Say I have a state vector and Keplerian elements of an orbiting spacecraft:
- Position = [x, y, z]
- Velocity = [vx, vy, vz]
- Elements = [a, e, i, $\omega$, $\Omega$, $\nu$]
And I have the maneuver I wish to perform, expressed as a vector of prograde, normal, and radial velocities:
- Maneuver = [vp, vn, vr]
How would I transform my maneuver velocities into a Cartesian vector (to add to my initial velocity state)? What does the rotation matrix look like?
I can qualitatively express how each maneuver component translates into Cartesian XYZ coordinates but I cannot yet figure out how to quantitatively express that.