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Applied Mathematics and Mechanics

, Volume 37, Issue 12, pp 1721–1738 | Cite as

Synchronization of two coupled pendula in absence of escapement

  • F. TalamucciEmail author
Article
  • 45 Downloads

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

synchronization coupled pendula characteristic equation eigenvalue localization 

Chinese Library Classification

O22 O23 

2010 Mathematics Subject Classification

34C15 34L15 70E55 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.DIMAI, Dipartimento di Matematica e Informatica “Ulisse Dini”Università degli Studi di FirenzeFirenzeItaly

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