Stability of the parametrically excited damped inverted pendulum

Theory and experiment

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

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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
Volume128
Issue number4
DOIs
StatePublished - Oct 1 2010

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pendulums
stabilization
Taylor instability
interfacial tension
damping
approximation
Stabilization
Experiment
Pendulum
simulation

All Science Journal Classification (ASJC) codes

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics

Cite this

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Stability of the parametrically excited damped inverted pendulum : Theory and experiment. / Carbo, Randy M.; Smith, Robert William; Poese, Matthew E.

In: Journal of the Acoustical Society of America, Vol. 128, No. 4, 01.10.2010, p. 1623-1631.

Research output: Contribution to journalArticle

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