Impact–contact dynamics in a disc–ball system

Abstract

This paper concerns a disc-ball system, in which a moving ball collides against a disc resting on a rough, fixed horizontal surface. The complexity in such a simple object is due to the presence of the line contact between the disc and the fixed plate, which significantly influences the impact-generated state of the disc. We deal with this problem in a uniform framework that encapsulates different structures of the mathematical model, including contacts, impacts, stick-slip in friction, as well as the transitions among different states of the variablestructure dynamics. We design specific experiments that provide useful information to help determine the macroscopic parameters in impact and friction. Other complicated cases concerned with the couplings between impacts and friction are theoretically and experimentally investigated. Excellent agreements between numerical and experimental results support our theoretical developments.

Rolling friction and energy dissipation in a spinning disc

“…The impacted surface of the disc is positioned with a distance of the ball's radius from the equilibrium point of the pendulum ball so that the ball hits the disc with a horizontal velocity perpendicular to the surface of the disc. We refer the details of the experiment set-up to [19].…”

“…Intuitively, one may tend to believe that the disc would terminate its motion by the collapse without leaving from the table. In our recent work for a planar disc falling down to a surface [19], theoretical analysis and experiments also indicated that it is impossible for the disc to leave the surface.…”

“…Firstly, we build a set of apparatuses to make a pendulumbased ball collide against the disc standing on the flat surface to start its motion. This design, same as the one in our prior work for investigating the impact dynamics in a disc-ball system [19], allows us to precisely repeat experiments with one specific initial conditions. Secondly, a pair of high-speed cameras were synchronized to sample the images of the disc in motion.…”

Experimental study of transport of a dimer on a vertically oscillating plate

“…By the normal constraint equation, together with the friction relationship, we can use an LCP formulation [8,23] to uniquely determine the contact forces F n and F τ , except for certain singular situations that need special treatments [25].…”

“…In these cases, the solutions of post-impact response cannot be directly obtained using a coefficient of restitution, yet require a sophisticated model to capture the dissipation and dispersion of energy evolving within the impact dynamics. Recently, we have developed a method [20] to solve these complex impact events, and have found successful applications for it in a variety of systems [21][22][23][24]. The theoretical development in understanding the dynamics of frictional impacts paves the way of characterizing the physical mechanism underlying the self-organized behaviours in the dimer system.…”