Instability dynamics of a horizontally shaken pendulum

Yan Xu, Tristram Alexander, Harvinder Sidhu

Abstract


We consider the effect of horizontally shaking the pivot point of a damped pendulum. While similar systems have been considered in engineering in specific circumstances, for instance in the design of isolation systems in an earthquake zone, a careful analysis of the shaken damped pendulum behaviour has not been carried out. We identify the periodic solutions in the system, examine their bifurcation behaviour, and explore the development of chaos. We find that the horizontal shaking supports bistability in a critical frequency range and that the development of chaos depends sensitively on the driving frequency. Our work complements recent experiments on coupled pendulums with horizontal shaking, providing a foundation for further study of the pendulum dynamics.

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Keywords


shaken pendulum; instability dynamics

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DOI: http://dx.doi.org/10.21914/anziamj.v53i0.5153



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