Research on a special pendulum

Abstract

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.

Keywords

• theoretical mechanics
• circular motion
• Lagrange equations
• four-order Runge-Kutta method