If you express the angular velocities in the body fixed reference frame for each body and thus also the applied moments, you get time invariant inertia matrices for each body. This means that M is constant wrt time and the $\dot{M}T$ term is zero. This matches how most of the literature does it. See more info in #217.
If you express the angular velocities in the body fixed reference frame for each body and thus also the applied moments, you get time invariant inertia matrices for each body. This means that M is constant wrt time and the$\dot{M}T$ term is zero. This matches how most of the literature does it. See more info in #217.