一种特殊摆的研究

为了解决交通运输和工业行业中移动重物的起重机动臂和支撑点不稳定的摆动幅度问题，采用一个悬挂点在水平面内做圆周运动的摆球系统模型来模拟这一问题的动力学过程。应用拉格朗日方程推导了摆球运动的微分方程，采用四阶龙格-库塔算法进行了数值求解，得到了给定悬挂点圆周运动半径、频率和摆长的条件下，摆球做稳定圆周运动的摆角，计算了摆球的稳定运动轨迹，并将计算结果与实验进行了对比，理论计算和实验结果精确吻合。研究内容在科研和工程技术领域有着广泛的应用，研究结果对起重机的机械吊臂设计有重要的参考价值。同时，文中所用到的理论建模、计算机编程、数值计算、实验设计等也可以作为一个非常好的教学案例，培养学生应用所学理论解决实际问题的能力。

Research on a special pendulum

In order to solve the problem of unstable swinging amplitudes of the crane''s boom and supporting points for moving heavy objects in the transportation and industrial industries, a pendulum system model with circular motion in the horizontal plane is used to simulate the dynamic process of this problem. The differential equations of the pendulum ball are deduced using the Lagrange equation, and the numerical solution is obtained using the fourth-order Runge-Kutta algorithm. The suspension angles are obtained for the pendulum to make a stable circular motion under the designated conditions of the radius, frequency, and pendulum length of the suspension point. The stable trajectory of the pendulum ball is calculated, and the calculation results are compared with the experimental results. The theoretical calculations and the experimental results are in good agreement. The research content of this paper has a wide range of applications in scientific research and engineering technology. The research results have important reference value for the crane''s mechanical jib design. At the same time, the theoretical modeling, computer programming, numerical calculation, and experimental design used in this paper can also be used as a very good teaching case to cultivate students'' ability to apply the learned theory to solve practical problems.