Synchronization of two coupled pendula in absence of escapement
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A model of two oscillating pendula placed on a mobile support is studied. Once an overall scheme of equations, under general assumptions, is formulated via the Lagrangian equations of motion, the specific case of absence of escapement is examined. The mechanical model consists of two coupled pendula both oscillating on a moving board attached to a spring. The final result performs selection among the peculiar parameters of the physical process (the length, the ratio of masses, the friction and damping coefficients, and the stiffness of the spring), providing a tendency to synchronization.
Key wordssynchronization coupled pendula characteristic equation eigenvalue localization
Chinese Library ClassificationO22 O23
2010 Mathematics Subject Classification34C15 34L15 70E55
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