Stability and Hopf bifurcations in an inverted pendulum

James A. Blackburn, H. J. T. Smith, Niels Grønbech-Jensen

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Abstract

The inverted state of a simple pendulum is a configuration of unstable equilibrium. This instability may be removed if the pivot is harmonically displaced up and down with appropriate frequency and amplitude. Numerical simulations are employed to investigate the stable domains of the system. The associated basins of attraction, extracted by interpolated cell mapping, are seen to be fractal. Loss of stability at high excitation amplitudes is observed to follow a Hopf bifurcation.
Original languageEnglish
JournalAmerican Journal of Physics
Volume60
Issue number10
Pages (from-to)903-908
ISSN0002-9505
DOIs
Publication statusPublished - 1992
Externally publishedYes

Bibliographical note

Copyright (1992) American Association of Physics Teachers. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Association of Physics Teachers

Cite this

Blackburn, J. A., Smith, H. J. T., & Grønbech-Jensen, N. (1992). Stability and Hopf bifurcations in an inverted pendulum. American Journal of Physics, 60(10), 903-908. https://doi.org/10.1119/1.17011