Stability of the parametrically excited damped inverted pendulum: Theory and experiment

Randy M. Carbo, Robert W.M. Smith, Matthew E. Poese

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


The parametrically driven, damped, inverted pendulum can be dynamically stabilized in particular regions of the parameter space. The impact of damping on dynamic stabilization can be stabilizing or destabilizing depending on the location in parameter space (i.e., drive frequency and amplitude). Floquet analysis and numerical simulations were used to determine the stable regions. An experiment was conducted that verifies the model. Physical explanations and simple bounding approximations are provided to summarize findings. The utility of the highly damped pendulum results are illustrated by drawing the analogy to dynamic stabilization of the Rayleigh-Taylor instability: it permits ready demonstration that dynamic stabilization is impossible in that system absent surface tension.

Original languageEnglish (US)
Pages (from-to)1623-1631
Number of pages9
JournalJournal of the Acoustical Society of America
Issue number4
StatePublished - Oct 2010

All Science Journal Classification (ASJC) codes

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics


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