Question about Quaternions

[Simon9050]

Hi Eric,

Thank you for your work, I have a few questions concerning quaternions in 42.
I am using SC[0].B[0].qn from 42. My understanding is that the quaternion represents the attitude from ECI to body. Is it correct ?
What is the elements order (W-X-Y-Z ?) ? What about rotations convention ? 213 ?
If I consider SC[0].AC.ST[0].qn with no mounting angles and boresight for example on Y, what is the convention for the star tracker reference frame with respect to body frame ?
If I can compute Greenwich Mean Sidereal Time (GMST) in degrees, can I approximate the quaternion from ECEF to body by simply rotating qn of GMST degrees around the Z-axis ?

Thank you for you help,
Best Regards,

Simon

[ericstoneking]

Hi Simon,

Yes, SC[0].B[0].qn is the rotation from ECI to Body 0, assuming you're in the neighborhood of Earth. N is a generalization of ECI: every world has an N, but only Earth has an ECI. See Docs/Nomenclature.pdf.

Quaternions are in order X-Y-Z-W; the scalar is the fourth element. For Euler angles, you get to pick any "Body-2" or "Body-3" sequence as described in Kane, Likins, and Levinson, "Spacecraft Dynamics". (Warning: Watch out for matrix transposes when applying KLL in other contexts.)

For the star tracker mounting, you get to define your ST mounting orientation and boresight axis in your SC_foo.txt input file. See InOut/SC_SensorFOV.txt for examples.

GMST is the rotation angle from ECI to ECEF (N to W, in 42's nomenclature). If you want to align your SC with ECEF, then yes, make SC[0].B[0].qn a rotation about Z through the angle GMST. I'm not sure that's what you're asking for, though. Jamming your attitude directly into SC.B.qn is, generally speaking, doing it the hard way and is not recommended. Peruse your Orb_ and SC_ input files, and Inp_Cmd.txt. (Both in InOut and in Demo.) Odds are there's an easier way to get what you want. If I missed the point of your question, come back.

Regards,
-Eric