Abstract
We consider the problem of the time-optimal movement of a rigid body moving translationally along a horizontal straight line and carrying n-linear oscillators. The only control force is applied to the platform and is limited in magnitude, there is no friction. The system is transferred from a state of rest to a specified distance with vibration damping. The evolution of optimal control functions depending on the distance of movement is investigated. A general approach to constructing a visual diagram reflecting such evolution is proposed. To do this, a geometric interpretation of the necessary optimality conditions is used as properties of an auxiliary “control” curve in n-dimensional space. Numerical examples of constructing diagrams of optimal control functions for a platform with three oscillators are given.
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