Abstract

In a flat case, we consider the task of rotating a solid body by the given angle for the minimum possible time by using a mobile mass (interacting with this body) whose movements are restricted by the interior of the given circle. The corresponding two-point time-optimal control problem for a system with three phase variables (in the presence of a phase constraint) is investigated. The presence of the continuum of, first, curves that meet the necessary conditions of optimality and, second, the sought optimal trajectories are shown. In the case where the mobile mass begins and ends its movement on the edge of the circle, the optimal trajectories and the duration of the movement of this mass are obtained. The study is based on the analysis of a one-dimensional mechanical system whose movements correspond to the solutions of the equations of the three-dimensional problem for the optimal controls.

中文翻译：

---

控制具有运动区域边界上的初始和最终位置的运动质量以实现实体的最快旋转

摘要

在平坦的情况下，我们考虑使用移动质量（与该物体相互作用）将固体旋转给定角度尽可能短的时间的任务，该物体的运动受给定圆的内部限制。研究了具有三相变量（存在相位约束）的系统的相应两点时间最优控制问题。首先显示了满足最优性必要条件的曲线的连续体，其次显示了所寻求的最佳轨迹。在移动质量在圆的边缘开始和结束其运动的情况下，获得该质量的最佳轨迹和运动持续时间。