Even without examining a complicated trajectory, the collision
matrix can provide some insight into the behavior of a
more realistic superball. Consider what happens to a superball
that is bouncing along a flat surface under the action of
gravity. Because gravity is the only external force, there is no
change in the horizontal velocity or spin between collisions.
Because the velocity in the y direction has no effect on the x
component of the velocity or the rotation of the ball, the
matrix equation describing the horizontal components becomes