Put the gas driven moving mass (BCG) and recoil spring into that system. Its not as simple as Newtons action/reaction experiment, from the perspective of the felt recoil of the operator.
See also #50.
#48 is a “first approximation”, and at least gets the basic mathematical relationships correct. “Felt recoil” is a squishy term, which requires discussion of Impulse, Torque, and various structural of the firearm to address.
Which is one of the reasons why the perceived recoil of my Remington 600 in .308 is significantly more than an AR-10 firing the same ammo. There is also the lighter weight of my 600.