Kinematic Approach in the Impact Problem of Rigid Bodies

Abstract

The aim of this work is to analyze, by means of a kinematic approach, the problem of the impact between rigid bodies, when the surfaces involved in the impulsive phenomenon are of finite extent. The formulation here adopted permits to use the Gauss variational principle of “least compulsion” and to formulate the dynamic evolution of the system, after an impact, as a minimization problem. In this case, among all the possible subsequent motions, the real one is that which minimizes the kinetic energy connected to the sudden velocities variations. Interesting results are obtained in the case of the impact between a rigid column (either monolithic or made of several blocks) and a rigid ground. In particular, it can be shown that if the previous motion of a rigid block is a rotation around its base corner edge, the motion after the impact is either a rototranslation or merely a translation, depending on the dimensional ratio. In any case, the subsequent motion is characterized by a component of sliding, so that the impact plays the role of filter between the possible degrees of freedom of the system and, at the same time, determines a possible coupling between rotation and translation. This conclusion is a novelty with respect to the results obtained in other papers [4–6], where a classical approach for the impact has been adopted.