More exactly, I want to translate polar coordinates to spherical ones, knowing the euler angles that define the polar plane in the spherical basis.(adsbygoogle = window.adsbygoogle || []).push({});

Polar coordinates: (r_{p},θ_{p})

it's actually the position of a satellite on its orbitSpherical coordinates: (r_{s},θ_{s},φ_{s})

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 periapsis

What I end up with (looks correct as far as I can tell) :

r_{s}=r_{p}

θ_{s}=α+atan2(u,v)

φ_{s}=atan2(|u,v|, sin(θ_{p}+γ)sin(β))

with:

u=cos(θ_{p}+γ)

v=sin(θ_{p}+γ)cos(β)

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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# Spherical basis change through euler angles

Can you offer guidance or do you also need help?

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