On multiple attractors and critical parameters and how to find them numerically: The right, the wrong and "the American way"

In recent years several authors have proposed, "easier" numerical methods' to find the critical speed in railway dynamical problems. Actually the methods do function in some cases, but in most cases it is really a gamble. In this presentation the methods will be discussed and the pros and contras commented. We shall also address the questions when a linearisation is allowed and the curious fact that the hunting motion is more robust than the ideal stationary state motion in the track. Concepts such as "multiple attractors", "permitted linearisation", "subcritical and supercritical bifurcations", "the danger of running at supercrititical speeds" and "chaotic motion", will be addressed.