Breaking the symmetry of the parametrically excited pendulum

DOI10.1016/j.chaos.2005.07.014zbMath1121.70018OpenAlexW1995488788MaRDI QIDQ2497576

Anastasia Sofroniou, Steven R. Bishop

Publication date: 4 August 2006

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2005.07.014

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Bifurcations and instability for nonlinear problems in mechanics (70K50)

Related Items (12)

A direct method for the numerical computation of bifurcation points underlying symmetries ⋮ Approximations for period-1 rotation of vertically and horizontally excited parametric pendulum ⋮ Chaos of several typical asymmetric systems ⋮ Dynamics of a parametrically excited system with two forcing terms ⋮ The Effects of a Constant Excitation Force on the Dynamics of an Infinite-Equilibrium Chaotic System Without Linear Terms: Analysis, Control and Circuit Simulation ⋮ Symmetry-breaking analysis for the general Helmholtz-Duffing oscillator ⋮ Comparisons between the pendulum with varying length and the pendulum with oscillating support ⋮ The effect of symmetry-breaking on the parameterically excited pendulum ⋮ Influence of nonlinearity on transition curves in a parametric pendulum system ⋮ Stability analysis of nonlinear ship-roll dynamics under wind and wave ⋮ STEADY STATE SYMMETRY BREAKING IN PERIODICALLY EXCITED SYSTEMS INVOLVING TIME DELAY BY HARMONIC HOMOTOPY ⋮ Reversal of period doubling, multistability and symmetry breaking aspects for a system composed of a van der Pol oscillator coupled to a Duffing oscillator

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Rotating orbits of a parametrically-excited pendulum
• Inverted dynamics of a tilted parametric pendulum
• Symmetry-breaking in the response of the parametrically excited pendulum model
• Approximating the Escape Zone for the Parametrically Excited Pendulum
• Periodic oscillations and attracting basins for a parametrically excited pendulum
• The nonlinear dynamics of ship motions: a field overview and some recent developments
• THE GLOBAL BIFURCATIONS THAT LEAD TO TRANSIENT TUMBLING CHAOS IN A PARAMETRICALLY DRIVEN PENDULUM
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