I'm doing some orbital mechanics and have calculated the Keplerian Elements (Euler angles) and now I want to plot it in 3D but I'm constrained to only doing rotations about the x, y or z-axis. I've seen how to convert the Euler angles to a rotation matrix but I haven't figured out a way to recover the rotation angles and the order that I need to do the individual rotations in. The software I have to use doesn't support matrices so if possible scalar or vector equations are preferred.
The Euler angles are intrinsic:
intrinsic (rotations about the axes of the rotating coordinate system XYZ, solidary with the moving body, which changes its orientation after each elemental rotation).
Thank you very much in advance :-)