where m is the mass of the ball and N(t) is the contact force of the table, and g is the gravitational acceleration. Note that both y(t) and N(t) are a priori unknown. While the ball and the table are separated, there is no contact force. There cannot be penetration (for a rigid ball and a rigid table), so y(t)-r\geq 0 for all t. If y(t)-r> 0 then N(t)=0. On the other hand, if y(t)-r=0, then N(t) can take on any non-negative value. (We do not allow N(t)< 0 as this corresponds to some kind of adhesive.) This can be summarized by the complementarity relationship
