A mathematical study of the pantograph/catenary dynamic interaction on transition spans

This paper presents the work carried out by CALPE team on the development of a mathematical model used in the study and simulation of the pantograph-catenarydynamic interaction in high speed railways considering two independent spans ofcatenary where the transition spans are overlapped. According to the developedmathematical model, a non lineal system of differential equations with variableconstraint depending on the pantograph position has been obtained. In order to verify the correctness of the model, a numerical integration algorithm based on an explicit method of the central differentials has been implemented. The procedure that has been designed allows us to study the more appropiate contact wire configuration, in order to make smoth transition of the pantograph between sets ofspans. This procedure can be generalized considering the case of several pantographs, obtaining very realistic simulations.