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This is from my homework on PDE.

I need to find a geodesic on a plane using polar coordinates. Now, I know

$dl^2 = x^2+y^2$ hence $l=\int \sqrt{dx^2+dy^2}$,

but I get stuck while converting coordinates. I guess it's the result of a hole in education. Nevertheless, could you help me?

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up vote 2 down vote accepted

In polar coordinates the arc length is given by: $$l=\int_{a}^{b}\sqrt{[r(\theta)^2+(\frac{dr(\theta)}{d\theta})^2}d\theta$$

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Thank you very much. Could you please explain, how do I make this conversion? Or maybe you could point at some good material? –  Michael Sazonov Apr 23 '12 at 7:16
    
You can find 'coordinates change' on google. 'eaeeie.org/theiere/curvilinear/GenCurvilinCoord.htm'; is an example. –  Riccardo.Alestra Apr 23 '12 at 7:28
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