An improved model for the classical Huygens׳ experiment on synchronization of pendulum clocks

Ramirez, J. Peña; Fey, Rhb Rob; Aihara, Kazuyuki; Nijmeijer, Henk

doi:10.1016/j.jsv.2014.08.030

Cited by 26 publications

(24 citation statements)

References 30 publications

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“…The mechanical and geometrical properties for the structure and for the clocks, are provided in Tables 1 and 2 , respectively. At this point, it is worth mentioning that the design of the coupling structure is inspired by our previous theoretical work 24 . Additionally, it should be noted that the experimental setup depicted in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…First, the wooden coupling structure is modelled by using the Finite Element (FE) method 33 . In this way, the flexibility of the structure (bending and elongation) is taken into account 24 . The FE formalism requires to divide the structure into finite pieces, i.e.…”

Section: Resultsmentioning

confidence: 99%

“… 34 35 . This is the reason why some authors have modelled the escapement by using continuous 10 16 22 and discontinuous 21 24 29 nonlinear functions. These approximations seem to be sufficient to capture the essential behaviour of an escapement.…”

Section: Resultsmentioning

confidence: 99%

“…In the last years, Huygens’ synchronization has become a relevant topic among scientists and researchers. By designing novel experimental platforms 9 10 11 12 13 and/or by conducting theoretical analyzes 14 15 16 17 18 19 20 21 22 23 24 , further understanding about the exciting phenomenon described by Huygens has been obtained. In particular, the aforementioned studies somehow convey the same message: the key element in Huygens’ setup of pendulum clocks is the coupling structure and its mechanical properties.…”

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confidence: 99%

“…Likewise, it is still necessary to determine ‘all’ possible limit solutions, besides synchronous solutions, in Huygens’ system of coupled pendulum clocks cf. 24 .…”

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confidence: 99%

See 4 more Smart Citations

The sympathy of two pendulum clocks: beyond Huygens’ observations

Ramirez

Olvera

Nijmeijer

et al. 2016

Sci Rep

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This paper introduces a modern version of the classical Huygens’ experiment on synchronization of pendulum clocks. The version presented here consists of two monumental pendulum clocks—ad hoc designed and fabricated—which are coupled through a wooden structure. It is demonstrated that the coupled clocks exhibit ‘sympathetic’ motion, i.e. the pendula of the clocks oscillate in consonance and in the same direction. Interestingly, when the clocks are synchronized, the common oscillation frequency decreases, i.e. the clocks become slow and inaccurate. In order to rigorously explain these findings, a mathematical model for the coupled clocks is obtained by using well-established physical and mechanical laws and likewise, a theoretical analysis is conducted. Ultimately, the sympathy of two monumental pendulum clocks, interacting via a flexible coupling structure, is experimentally, numerically, and analytically demonstrated.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

“…Likewise, it is still necessary to determine ‘all’ possible limit solutions, besides synchronous solutions, in Huygens’ system of coupled pendulum clocks cf. 24 .…”

mentioning

confidence: 99%

See 3 more Smart Citations

The sympathy of two pendulum clocks: beyond Huygens’ observations

Ramirez

Olvera

Nijmeijer

et al. 2016

Sci Rep

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Review of Synchronization in Mechanical Systems

Sen

Cajún

2019

Nonlinear Structural Dynamics and Damping

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Modeling Fireflies Synchronization

Ramírez-Ávila

Kurths

Depickère

et al. 2018

Nonlinear Systems and Complexity

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Albeit synchronous behavior of some fireflies species is one of the paradigmatic examples of synchronization, there are not many efforts to model in a realistic way this astounding phenomenon. One of the most important features of fireflies synchronization is the cooperative behavior of many fireflies giving rise to the emergency of synchronization without any leader, a fact that took a long time to be recognized. In this chapter, we review the main attempts to build models allowing the explanation of how and why fireflies synchronize. The starting point is qualitative models based on simple observations. The latter served to formulate original mathematical models enabling not only to explain fireflies synchronization but also some other collective phenomena. Integrate-and-fire oscillators (IFOs) constitute an emblematic model to describe the fireflies' synchronous behavior, and they have also inspired ones to build electronic circuits with similar features and adapted to fireflies in the sense that they communicate with each other by means of light-pulses. The above-mentioned electronic circuits received the name of electronic fireflies or more technically, light-controlled oscillators (LCOs). These en-

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An improved model for the classical Huygens׳ experiment on synchronization of pendulum clocks

Cited by 26 publications

References 30 publications

The sympathy of two pendulum clocks: beyond Huygens’ observations

The sympathy of two pendulum clocks: beyond Huygens’ observations

Review of Synchronization in Mechanical Systems

Modeling Fireflies Synchronization

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