Reaching any point mass configuration by internal forces

[uekstrom]

If we have N unique point masses, is it possible to use only internal forces (i.e. forces between each pair of masses) to reach any configuration of the points (modulo rotations and translations)?

I assume this is well known, but don't know where to find a proof. Perhaps by induction from N=2 where it's obvious? Or of it's not true, I would like to find a counter example for some low N.

Edit: Ok, now I see that it cannot be true in general, for example three masses on a line can never leave the linear configuration. But is it true for "most" configurations?

 

[Matterwave]

As internal forces cannot produce a net force on the center of mass, you cannot create any center of mass accelerations due to internal forces.

Another counter example is that N=2 masses orbiting each other necessarily orbit in a plane to conserve angular momentum. Therefore, they cannot move out of the plane of orbit.

In fact, Newtonian mechanics is deterministic, and with any specified set of initial conditions (6N conditions for 6 degrees of freedom for each particle) the system will only have necessarily 1 path of evolution.

 

[uekstrom]

That's why I wrote 'modulo rotations and translations', I consider two positional configurations equivalent if they can be translated and rotated into each other.

Edit: I should perhaps clarify that there is some means of controlling the forces between the particles, i.e. the particles can be spaceships connected by rods or something.