Analytic Model of Variable Characteristic of Coefficient of Restitution   and Its Application to Soccer Ball Trajectory Planning
  In this article, we investigate the behavior of the coefficient of restitution (COR) which is an important parameter in many impact-related fields. In many cases, the COR is considered as a constant value, but it varies according to many variables. In this paper, we introduce an analytical variable COR model considering aero dynamics along with its verification through experiment. To introduce and analyze the variable characteristic of the COR model, the collision phenomenon between a pendulum and two kinds of ball is employed as an example and aerodynamics such as drag force is considered for analyzing the after-effect of the collision. Collision velocity of the pendulum, dynamic parameters of colliding bodies, contact time, drag coefficient, the air density, and the cross-sectional area of the ball are found as the typical variables of analytical COR model. This observation generalizes the result in previous researches. To verify new COR model, the travel distances for the curve-fitted constant COR model and the curve-fitted variable COR model are compared through simulation and experiment. Moreover, comparison between constant COR and variable COR is presented in several point of views. Finally, using the variable COR model, the travel distance of the ball for collision velocity, which is beyond the curve-fitted range, is estimated. 
Hwan-Taek Ryu, Byung-Ju Yi, Younghun Kwon
physics.class-ph