Lots of posts, not enough time...
Had not seen this explanation yet, so:
Recoil starts at ignition. Equal/opposite stuff. The next bit is key in my mind. As the pressure builds and gas expands, the pressure vessel grows as the bullet travels forward. As a pressure vessel applies a uniform amount of force in all directions, the center of the vessel must travel forward to remain central of the vessel. Equal/Opposite forces and resistance come into play here as the rifle and bullet both resist the movement of the center of pressure. The 22lb rifle versus the .0307lb (215 Berger) have very different amounts of resistance. The bullet also has the aid of rifling friction, which can be treated as negligible, so long as the bullet escapes.
To the OPs other question about an infinitely long barrel, the rifling will eventually slow the bullet back to stationary, as will the vacuum created by a negative pressure as the gas expansion ceases and the bullet temporarily remains in motion. The slowing of the bullet will act as a brake to end the recoil but will not return the rifle to its initial position, because the bullet & powder/gas are no longer in the same position as before charge was lit. In this hypothetical scenario, the center of mass (assuming a perfectly linear recoil) should remain the same, because of the closed system principle.
This would be the same as if you were in a cargo van and pushed off a seat back to propel yourself to the rear before hitting the back doors. The van would move to account for the change in center of mass. Another way to think about the shift in center of mass is with the closed system of a person on a motorcycle. While balanced and stationary, the rider can thrust their body to push/pull the bike a small amount. The motion of the system on a flat surface is a direct correlation to the change in center of mass.
I hope there was some value somewhere in there...
This phenomenon is actually what spurred my post. I didn’t want to theorize or converse solely alone on the question of whether a center of gravity shift (or CM and especially as worded in your original post) is all that’s really, or possibly, going on in the rifle pre-exit.
Besides the firehose nozzle, there are a couple of visualization analogies that bother me, fairly relentlessly. I’d be the first to admit that if we put a grandfather clock on a platform over ball bearings, the motion of the pendulum is going to ever so slightly move the clock in counter step to its swing, until that brings it to a premature stoppage, and that slight side to side displacement is not what I’d call self-propulsion, but simply finding COG.
Second, is the powerful image of an Olympic hammer thrower. The moment of dramatic “disconnection” between the person and the weight is when the rotating person now recoils in the opposite direction of the hammer, very violently to a near fall. All the energy is contained in that system until disconnection. If he never let go, and just slowed down back to a stop, is that not like a bullet that never exited, I wonder.
A system finding its COG is a really “mild” process. I don’t think it’s even speed dependent; - if you used your finger to manually move the pendulum of the grandfather clock on ball bearings 5 inches to one side, spread over an hour’s time, I think the clock would end up in the exact same place at swing’s max, even though the pendulum’s hour long swing developed infinitesimally low momentum. Absent ball bearings, it’s not even close to wanting to move on its own. I alluded way up top to whether this fixed and limited amount of work is all that’s being done pre-exit. I still wonder that. If COG dislocation is not a function of momentum, then it’s not affected by how fast or slowly the bullet and gasses move from one end of the barrel to the other, and in pre-exit recoil terms, a magnum’s higher velocity would not change anything. (?)
I hear you on pre-exit velocity affecting pre-exit recoil. But while the bullet is still inside the barrel, probably pulling very hard forward on it, how is that not like throttling up on a model jet engine contained on a stand inside a steel cargo container? Whether we give it half or max fuel, the container is still absorbing and negating all its thrust. But at the same time there is no question that if instead of a bullet in front of the charge, there was an immobile rod, the rifle would go backward on firing. A rifle prevented from recoil should chrono a bullet faster than one that is recoiling while the bullet is still in it. I wonder if there is data on this. I don’t personally see it shooting LR Fclass, though.
If I visualize a pressure bubble of heated air in the middle of a balloon, (relevant because nothing escapes) I certainly agree that it seeks center and all sides try to move away from it.
On the other hand if pre-exit recoil is really a net of nothing more than COG dislocation, (and I’m not saying it is but have sure wondered about that because it’s a closed system until exit), and if COG adjustment to dislocation is not even a function of momentum, as the grandfather clock pendulum manually raised would indicate, then it, all by itself, truly is a very mild force, right? One that in many types of rifles would not overcome the inertia of the rifle sufficient to move, pre-exit, I’m thinking. That’s of course if those “ifs” are true.