Bi-potential method applied for dynamics problems of rigid bodies involving friction and multiple impacts

This study aims to extend the application of the bi-potential method to solve the dynamics problems of rigid bodies involving friction and multiple impacts. The key issue is the determination of the impact impulsion. The impact bi-potential function and the formula for calculating the bi-potential coefficient of rigid bodies are presented. The effects of the friction and normal restitutive coefficients on the results are analyzed. Extension from discrete granular systems to multibody systems is realized. Further, the internal software FER/Mech is used for realizing dynamic simulation of the entity object, and the comparison with the experimental video verifies the correctness of the proposed method. Results show that the achieved improvements of this study are more accurate. In the discrete granular systems, the numerical solutions of the proposed method are in good agreement with those of another numerical method. But in the multibody systems, the numerical solutions obtained by the proposed method are more stable. It is noteworthy that the bi-potential method not only does not increase the degree of freedom of the system, but also makes the programming simple and numerically robust, thus reducing the computing cost. Graphic abstract