Abstract
Formulations are presented of a number of optimization problems of the theory of longitudinal vibrations of rectilinear rods of constant cross section. Results of their solution, obtained by using the necessary condition of stationarity of the functional constructed in [1] and the necessary Weierstrass condition of a strong minimum of the functional established below, are described. Special attention is paid to optimization problems in which there are discontinuities in the Lagrange multipliers on the characteristic lines on equations of hyperbolic type by which longitudinal vibrations are described.
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