www.iop.org home page electronic journals
Journal of Physics A: Mathematical and General

Login | Create account | Alerts | Contact us 
List all IOP Journals EJs Extra J. Phys. A: Math. Gen. Home Search for articles in IOP Journals Information for authors Information for referees Information for librarians User options (e-mail alerts, etc) Context sensitive help
< Previous article | Next article > | This volume ^^ | Table of contents ^ | Article options & Content finder v

J. Phys. A: Math. Gen. 35 (2 August 2002) 6209-6231

Subharmonic resonances of the parametrically driven pendulum

Eugene I Butikov

St Petersburg State University, St Petersburg, Russia

E-mail: butikov@spb.runnet.ru

Received 31 January 2002, in final form 28 May 2002
Published 19 July 2002

Abstract. 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.

PACS numbers: 05.45.-a, 05.10.-a, 07.05.Tp, 45.10.-b

URL: stacks.iop.org/0305-4470/35/6209
DOI: 10.1088/0305-4470/35/30/301
PII: S0305-4470(02)33399-7

E-mail this abstract/Recommend this article

Article Options
[ PDF ] Acrobat PDF (388 KB)
[ HyperCite (not available) ] References - including HyperCite® links
[ File cabinet ] Information about filing cabinet
[ PostScript (not available) ] Gzipped PostScript
[ HyperCite (not available) ] Articles citing this article - including HyperCite® links
[ File cabinet (not available) ] Delete this article from filing cabinet
[ HTML (not available) ] HTML
[ Multimedia (not available) ] Multimedia enhancements
[ Journal Info ] Information about J. Phys. A: Math. Gen.
< Previous article | Next article > | This volume ^^ | Table of contents ^
Content finder
   Full search

Setup information is available for Adobe Acrobat.
EndNote, ProCite ® and Reference Manager ® are registered trademarks of ISI Researchsoft.
Copyright © Institute of Physics and IOP Publishing Limited 2002.
Use of this service is subject to compliance with the terms and conditions of use. Systematic downloading of files is prohibited.