Abstract

We consider a controlled mechanical system of many bodies, consisting of a load-bearing disk that rotates around its axis fixed in space, and a carried disk attached to it using weightless elastic elements. The presented bodies are in the same plane. The problem of minimizing the amplitude of radial oscillations is studied. To solve this problem over a sufficiently large interval, two numerical methods are used: the method of successive approximations in the control space and Newton’s method. The properties of the phase trajectories of the system are studied depending on the initial states of the disks. Various disk spin-up modes are detected. Using the smoothing procedure for optimal control, a continuous control is constructed that reduces the amplitude of radial oscillations.

中文翻译：

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二质量系统自旋问题中振荡的最优抑制

摘要

我们考虑一个由许多物体组成的受控机械系统，由一个绕其固定在空间中的轴旋转的承载盘和一个使用失重弹性元件连接到其上的承载盘组成。所呈现的物体位于同一平面上。研究了最小化径向振荡幅度的问题。为了在足够大的区间内解决这个问题，使用了两种数值方法：控制空间中的逐次逼近法和牛顿法。根据圆盘的初始状态研究系统相轨迹的特性。检测到各种磁盘旋转模式。使用优化控制的平滑过程，构建连续控制来减小径向振荡的幅度。