Exotic nonlinear metronomes dynamics

The spontaneous synchronisation of coupled non-linear oscillators is a recurring research topic in scientific literature. Since the invention of the pendulum clock from Huygens in 17th century, several studies have been carried out on this topic, which today keeps on captivate researchers. The paper, after a literature survey, tries to analyse this phenomenon, called the Huygens synchronisation, with theoretical simple mechanical models able to reproduce the phenomena of metronomes laid on the same structure. The metronome is a non-linear system powered by an external energy source provided by the escapement mechanism or other electromechanical devices. In this work it could be considered like an initial conservative nonlinear system that is provided of a suitable small dissipation, like every real system. The scope of this paper is to see whether the synchronisation is possible with progressive models characterised by increasing complexity to evaluate hypothesis and consequences. The final aim is to define necessary and sufficient conditions for simulating the phenomenon through numerical integration of models developed through bond-graph approach. These analytical models are compared, in order to emphasise the needed flexibilities, nonlinearities and dissipative effects that should be taken into account to model correctly the pendula behaviour. In particular phase lag between the metronomes are described through Hilbert transform and other time-frequency tools.