This is in context of classical Newtonian physics. Consider a system of n different point mass particles. Initially all are spread around on one plane. No particle possess any velocity to begin with. There is no external force acting on this system. Each particle has some mass. The only force to consider here is gravitation between any two particles. When two particles collide, lets say they form a lump with mass equal to sum of the two. This now behaves like one single particle.
My first assumption is, the centre of mass of this system, throughout time won't move. Right?
Given a sufficient amount of time, will everything collapse into one single particle at the centre of mass?
Or it's possible to see a system where few particles are rotating in one direction and other in other direction, so that angular momentum is conserved and net angular momentum is still zero?
If yes, can you give one simple example with points, mass and initial position which will achieve this kind of state.
EDIT: On similar note, can we have say 3 particles which are attracted to each other but never collide, something like a simple harmonic motion?