Multiple attractors and critical parameters and how to find them numerically: the right, the wrong and the gambling way

Hans True

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

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 article, the methods are discussed and the pros and contras are commented upon. I 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 on the track. Concepts such as multiple attractors, subcritical and supercritical bifurcations, permitted linearisation, the danger of running at supercritical speeds and chaotic motion are addressed.
Original languageEnglish
JournalVehicle System Dynamics
Volume51
Issue number3
Pages (from-to)443-459
ISSN0042-3114
DOIs
Publication statusPublished - 2013

Keywords

  • Bifurcation (mathematics)
  • State estimation
  • Dynamical systems

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