First off, I do NOT propose to predict the entire motion of the system generated by the collision.
I only want to make predictions for how the velocities have changed JUST AFTER the collision phase; how the non-colliding objects (in particular, the cube) thereafter choose to move, is not my concern.
Hence, the model for the cube should provide the INITIAL conditions for its motion after the collision phase, not the differential equations governing that period.
Secondly, this is certainly not my own invention; it is called classical impact theory, and was one of the first great successes of Newtonian mechanics.
The fact that only the simplest portions of this theory is generally taught today, is not because the theory is inaccurate for 3-D collisions in general, but because the focus of physics today is on completely different phenomena than it was earlier, as it should be.
However, when we, on occasion, DO want to analyze general collision phenomena , unless we want to try and solve some truly ugly differential equations, the only viable "theoretical" approach remains classical impact theory.
An alternate (and IMO, highly important) strategy for analysis, is, of course, the experimentalist approach.
Thirdly, as to chaotic behaviour:
Although it is quite true that several systems are extremely sensitive to initial conditions, and hence, that only the slightest deviation from the "true values" create radically different patterns of motion, this does not mean that EVERY imaginable system experience such effects.
To have a simple, general model to give good estimates of initial values (after a collision) remains quite useful.
Although it might be objected that the particular choice I made for an illustrative example is, for some parameter combinations, extremely chaotic in its ensuing motion, that example was chosen because the objects involved have relatively simple geometries.
I'll proceed further in a while..
