Transient tumbling chaos and damping identification for parametric pendulum

Bryan Horton, Marian Wiercigroch, Xu Xu

Research output: Contribution to journalArticlepeer-review

42 Citations (Scopus)


The aim of this study is to provide a simple, yet effective and generally applicable technique for determining damping for parametric pendula. The proposed model is more representative of system dynamics because the numerical results describe the qualitative features of experimentally exhibited transient tumbling chaotic motions well. The assumption made is that the system is accurately modelled by a combination of viscous and Coulomb dampings; a parameter identification procedure is developed from this basis. The results of numerical and experimental time histories of free oscillations are compared with the model produced from the parameters identified by the classic logarithmic decrement technique. The merits of the present method are discussed before the model is verified against experimental results. Finally, emphasis is placed on a close corroboration between the experimental and theoretical transient tumbling chaotic trajectories.

Original languageEnglish
Pages (from-to)767-784
Number of pages18
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences
Issue number1866
Early online date18 Oct 2007
Publication statusPublished - Mar 2008


  • dry friction
  • linear viscosity
  • parameter identification
  • transient tumbling chaos
  • parametric pendula
  • excited pendulum
  • friction
  • oscillators
  • coulomb
  • behavior
  • system


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