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惠更斯启发的多摆装置:实验与稳定性分析。

Huygens' inspired multi-pendulum setups: Experiments and stability analysis.

作者信息

Hoogeboom F N, Pogromsky A Y, Nijmeijer H

机构信息

Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands.

出版信息

Chaos. 2016 Nov;26(11):116304. doi: 10.1063/1.4965031.

Abstract

This paper examines synchronization of a set of metronomes placed on a lightweight foam platform. Two configurations of the set of metronomes are considered: a row setup containing one-dimensional coupling and a cross setup containing two-dimensional coupling. Depending on the configuration and coupling between the metronomes, i.e., the platform parameters, in- and/or anti-phase synchronized behavior is observed in the experiments. To explain this behavior, mathematical models of a metronome and experimental setups have been derived and used in a local stability analysis. It is numerically and experimentally demonstrated that varying the coupling parameters for both configurations has a significant influence on the stability of the synchronized solutions.

摘要

本文研究了放置在轻质泡沫平台上的一组节拍器的同步情况。考虑了该组节拍器的两种配置:一种是包含一维耦合的行式设置,另一种是包含二维耦合的交叉设置。根据节拍器之间的配置和耦合情况,即平台参数,在实验中观察到了同相和/或反相同步行为。为了解释这种行为,推导了节拍器和实验装置的数学模型,并将其用于局部稳定性分析。数值和实验结果表明,改变两种配置的耦合参数对同步解的稳定性有显著影响。

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