Regular and chaotic motions of the parametrically forced pendulum: Theory and simulations

Eugene I. Butikov

Research outputpeer-review

4 Citations (Scopus)

Abstract

New types of regular and chaotic behaviour of the parametrically driven pendulum are discovered with the help of computer simulations. A simple qualitative physical explanation is suggested to the phenomenon of subharmonic resonances. An approximate quantitative theory based on the suggested approach is developed. The spectral composition of the subharmonic resonances is investigated quantitatively, and their boundaries in the parameter space are determined. The conditions of the inverted pendulum stability are determined with a greater precision than they have been known earlier. A close relationship between the upper limit of stability of the dynamically stabilized inverted pendulum and parametric resonance of the hanging down pendulum is established. Most of the newly discovered modes are waiting a plausible physical explanation.

Original languageEnglish
Title of host publicationComputational Science, ICCS 2002 - International Conference, Proceedings
Pages1154-1169
Number of pages16
EditionPART 3
Publication statusPublished - 1 Dec 2002
EventInternational Conference on Computational Science, ICCS 2002 - Amsterdam
Duration: 21 Apr 200224 Apr 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 3
Volume2331 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceInternational Conference on Computational Science, ICCS 2002
CountryNetherlands
CityAmsterdam
Period21/04/0224/04/02

Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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