Abstract
The problem of finding the initial conditions in the boundary-value problem for the system of flexural-torsional vibrations of a bar with additional conditions on the straight line is reduced to an optimal control problem and studied by the methods of optimal control theory. The gradient of the functional is calculated and using the gradient expression a necessary and sufficient optimality condition are proved.
Highlights
It is known that some problems of mathematical physics, mechanics, are described by fourth order partial equations
It is imperative optimal control problems in processes described by these equations
The control connected with flexural-torsional vibrations of a bar has a great signifficance in dynamics of aircraft constructions
Summary
It is known that some problems of mathematical physics, mechanics, are described by fourth order partial equations. A tuning fork, a bar vibrations equation, a rotary shaft, oscillating motions equation and plate vibrations equation are among these equations give some references. It is imperative optimal control problems in processes described by these equations. The control connected with flexural-torsional vibrations of a bar has a great signifficance in dynamics of aircraft constructions. The study of bar vibrations problems controls described by differential equations is necessary both from practical and theoretical point of view
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