“旋转单摆”的Jacobi椭圆函数解

A Solution of a Revolving Single Pendulum usIng Jacobi Elliptic Function

对"旋转单摆"的运动进行研究,建立系统的动力学方程,用线性稳定性分析方法讨论平衡点附近邻域的稳定性,给出了系统静态分岔图和运动的相图,利用Jacobi椭圆函数得出不同转速下系统作周期运动的解析解,并绘出图形加以说明。

The model of a revolving single pendulum is researched. By using the method of the linear stability analysis, the stability of the system is discussed in the neighborhood of the equilibrium points and static bifurcation and phase diagram are obtained. Some solutions of the motion of a revolving single pendulum are obtained using Jacobi elliptic function under the conditions of the different angular velocity ω. Finally diagrams are provided to help understand.