Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (12): 1721-1738.doi: https://doi.org/10.1007/s10483-016-2150-8

• Articles • Previous Articles    

Synchronization of two coupled pendula in absence of escapement

F. TALAMUCCI   

  1. DIMAI, Dipartimento di Matematica e Informatica"Ulisse Dini", Università degli Studi di Firenze, Firenze 50100, Italy
  • Received:2016-02-23 Revised:2016-07-13 Online:2016-12-01 Published:2016-12-01
  • Contact: F. TALAMUCCI E-mail:federico.talamucci@math.unifi.it

Abstract:

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 words: eigenvalue localization, coupled pendula, characteristic equation, synchronization

2010 MSC Number: 

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