Control of damped vibrations of a rod by means of a concentrated force or moment loading

The optimal local loading regimes of a vibrating rod (one endpoint of the rod is fixed, while the second is stress-free), which ensure the damping of certain modes of elastic vibration over a minimal time interval, for a minimal norm of the control function and also under the simultaneous minimization of the time and the norm of the load function are given.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 71–75, 1987.