr[itex]^{2}[/itex]+r[itex]^{2}[/itex]dθ[itex]^{2}[/itex]
Homework Equations
standard euler-lagrange equation
The Attempt at a Solution
I was able to reduce the euler-lagrange equation to [itex]\frac{d^{2}r}{dθ^{2}}[/itex]-rλ=0 where λ=[itex]\sqrt{(\frac{dr}{dθ})^{2}+r^{2}}[/itex] is the Lagrangian itself (namely the linear element)
My main concern is that I have the correct differential equation, I'm curious because I can't possibly imagine how this author expects me to solve that if it is indeed the correct DE for the lagrangian.