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Introduction
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Synchronisation among oscillators with some form of coupling has been called universal [@strogatz2004] and is prevalent concept in Nature [@Pit].

In 1665 Huygens, the inventor of the pendulum clock, observed synchronisation between two pendulum clocks [@Huy] hanging from the same support. The first observation of Huygens was about the two clocks hanging in the same wall beam of his house when he was lying in bed with some indisposition. He observed both phase and phase opposition as a final state of the coupled system. The second observation was made later, when Huygens hung the two clocks on a board sitting on two chairs.

The two systems observed by Huygens are quite different, therefore originating two lines of research completely separated. The later case has been studied in many papers [@Benn; @Col; @Frad; @Jova; @Col2; @Martens; @Oud; @Sen] by considering momentum conservation in the clocks-beam system, since the plank supporting the clocks is able to move. The system in that case is non-perturbative, there are three bodies that can move, i.e., three degrees of freedom: the pendula and the wood beam. The model is a classical mechanics paradigm, and in most of the works cited above the 