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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2008, том 13, выпуск 3, страницы 155–165 (Mi rcd567)

Эта публикация цитируется в 3 статьях

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

Аннотация: 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.

Ключевые слова: elastic pendulum, stability condition.

MSC: 70G60, 70K20, 37J25, 37J45

Поступила в редакцию: 26.02.2008
Принята в печать: 28.04.2008

Язык публикации: английский

DOI: 10.1134/S1560354708030027



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