论文标题
Kapitza-Whitney Pendulum的渐近稳定的非坠落解决方案
Asymptotically Stable Non-Falling Solutions of the Kapitza-Whitney Pendulum
论文作者
论文摘要
在存在额外的水平力场的情况下，在存在振动枢轴点的平面反向摆。水平力不假定很小或迅速振荡。我们假设摆的枢轴点在垂直方向上迅速振荡，并且这些振荡的周期与水平力周期相符。该系统可以被视为卡皮扎摆的强烈概括。以前证明，对于任何水平力，始终存在于考虑系统中的非垂直周期性解决方案。特别是，当没有水平力时，该周期性解决方案是垂直向上的位置。在本文中，我们介绍了有关系统中渐近稳定的非垂直周期解决方案的分析和数值结果。
The planar inverted pendulum with a vibrating pivot point in the presence of an additional horizontal force field is studied. The horizontal force is not assumed to be small or rapidly oscillating. We assume that the pivot point of the pendulum rapidly oscillates in the vertical direction and the period of these oscillations is commensurable with the period of horizontal force. This system can be considered as a strong generalization of the Kapitza pendulum. Previously it was shown that for any horizontal force there always exists a non-falling periodic solution in the considered system. In particular, when there is no horizontal force, this periodic solution is the vertical upward position. In the paper we present analytical and numerical results concerning the existence of asymptotically stable non-falling periodic solutions in the system.
