Possibly incorrect results of keplerian_to_cartesian

[gaowutong]

In the AstrodynamicalCalculations library, the keplerian_to_cartesian function appears to produce incorrect results.

Here's a simple test: Take any valid state vector and its corresponding GM value, convert to orbital elements using cartesian_to_keplerian, then convert back using keplerian_to_cartesian. The resulting state vector does not match the original.

Test code:

rv = [6878.137, 10, 10, 0, 7.612, 0]
mu = 398600.4415
println(collect(keplerian_to_cartesian(cartesian_to_keplerian(rv..., mu)..., mu)) - rv)

Output:

[-9.094947017729282e-13, 6838.04881967674, -2.341273841466318e-10, 1.3768591025695304e-15, 2.6645352591003757e-15, 2.1487788277296093e-20]

[gaowutong]

The problem is possibly due to the incorrectness of perifocal_to_cartesian:

GeneralAstrodynamics.jl/lib/AstrodynamicalCalculations/src/R2BPCalculations.jl

Line 157 in 7356656

R_3Ω = SMatrix{3,3}(cos(Ω), sin(Ω), 0, -sin(Ω), cos(ω), 0, 0, 0, 1)

cos(ω) should be cos(Ω).

[cadojo]

Great find, thank you! If you wanted to add that change as a PR, that would be really appreciated. If not, I can add this change this week.

[gaowutong]

I'm not familiar with the project branch, you can add it directly ^_^