  The problem of the mechanical evolution of a shock between a cylindrically
symmetric bat and a spherical ball is solved in the strict rigid approximation
for arbitrary values of the initial conditions. The friction during the impact
is assumed to satisfy the standard rules. When the only source of energy
dissipation is friction, the problem is fully solved by determining the
separation point between the bodies. It also follows that whatever the
character of any additional form of dissipation is, it only affects the ending
value of the net impulse I done by the normal force of the bat on the ball at
separation, but not the dynamical evolution with the value of I during the
shock process. A relation determining whether the contact points of the two
bodies slides between them or become at rest (to be pure rotation state) at the
end of the impact, is determined for the case of the purely frictional energy
dissipation. The solution is also generalized to include losses in addition to
the frictional ones and then applied to the description of experimental
measures of the scattering of a ball by a bat. The evaluations satisfactorily
reproduce the measured curves for the output center of mass and angular
velocities of the ball as functions of the scattering angle and the impact
parameter, respectively.
