I've long assumed that, ignoring quantum effects, at least Newtonian mechanics is a continuous function of its inputs. Including things like steel balls bouncing off each other. (Of course, as RWG points out, a small error like an off-center collision can propagate into a large error. But in this theoretical problem we are assuming no built-in error like this.) Is it really true that for a triple collision in the plane the result depends on which sequence of double collisions is used to calculate it? (Even in the limit as the discrepancy from a perfect 3-way collision approaches 0 ?) --Dan << I've never been convinced that these problems are even well-defined, for the same reason that a simultaneous collision between three bodies in the plane is ill-defined. In that case, it's immediately obvious that you get completely different results according to how you decompose into a sequence of 2-body collisions.
Those who sleep faster get more rest.