From Geometry, Kinematics and Dynamics of Billiards to the Extended Theory of Skew Collision between Two Rolling Bodies and Methodology of Vibro-Impact Dynamics

Abstract

Starting from explanation of geometry, kinematics and dynamics of game billiards, and phenomena of impact a rolling ball into different types of curved surfaces and direct and skew central collision of two rolling, same dimension, balls we open question of collision of two rolling axial symmetrically bodies with different dimensions and different forms. Use elementary approach and Petrovic's theory presented in two books “Elements of mathematical phenomenology” and “Phenomenological mappings”, extended theory of direct and skew central collision of two rolling, axially symmetric, but different dimensions and forms, bodies is formulated with all additional and new analytical expressions, theorems , to define all pre- and post- collision kinetic states. Use these new results complete methodology of vibro-impact system dynamics is formulated and applied for investigation kinetic parameters and phenomena in vibro-impact systems with successive collisions between two or a finite number of rolling bodies. Energy jumps in collisions between rolling bodies in vibroimpact system dynamics are indicated and analytically described in a number of these systems.