Abstract

A simple pendulum is considered as a swing model. The distance between the suspension point of the swing and the center of mass of the person standing on it acts as a limited control action, and the swing with a person on it is a system with one degree of freedom. In the form of feedback, an optimal control is constructed, under which the most rapid increase in the oscillation amplitude occurs. If the coefficient of viscous friction at the suspension point of the swing is large enough, then under this control the swing asymptotically enters the steady-state oscillation mode with a constant amplitude. If the coefficient of friction is rather small, then the oscillations of the swing turn into rotation around the suspension point. A more realistic swing model is also considered with two degrees of freedom. In this model, the control is a force that moves the center of mass of a person along the swing.

中文翻译：

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论人站在秋千上的最佳摆动

摘要

单摆被认为是摆动模型。秋千的悬挂点和站在上面的人的质心之间的距离作为一个有限的控制动作，有人在上面的秋千是一个具有一个自由度的系统。以反馈的形式，构建了一个最优控制，在该控制下，振荡幅度出现最快的增加。如果秋千悬挂点处的粘性摩擦系数足够大，则在这种控制下秋千渐进地进入恒振幅稳态振荡模式。如果摩擦系数相当小，那么秋千的摆动就会变成围绕悬挂点的旋转。还考虑了具有两个自由度的更逼真的挥杆模型。在这个模型中，