(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculate the geodesic for euclidean polar coordinates givends[itex]^{2}[/itex]=dr[itex]^{2}[/itex]+r[itex]^{2}[/itex]dθ[itex]^{2}[/itex]

2. Relevant equations

standard euler-lagrange equation

3. The attempt at a solution

I was able to reduce the euler-lagrange equation to[itex]\frac{d^{2}r}{dθ^{2}}[/itex]-rλ=0where 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.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Calculus of Var, Euclidean geodesic

**Physics Forums | Science Articles, Homework Help, Discussion**