The theory of body collisions in rolling through geometry, kinematics and dynamics of billiards

Abstract

The elements of geometry, kinematics and dynamics of rolling homogeneous balls along curvilinear lines are defined. The complete theory of the impact and collision of heavy rolling balls, through geometry, kinematics and dynamics of rolling balls, is defined. A new definition of the coefficient of restitution (collision) was introduced, starting from the hypothesis of the conservation of the sum of angular momentum of the balls in rolling, for instantaneous rolling axes, after the collision in relation to the before collision of the bodies. The expressions for the outgoing angular velocities of the ball rolling after the collision have been derived and their rolling paths after the impact or collision have been determined and various possible anchors have been shown. The difference between the content of the term billiards used in mathematical works of many mathematicians, as well as the research that remains in the field of geometry is pointed out. Our theory of ball rolling and collision is based on the examples of the abstraction of real systems of rolling heavy homogeneous billiard balls to a mechanical model.