Method of Integration for Equation of Two Balls in Dumped Collision

6th International Workshop on Multi-Rate Processes and Hysteresis

Alaci, S.^1 ; Cerlinc, D.A.^1 ; Ciornei, F.C.^1 ; Filote, C.^2 ; Frunz, G.^1

Mechanics and Technology Department, University of Suceava, 13 Universitatii Street, Suceava

720229, Romania^1

Faculty of Electrical Engineerig and Computer Science, University of Suceava, 13 Universitatii Street, Suceava

720229, Romania^2

关键词: Coefficient of restitution;    Integration method;    Method of integration;    Second orders;    Two equation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/585/1/012008/pdf
DOI  :  10.1088/1742-6596/585/1/012008

来源: IOP

【 摘 要 】

The paper presents an integration method for the equation characteristic to a dumped collision. The equation which describes the dumped collision is nonlinear ODE of second order. The solution consists from two stages: in the first stage the equation order is reduced with a unity finding a prime integral. In this moment the maximum approach can be evaluated. Next, using a elementary numerical method the relation between approaching versus time is found. The method is applied for two equations which describe a dumped collision. The results obtained with the proposed method are in a perfect agreement with those from original paper. Finally, in order to emphasize the difference between the two models and the effect of dumping, the hysteresis loops for two values of the coefficient of restitution, corresponding to the two models are plotted to emphasize the difference are plotted.