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

• 论文 • 上一篇    

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
  • 收稿日期:2016-02-23 修回日期:2016-07-13 出版日期:2016-12-01 发布日期:2016-12-01
  • 通讯作者: F. TALAMUCCI E-mail:federico.talamucci@math.unifi.it

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

摘要:

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.

关键词: characteristic equation, synchronization, coupled pendula, eigenvalue localization

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

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