The mapping (11)–(14) must be supplemented by initial data.
Thus we assume that the ball is launched from the floor with
velocity components u0o0, v040 and o0, with the centre C at an
initial position (x0,0). These initial data are the output of a zeroth
bounce arising from projecting the ball onto the floor. To simplify
matters we assume that the floor and the wall are constructed
from the same material so that aw ¼ af ¼ a and ew ¼ ef ¼ b, say.
We also non-dimensionalise by defining