How can I find the collision time of 2 ellipsoids that rotate

[Guy Ab]

I have 2 ellipsoids:

Ax^2/a^2+Ay^2/b^2+Az^2/c^2=1; (*a,b,c>0 constants*)
Bx^2/a^2+By^2/b^2+Bz^2/c^2=1;
Ellipsoid A rotates around axis [wax;way;waz] (unit vector) with an infinite speed;
Ellipsoid B rotates around axis [wbx;wby;wbz] (unit vector) with an infinite speed;
[Dx;Dy;Dz] is the vector from ellipsoid A center to ellipsoid B center;
The velocity of ellipsoid A center is [VAx;VAy;VAz];
The velocity of ellipsoid B center is [VBx;VBy;VBz];

How can I find the collision time?

 

[Stephen Tashi]

You should clarify the question.

How does it make sense to ask for a collision "time" when things are happening at "infinite" speed? Are you seeking "the fraction of time" that two figures would have some intersection?