On multiple Attractors and critical Parameters and how to nd them numerically: The Right, the Wrong and the American Way

In recent years several authors have proposed 'easier numerical methods' to _nd multiple attractors and the critical speed in railway dynamical problems. Actually, the methods do function in some cases, but they are not safe in the sense that you will calculate the relevant critical parameter values with a reasonable accuracy. In some cases the 'easier numerical methods' are really just a gamble. In this presentation the methods will be discussed. In this relation the linearisations of the nonlinear dynamical problem are made. A linearisation of the nonlinear dynamical problem simpli_es the calculations and may give relevant answers to important questions such as the possibility of resonance phenomena in the designs, but a linearisation is not always allowed. We shall also address the curious fact that the hunting motion is more robust than the ideal stationary state motion in the track.