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A mathematical model of the static pantograph/catenary interaction

In this paper, we present a mathematical model of the static pantograph/catenary interaction for high-speed railways, with an outline of the development of a computing algorithm which can be used to obtain the solution of the static equilibrium equation of the pantograph/catenary system which has been reached after an exhaustive study of the traditional mechanical approach based on a set of coupled strings. In order to obtain favourable behaviour in the pantograph/catenary system, it is necessary to obtain adequate conditions in the line; thus we need a precise mechanical calculus. The resulting stiffness matrix shows a high degree of sparsity. Hence, this result can be interpreted in two ways: less memory storage requirements as well as the use of suitable methods to solve the static equilibrium equation as projection methods.