Pantograph motion on a nearly uniform railway overhead line

Representing the line by a tensioned string supported by an elastic medium, whose spring constant varies periodically with position by a small amount, a mathematical investigation is made into the oscillations of overhead equipment produced by the passage of a pantograph. The simplicity of the representation allows analytical results to be obtained for a pantograph whose impedance is of quite general type. For the pantograph in current use, the analysis shows how the oscillations increase at certain critical speeds and how these speeds, and the magnitude of the oscillations, depend on the parameters of the pantograph/line combination.