# What is the result of a classical collision between THREE point particles at the same precise instant?

Classical Mechanics is said to be deterministic, a statement that nearly always is followed by that quote from Laplace, something like

If at one time, one knew the positions and velocities of all the particles in the universe, the laws of science should enable us to calculate their positions and velocities at any other time, past or future.

I always scratch my head after hearing/reading that. If 3 or more rigid point particles happen to collide elastically at the same precise instant, is it not impossible to predict the resulting trajectories? If it is possible, how?

-
Of course, a two-particle classical collision is easily solved by examining the problem in the center of mass reference frame, where both conservation of energy and momentum together allow to solve the problem... The question is about 3 classical point particles colliding exactly at the same instant. How to solve the problem? And if it cannot be solved, why is it said that classical mechanics is deterministic? – Mephisto Jan 16 '13 at 23:10
Why is this more difficult than 2 points? – Keep these mind Jan 16 '13 at 23:10
@Gugg: because (if I am not wrong) the two conditions (conservation of energy and conservation of momentum) are not enough to determine the resulting system of equations in the case of three or more particles. – Mephisto Jan 16 '13 at 23:12
And for 2 particles they are? – Keep these mind Jan 16 '13 at 23:13
In the n-body problem, collisions of more than 2 simultaneous particles cannot be analitically continuated, see en.wikipedia.org/wiki/…, the "trick" is to disregard them as highly improbable,i.e. the initial data that would produce one has Lebesgue measure zero. – Jaime Jan 17 '13 at 0:11