摘 要：对耦合双摆模型中的测度同步现象进行了研究。该系统是一个哈密顿系统。主要对悬挂在同一横梁下的两个双摆的一个非耗散耦合系统进行分析。通过系统哈密顿量得到系统的运动方程，改变系统耦合强度 R（横梁质量与摆上小球质量之比），计算摆角随时间演化图，相空间轨迹图，摆的平均能量图来研究本物理系统到达测度同步现象。当耦合参数达到并且小于临界耦合参数时，从中可以观察到耦合双复摆系统达到了测度同步的状态。该研究完善对于测度同步现象的认知。
关键词：测度同步；哈密顿系统；非耗散系统
DOI:10.19850/j.cnki.2096-4706.2022.02.021
中图分类号：TP391.9 文献标识码：A 文章编号：2096-4706（2022）02-0081-06
Research on Measure Synchronization of Coupled Double Compound Pendulum Model
MENG Yueyan
(Xi’an University of Posts & Telecommunications, Xi’an 710100, China)
Abstract: The phenomenon of measure synchronization in the coupled double pendulum model is studied. The system is a Hamiltonian system. Mainly analyzes a non-dissipative coupling system of two double pendulums suspended under the same beam. The equation of motion of the system is obtained through the system Hamiltonian, the coupling strength R of the system is changed (the ratio of the mass of the beam to the mass of ball in the pendulum), the evolution diagram of the pendulum angle with time, the phase space trajectory diagram, and the average energy diagram of the pendulum are calculated, the synchronization phenomenon of arrival measure of this physical system is studied. When the coupling parameter reaches and is smaller than the critical coupling parameter, it can be observed that the coupled double compound pendulum system reaches the state of measurement synchronization. This study refines our understanding of the phenomenon of measure synchronization.
Keywords: measure synchronization; Hamiltonian system; non-dissipative system
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作者简介：孟乐言（1996.08—），男，汉族，陕西铜川人，硕士研究生在读，研究方向：非线性动力学。