Rotational dynamics equation for a variable mass system? I'm searching for the formulation of Euler's rigid body dynamics in the case of a variable mass system. I'm reading the book Mechanics of Flight by Warren F. Phillips (2nd edition) and unfortunately the author does not go into detail of how he obtains the rotational dynamics for a body that is ejecting mass. Here is the relevant passage extracts from that book:
The author states rotational dynamics for a constant-mass system:

Then, assuming symmetry along axis y_b of the airplane (symmetry of the two wings), we have:

Now, here is the key passage that I don't understand:

Notice how the terms $M_{sxb}$ change to $M_{xb}$, $M_{syb}$ to $M_{yb}$ and $M_{szb}$ to $M_{zb}$. Something is hiding behind those new terms, the author does not specify it and I don't know what it is. I searched for rotational dynamics of variable mass systems, but my searches turned up nothing - at least not in notation I could understand.
Could you please write to me the formulation of rotational dynamics of a variable mass, rigid system?  And, what would be great, if you could explain to me how this fits into what Professor Phillips is saying here?
Thank you, I truly appreciate it.
 A: Firstly, there are several schools of thought when it comes to deriving the equations of motion of a variable mass system. The current preference of researchers is to use a model that incorporates continuous mass variation.
In this case, the rotational dynamics of a rigid variable mass system are derived by starting at the standard rules of mechanics (Newton's Law or Lagrange's Method or Kane's Method) and then invoking Reynolds' Transport Theorem (RTT) appropriately. The RTT shifts the perspective from following all the matter (i.e. a constant mass system of variable volume) to that of a specific region of space (a.k.a. the control volume of varying mass).
Your final equations above are the scalar form of the vector equation of rotational motion. It appears to me that the moment terms are these additional RTT terms that come from mass variation (and possibly other external moments). Setting these moment terms to $0$ enforces that there is no mass variation. Consequently, as you probably already noticed, you retain the standard Euler equations of rigid body motion.
A good paper that discusses the derivation using Newton's Law+RTT can be found here: http://appliedmechanics.asmedigitalcollection.asme.org/article.aspx?articleid=1411401
