I see that in the SITL sim_aircraft and sim_frame, the linear momentum equation can be accepted as it calculates forces in body coordinate and the using F=ma, it finds acceleration in body frame (although this is not correct, but the final result is correct) then using dcm, the body coordinate transforms to earth frame.
but for angular momentum equation, in sim_frame it finds moments in body coordinate and simply finds angular acceleration by wdot=M/I. this is not correct as the body frame is not an inertial frame. thus, another term should be added to it just like w*Iw. also, the moment of inertia should be in a tensor manner including Ixy, Ixz and Iyz.
I think it should be changed to the correct form, am I correct?
SITL model is meant to be extremely simplified. It only needs to be good enough to run a mission simulation that resembles reality and fast enough tu run in autotests in reasonable time and at high speed up.
It ultimately doesn’t really matter as long as it can be controlled by SITL autopilot with control imputs resembling real life.
If you need accurate simulation, use JSBSim or other compatible simulators.