Helio - You are quoting Catastrophe and crediting it to me.
Oops. Sorry. I was rushing to get done to get to a meeting.
As for Catastrophe's question: "What would you predict, for example, for the Pluto-Charon plus three more moons system? And what if it were Pluto plus 4 Charon-sized moons?"
The problem with other bodies is their relative mass, distance and periods. The animation doesn't seem to represent any of those variables.
The same thing would happen for any number of bodies in an isolated system. The barycenter does not move around. Its velocity vector cannot be changed except by an external influence.
I'm unclear what you mean. The barycenter is a dynamic c.g., so it all depends on what one chooses to use for a reference frame, though the barycenter itself is the normal one, so, by definition it doesn't move, to your point. Yet, relative to "space coordinates", if one could establish them from say 2 light years away, it does wobble as planets align, for instance.
A see-saw analogy, though limited, might help. With two people on a balanced see-saw, there is one fixed c.g. (baryenter). But what happens when one big person is on one side and you have four little guys moving back and forth on the other side? An auto-c.g. centering mechanism would have to either move the board quickly (and all that are on it) or move along the ground. Either way, it must be moved.