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Regular and Chaotic Dynamics, 2008, Volume 13, Issue 3, Pages 155–165
DOI: https://doi.org/10.1134/S1560354708030027 (Mi rcd567) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Stability Condition for Vertical Oscillation of 3-dim Heavy Spring Elastic Pendulum

P. Pokorny

Department of Mathematics, Prague Institute of Chemical Technology, Technicka 5, Prague 6, Czech Republic
Citations (3)
DOI: https://doi.org/10.1134/S1560354708030027
Abstract: Equations of motion for 3-dim heavy spring elastic pendulum are derived and rescaled to contain a single parameter. Condition for the stability of vertical large amplitude oscillations is derived analytically relating the parameter of the system and the amplitude of the vertical oscillation. Numerical continuation is used to find the border of the stability region in parameter space with high precision. The stability condition is approximated by a simple formula valid for a large range of the parameter and of the amplitude of oscillation. The bifurcation responsible for the loss of stability is identified.
Keywords: elastic pendulum, stability condition.
Received: 26.02.2008
Accepted: 28.04.2008
Bibliographic databases:
Document Type: Article
MSC: 70G60, 70K20, 37J25, 37J45
Language: English
Citation: P. Pokorny, “Stability Condition for Vertical Oscillation of 3-dim Heavy Spring Elastic Pendulum”, Regul. Chaotic Dyn., 13:3 (2008), 155–165
Citation in format AMSBIB
\Bibitem{Pok08}
\by P.~Pokorny
\paper Stability Condition for Vertical Oscillation of 3-dim Heavy Spring Elastic Pendulum
\jour Regul. Chaotic Dyn.
\yr 2008
\vol 13
\issue 3
\pages 155--165
\mathnet{http://mi.mathnet.ru/rcd567}
\crossref{https://doi.org/10.1134/S1560354708030027}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2415370}
\zmath{https://zbmath.org/?q=an:1229.70046}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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