Example the central force problem

In spherical polar coordinates, for one mass point moving in a central potential V = V(r), 

For specified energy E and angular momentum pe = const = l, on solving H = E for pr, 

A trajectory rtf) is obtained by integrating r between turning points, where the argument of the square root vanishes. Using dO = A, this formula for r provides an equation to be integrated for a classical orbit, 

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