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Regular and Chaotic Dynamics

, Volume 13, Issue 3, pp 155–165 | Cite as

Stability condition for vertical oscillation of 3-dim heavy spring elastic pendulum

  • P. Pokorny
Research Articles

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.

Key words

elastic pendulum stability condition 

MSC2000 numbers

70G60 70K20 37J25 37J45 

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Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  1. 1.Department of MathematicsPrague Institute of Chemical TechnologyPrague 6Czech Republic

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