Bifurcation analysis of a double pendulum with internal resonance

DOI10.1007/BF02459003zbMath0963.70015OpenAlexW2037701479MaRDI QIDQ1574986

Qinsheng Bi, Yu-Shu Chen

Publication date: 14 August 2000

Published in: Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02459003

zbMATH Keywords

numerical methodHopf bifurcationcritical pointroute to chaosnormal form theorytransition boundary\(1:1\) internal resonancenon-autonomous systemautonomous double pendulum

Mathematics Subject Classification ID

Bifurcations and instability for nonlinear problems in mechanics (70K50) Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Nonlinear resonances for nonlinear problems in mechanics (70K30) Normal forms for nonlinear problems in mechanics (70K45)

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Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
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• Non-linear bifurcation analysis of non-gradient systems
• Steady state motions of shallow arch under periodic force with \(1:2\) internal resonance on the plane of physical parameters
• Symbolic computation of normal forms for semi-simple cases
• Static and dynamic bifurcations associated with a double-zero eigenvalue
• A perturbation analysis of interactive static and dynamic bifurcations
• ANALYSIS OF NON-LINEAR DYNAMICS AND BIFURCATIONS OF A DOUBLE PENDULUM

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