This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation. The pendulum has two degrees of freedom: a rotational angle defined in the horizontal plane and an inclination angle defined by the pendulum with respect to the vertical z axis. The results of numerical simulations are illustrated with the mathematical model in the form of multi-colored maps of the largest Lyapunov exponent. The graphical images of geometrical structures of the attractors placed on Poincaré cross sections are shown against the maps of the resolution density of the trajectory points passing through a control plane. Drawn for a steady-state, the graphical images of the trajectory of a tip mass are shown in a three-dimensional space. The obtained trajectories of the moving tip mass are referred to a constructed bifurcation diagram.

本文研究了具有水平李萨如激发的球形摆的振动。摆具有两个自由度：在水平面中定义的旋转角度和由摆相对于垂直z定义的倾斜角度轴。数学模型以最大Lyapunov指数的彩色映射的形式说明了数值模拟的结果。相对于通过控制平面的轨迹点的分辨率密度图，显示了放置在庞加莱横截面上的吸引子几何结构的图形图像。绘制为稳态时，尖端质量轨迹的图形图像显示在三维空间中。所获得的运动尖端质量的轨迹称为构造的分叉图。