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Perhaps your effort would be enhanced if you indicated that you were
starting with Newton's second law for a system (F_net = Ma_cm) and that
the mathematics parallels the math used in integrating Newton's second
law for a particle.
This is certainly what I would do if I were offering a PROOF of the MET.
My purpose is only a clear statement of the result.
I think "division of labor (not work)" dictates that the derivation of
MET should come from elswhere (like Annapolis?) :)