Sure.
If the center of gravity moves, it moves with the velocity v. So it will be in the position r+v*t after some time t. Now it's at the position r. A different position of gravity (mass) center means different position. For the whatever finite t.
In the case when the gravity center doesn't move, you can divide the composition into two sub-compositions, where both gravity centers do move. If only one had moved, then the combined gravity center would move and we would have the solved case above.
But if both gravity centers move, they can either move apart and never collide - in which case they will both have different position vectors lately - or they will collide. In that case, they will reverse their directions after the elastic collision and we have a solved case then.
Well, that's an approximate proof.
But if both gravity centers move, they can either move apart and never collide - in which case they will both have different position vectors lately - or they will collide. In that case, they will reverse their directions after the elastic collision and we have a solved case then.
I'm not convinced by this bit. Usually we can calculate the results of an elastic collision by using both conservation of energy and conservation of momentum. But we can't know the energy of the sub-compositions based just on the velocity of their centres of mass. They will also have some internal energy. So we can't calculate the results of the collision.
If it's worth saying, but not worth its own post, then it goes here.
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