|Jun27-12, 11:02 AM||#1|
spherical basis change through euler angles
More exactly, I want to translate polar coordinates to spherical ones, knowing the euler angles that define the polar plane in the spherical basis.
Polar coordinates: (rp,θp)
it's actually the position of a satellite on its orbitSpherical coordinates: (rs,θs,φs)
its position relative to the planet so φ is the elevation angle(latitude), not the polar angleEuler angles: (α,β,γ)
the orbit parameters: longitude of ascending node, inclination, argument of periapsisWhat I end up with (looks correct as far as I can tell) :
But the calculation of |u,v| (length) is killing my timings with the square root.
So my question is : is there a way to simplify those equations ? And specifically to get rid of the |u,v| ?
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