A simple qualitative physical explanation is suggested for the phenomenon of subharmonic resonances of a rigid planar pendulum whose axis is forced to oscillate with a high frequency in the vertical direction. An approximate quantitative theory based on the suggested approach is developed. The spectral composition of the subharmonic resonances is investigated quantitatively, and the boundaries of these modes in the parameter space are determined. New related modes of regular behaviour are described and explained. The conditions of the inverted pendulum stability are determined with greater precision than previous results. A computer program simulating the physical system supports the analytical investigation.

Original languageEnglish
Pages (from-to)6209-6231
Number of pages23
JournalJournal of Physics A: Mathematical and General
Volume35
Issue number30
DOIs
StatePublished - 2 Aug 2002

    Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

ID: 51954575