循环摆运动的理论建模与数值模拟

Theoretical Modeling and Numerical Simulation of Circular Pendulum Motion

  • 摘要: 该文深入分析了循环摆重轻物的受力与运动过程,构建描述循环摆整个系统运动的理论模型,得到了轻物和重物运动的微分方程组。基于欧拉算法,利用MATLAB软件对所提出的理论模型进行数值求解,有效模拟出循环摆的运动行为。该文研究了配重比对循环摆运动的影响,结合实验对所建立的理论模型进行了验证。数值模拟和实验结果相吻合,表明所构建理论模型在误差允许范围内的有效性。所做工作可对循环摆的实验设计提供参考,同时也能从理论上预测不同参数变化对循环摆系统运动的影响。

     

    Abstract: In this paper, the force and motion process of the heavy and light object of the circular pendulum are analyzed. Not only the theoretical model describing the motion of entire circular pendulum system is constructed, but also the differential equations of the light object and the heavy object motions are obtained. Based on Euler algorithm, MATLAB software is used to solve the theoretical model, which can effectively simulate the motion behavior of the circular pendulum. In this paper, we have studied the impact of balance weight ratio on the motion of the circular pendulum, and combined the experiment to verify the theoretical model. The numerical simulation and experiment results are in line with each other, indicating that the theoretical model is effective within the allowable error range. These works can provide a reference for experimental design of the circular pendulum, and can also theoretically predict the influence of different parameter changes on the motion of the circular pendulum system.

     

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