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February 28th, 2014, 06:47 PM   #1
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Connection between cesaro equation and polar coordinates

First, I'd like that you read this littler article (http://mathworld.wolfram.com/NaturalEquation.html). The solution given by Euler that coonects the system cartesian (x, y) with the curvature ? of the "cesaro system" (s, ?), is that the derivative of the cartesian tangential angle ?* wrt arc length s results the curvature ?.

However, in the 2D plane is definied the polar tangential angle ?* too. Thus if I want express a curve given s and ? in terms of r and ? (or vice-versa) I need to establish a connection between the curvature ? and the polar system. So, would be correct to say that the derivative of ? wrt s is equal to ??

*
https://en.wikipedia.org/wiki/Tangential_angle
https://en.wikipedia.org/wiki/Subtangent
https://en.wikipedia.org/wiki/List_o....A0ro_equation

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