Control of a Moving Mass with the Initial and Final Position on the Boundary of the Area of Motion in Order to Achieve the Fastest Rotation of a Solid Body
Tóm tắt
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.
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