Abstract One example of stabilizing a statically unstable system is the dynamic stabilization of the pendulum by means of oscillations of its suspension point. The pendulum whose suspension point oscillates in the vertical direction which stabilizes it in the inverted position is the so-called Kapitza pendulum. It turns out that it is possible to stabilize the pendulum in other positions by choosing the right direction of oscillations of the pendulum’s suspension point. In addition, if the direction of oscillations of the pendulum suspension point can change over time, some interesting control problems may arise, such as transition of the pendulum from point to point or active damping control. This paper presents the experimental results that confirm the occurrence of the above-mentioned processes in practice. The work also describes the analytical approximation of the pendulum motion. Moreover, it turns out that the results obtained with this approximation largely agree in the experiment, which was also presented in this work.

中文翻译：

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钟摆在任何所需位置的动态稳定和反馈控制

摘要 稳定静态不稳定系统的一个例子是通过其悬挂点的振荡实现摆的动态稳定。其悬点在垂直方向上摆动并使其稳定在倒置位置的摆就是所谓的卡皮察摆。事实证明，通过选择摆锤悬挂点的正确振荡方向，可以将摆锤稳定在其他位置。此外，如果摆锤悬挂点的振荡方向可以随时间变化，则可能会出现一些有趣的控制问题，例如摆锤点到点的过渡或主动阻尼控制。本文提供的实验结果证实了上述过程在实践中的发生。这项工作还描述了钟摆运动的解析近似。此外，事实证明，通过这种近似获得的结果在实验中大体上是一致的，这也在这项工作中提出。