Controlled Synchronization of Two 1-Dof Coupled Oscillators

Kumon, Makoto; Washizaki, Ryota; Sato, Junichi; Kohzawa, Ryuichi; Mizumoto, Ikuro; Iwai, Zenta

doi:10.3182/20020721-6-es-1901.01486

Cited by 39 publications

(29 citation statements)

References 6 publications

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“…Recently, this idea has been validated by a few groups of researchers who tested Huygens' idea [11,90,55,96,39,62,43,87,102,[31][32][33][34][35]. These studies do not give the definite answer to the question: what Huygens was able to observe.…”

Section: Introductionmentioning

confidence: 99%

“…(41,42) and (59) Eqs. (61,62) give relation between the pendula's amplitudes Φ 1 and Φ 2 and the phase angle β 2 . Note, that eq.…”

Section: (I)mentioning

confidence: 99%

“…This theory explicitly includes the essential nonlinear elements of Huygens' system, i.e., the escapement mechanisms but also includes many simplifications. A device mimicking Huygens' clock experiment, the so-called "coupled pendula of the Kumamoto University" [62], consists of two pendula which suspension rods are connected by a weak spring, and one of the pendula is excited by an external rotor. The numerical results of Fradkov & Andrievsky [43] show simultaneous approximate in-phase and antiphase synchronization.…”

Section: Introductionmentioning

confidence: 99%

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Synchronization of clocks

et al. 2012

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Abstract:In this report we recall the famous Huygens' experiment which gave the first evidence of the synchronization phenomenon. We consider the synchronization of two clocks which are accurate (show the same time) but have pendulawith different masses. It has been shown that such clocks hanging on the same beam can show the almost complete (in-phase) and almost antiphase synchronizations. By almost complete and almost antiphase synchronization we defined the periodic motion of the pendula in which the phase shift between the displacements of the pendula is respectively close (but not equal) to 0 or π.We give evidence that almost antiphase synchronization was the phenomenon observed by Huygens in XVII century. We support our numerical studies by considering the energy balance in the system and showing how the energy is transferred between the pendula via oscillating beam allowing the pendula's synchronization. Additionally we discuss the synchronization of a number of different pendulum clocks hanging from a horizontal beam which can roll on the parallel surface. It has been shown that after a transient, different types of synchronization between pendula can be observed;(i) the complete synchronization in which all pendula behave identically, (ii) pendula create three or five clusters of synchronized pendula. We derive the equations for the estimation of the phase differences between phase synchronized clusters. The evidence, why other configurations with a different number of clusters are not observed, is given.

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Section: Introductionmentioning

confidence: 99%

“…(41,42) and (59) Eqs. (61,62) give relation between the pendula's amplitudes Φ 1 and Φ 2 and the phase angle β 2 . Note, that eq.…”

Section: (I)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Synchronization of clocks

et al. 2012

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“…Kumon and his group [7] have studied a similar system consisting of two pendulums, one of them having an excitation mechanism, and the two pendulums being coupled by a weak spring. Fradkov and Andrievsky [8] developed a model for such a system, and obtained from numerical solutions that both in-and anti-phase synchronizations are possible, depending on the initial conditions.…”

Section: Introductionmentioning

confidence: 99%

The rhythm of coupled metronomes

et al. 2013

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Spontaneous synchronization of an ensemble of metronomes placed on a freely rotating platform is studied experimentally and by computer simulations. A striking in-phase synchronization is observed when the metronomes' beat frequencies are fixed above a critical limit. Increasing the number of metronomes placed on the disk leads to an observable decrease in the level of the emerging synchronization. A realistic model with experimentally determined parameters is considered in order to understand the observed results. The conditions favoring the emergence of synchronization are investigated. It is shown that the experimentally observed trends can be reproduced by assuming a finite spread in the metronomes' natural frequencies. In the limit of large numbers of metronomes, we show that synchronization emerges only above a critical beat frequency value.

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“…Two pendulums coupled with a weak spring were proposed by Blekhman (1988). Kumon et al (2002) showed the synchronization phenomenon by designing the controller with applying speed the Gradient Energy method. Fradkov and Andrievsky (2007) focused on the study of phase relations between coupled oscillators.…”

Section: Introductionmentioning

confidence: 99%

Synchronization and stability of an elastically coupled tri-rotor vibration system

Hou

Fang

et al. 2017

jtam

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A new mechanism, an elastically coupled tri-rotor system, is proposed to implement synchronization. It is composed of a rigid body, three induction motors, coupling unit and springs. According to the Lagrange equation, the model of the system is established. The average method of small parameters is applied to study the synchronization characteristics of the system, therefore, the balance equation and stability criterion of the system can be obtained. Obviously, many parameters affect the synchronous state of the rotors, especially the spring stiffness, the stiffness of the coupling unit and the installation location of the system. Finally, computer simulations are used to verify the correctness of theoretical analysis.

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Controlled Synchronization of Two 1-Dof Coupled Oscillators

Cited by 39 publications

References 6 publications

Synchronization of clocks

Synchronization of clocks

The rhythm of coupled metronomes

Synchronization and stability of an elastically coupled tri-rotor vibration system

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