The simulation of pantograph and catenary: a PDAE approach

Recently, the coupled dynamical simulation of pantograph and catenary in high speed trains has found much interest. The equations of motion form a partial diierential-algebraic equation (PDAE) that combines a partial diierential equation (PDE) for the catenary and a diierential-algebraic equation (DAE) for the pantograph. In the present paper we discuss the relation of this PDAE model to current work on the analysis of PDAE's 3, 17, 18] and formulate a benchmark problem to stimulate further research on this topic. The benchmark problem is solved numerically using a semi-discretization in space (by nite elements or nite diierences). For time discretization, typical DAE techniques are applied (index reduction, projection steps, handling of systems with varying structure).