【摘要】 理论分析了循环摆系统的动力学过程，从Euler缰绳方程出发推导出微分方程组，探讨不同运动情境间的方程衔接条件.利用Mathematica对运动方程做数值计算，采用控制变量实验验证理论分析.通过展示4种运动模式的相图，讨论了相图中各参量变化的物理图像.在主要参量的影响下，得到绳绕转圈数、重物下落高度以及摆动持续时间的相图.更多还原

【Abstract】 Theoretical analysis of the dynamics equations of the cycloidal pendulum was presented, and differential equation sets from Euler’s rope equation were derived. Continuity conditions between different motion scenarios were explored, and numerical calculations were performed using Mathematica and validated through controlled variable experiments. The phase diagrams of four distinct motion modes were displayed, and the physical illustration behind parameter variation in the phase diagrams were deeply discussed. Finally, phase diagrams illustrating the influences of parameters on the number of rope revolutions, the height of the weight fall, and the duration of swinging were plotted.更多还原