Central collision of two rolling balls: theory and examples

Abstract

Paper is focused to central collision of two rolling rigid and heavy smooth balls and using elements of mathematical phenomenology and phenomenological mapping obtain corresponding post collision and outgoing angular velocities of the balls and applied these results for investigation vibro-impact dynamics of two rolling balls along circle trace. This task is fully solved and obtained results are original and new! Original plans of component impact velocities and angular velocity of each of two different rolling balls in central collision and corresponding outgoing angular velocities are presented. Use Petroviċ's elements of mathematical phenomenology, especially mathematical analogy between kinetic parameters of collision of two bodies in translator motion and collision of two rolling different size balls, new original expressions of two outgoing angular velocities for each of rolling balls after collision are defined. Using this new and original result vibro-impact dynamics of two rolling different heavy balls on the circle trace in vertical plane in period of series collisions is investigated. Use series of the elliptic integrals, new nonlinear equations for obtaining angles of balls positions at positions of collisions are defined. Branches of phase trajectories of the balls in vibro-impact dynamics are theoretically presented.

Nonlinear phenomena of contact in multibody systems dynamics: a review

“…Later, Stronge introduced an energy loss term associated with the wave propagation phenomena during the deformation process [54]. • Hedrih (Stevanović) proposed, in the context of the dynamical analysis of central collision of two balls rolling along a curvilinear circle trace, a definition of the coefficient of restitution based on the ratio of the relative angular velocities after and before the impact [55][56][57] the angular velocities before at the when contact event starts.…”