Simulations are playing an important role to predict derailment, switching, wheel climbing and curving in the study of dynamics of railroad vehicles. For a successful simulation, a robust and efficient approach for computation of all common normal between wheel and rail surface is needed. In a previous work, the authors had devised an approach based on sign distant function to compute all common normal between a pair of wheel and surface. As part of this approach, two major computational tasks were formulated. They were computation of cauchy index around a cell (a closed curve) and computation of the zero’s of the gradient of the signed distance function. In this study, a bookkeeping technique is devised to compute the cauchy index more efficiently. Also the performance of trust region method as a solver for a set of nonlinear equation is compared to Newton’s method.
Some remarks on the Cauchy index theorem