Then, both gravity centers travel with a certain velocity each and will collide. How can they return back here? If they will reverse both velocities after the collision. Then, they can return. But with the opposite velocities, and therefore this will not be the same state.
Since they always move in lines, there will be no another collision. And therefore no return to the present state.
Doesn’t matter how many collisions will happen, the momentum conservation will hold. Even if only two small balls of each gravity center will collide, the sum of momentums of that two gravity centers will remain the same. Doesn’t matter which partition of balls we chose, only that is the same before and after the collision.
After some collisions have happened and the two parts are heading away from each other the two parts could still overlap and then some more of their balls could collide. This could lead to the two parts heading back together.
Then, both gravity centers travel with a certain velocity each and will collide. How can they return back here? If they will reverse both velocities after the collision. Then, they can return. But with the opposite velocities, and therefore this will not be the same state.
Since they always move in lines, there will be no another collision. And therefore no return to the present state.
What do you mean by “the” collision? If each part has several balls then there will be multiple collisions.
Doesn’t matter how many collisions will happen, the momentum conservation will hold. Even if only two small balls of each gravity center will collide, the sum of momentums of that two gravity centers will remain the same. Doesn’t matter which partition of balls we chose, only that is the same before and after the collision.
After some collisions have happened and the two parts are heading away from each other the two parts could still overlap and then some more of their balls could collide. This could lead to the two parts heading back together.
No, that’s impossible. However you choose to divide this set of balls and however they later collide, both impulses are still conserved.