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Correct calculation of L2 distance #1427

@reinhold-willcox

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@reinhold-willcox

In the Macleod AM loss prescription (and soon, the Klencki one as well), the position of the L2 point is approximated as 2^(1/4). While gamma is only weakly dependent on a, this is still an approximation which does not need to be made. As pointed out by Pablo Marchant, calculating the actual position of the L2 point is analytical and not extremely time-consuming.

Here are instructions for implementing a root solver for the polynomial whose solution gives the Lagrange point positions: https://map.gsfc.nasa.gov/ContentMedia/lagrange.pdf

The trickiest part will be implementing a 5th-order polynomial root solver in COMPAS, which is probably not too hard for C++ experts.

Describe the solution you'd like
An analytical calculating of the distance of the L2 point from the center of mass, for use in the AM loss prescriptions above.

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