I don't have the solutions, but I have an impression that the trig approach is a bit
contrived.

Perhaps you should be looking for a more generalized method.

The sphere is is a conic cross section (angle 90) formed by revolution. It's perfectly
described
by the math for conics. Size is derived by locating the cross section along the
vertical axis.
Using this seems fairly simple, plus it would also solve the problem of rolling
ellipsoids along
the floor. Instead of scaling, use the location of the cross section to derive the
size.

A generalized solution of this type would further yield parabolic and hyperbolic
movements.

Just an idea from my old optics days.

steve

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