Pantograph and catenary dynamics: a benchmark problem and its numerical solution

Kurzfassung

Coupled systems of partial differential equations (PDE’s) and differential-algebraic equations (DAE’s) are of actual interest in various practical applications. From this point of view we have recently studied the interaction of pantograph and catenary in high speed trains. To stimulate further research on this topic we formulate in the present paper a simplified model problem that reflects basic parts of the nonlinear dynamics in the technical system pantograph/catenary. Following the method of lines the equations of motion are semi-discretized in space using finite differences. For time discretization, typical DAE techniques are applied such as index reduction, projection step and handling of systems with varying structure.