A mathematical model of the static pantograph/catenary interaction

Abstract

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.

Keywords:

• high-performance computing
• interaction pantograph/catenary
• static equilibrium equation
• sparse linear algebra libraries

Acknowledgements

This work was supported by the Castilla-La Mancha project JCCM-PCI-05-019.