Dynamics of impacts and collisions of the rolling balls

Abstract

In the chapter the theory of dynamics of impacts and collisions of the rolling balls is presented for different types of impacts and collisions depending on the balls’ configuration in the kinetic state of impacts and collisions. By use of analogy between central impacts or collisions of balls in translator motion and balls’ rolling motions before impacts or collisions, corresponding relations between outgoing velocities and outgoing angular velocities of rolling and impact velocities are expressed. Also, change of impact impulse (linear momentum) and moment of impulse (angular momentum) of the balls’ rolling motion after and before impacts and collisions are expressed. By use of phenomenological mappings between a set of element dynamics of balls’ impact and collisions for central and skew impacts as well as collisions corresponding analogies are identified. Different ball-rolling traces before and after skew impacts and skew collisions as a set of different kinematic elements for each type of impact and collision are discussed and kinematic plans of impacts and corresponding outgoing translator and angular velocities are graphically presented by a series of figures. In conclusion, dynamics of elliptic billiards are presented.