A model for three spheres in colinear impact

Summary

 We analyze the problem of an elastic sphere impacting on two spheres being in contact at rest for the case when adhesive forces act between the spheres. By use of the basic assumptions of Hertz's theory and Johnson's model of adhesion between elastic bodies, the differential equations of the problem are derived. This approach ensures a sufficient number of equations that uniquely determine the velocities after impact. By numerical integration, the significance of the parameters describing the influence of the adhesive forces is examined. It is shown that both separation and capture behavior patterns of the spheres after impact are predictable. The classical Hertz case for the three spheres in impact is obtained for special values of introduced parameters.