Hi Hicham Henna

If the satellite is not doing any orbital maneuver (e.g., inclination change, orbit transfer, space rendezvous), then it is generally safe to disregard the orbital equations of motion. For the coupled satellite orbital and attitude dynamics, the full equations of motions can written as twelve 1st-order ODEs with the following states:

{ϑ, ω, r, v}

where

ϑ = [ϕ, θ, ψ]T are the Euler angles (or quaternions, if you wish),

ω ∈ ℝ3 is the satellite angular velocity vector,

r ∈ ℝ3 is the satellite inertial orbital position vector, and

v ∈ ℝ3 is the satellite inertial velocity vector.

Edit: You have a review paper on Satellite Attitude Control Systems published 2 or 3 months ago (as the 1st author).

Conference Paper Towards Fault-Tolerant Strategy in Satellite Attitude Contro...

thank you Yew-Chung Chak ;

Actually, the coupled equations of motion are clear to me when terms with orbital parameters are included in the rotational dynamics equation such as the gravity gradient torque (including orbital position r). But, when omitting such a term (neglected w.r.t the actuator torques), the procedure is not 100% clear to me.

And yes I'm the first author of the paper in question. I'm working right now on how to explore machine learning techniques for orbital correction enhancement of µsat at LEO.