Sergei Pavlovich Bezglasnyi, Candidate of Physics and Mathematics, Associate Professor at the Department of Theoretical Mechanics of Samara State Aerospace University named after Academician S.P. Korolev (National Research University); graduated from the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University; an author of articles in the field of theoretical mechanics, theory of stability and control, dynamics of space systems, [email: bezglasnsp@rambler.ru]S. Bezglasnyi, Viktor Sergeevich Krasnikov, Samara State Aerospace University named after Academician S.P. Korolev (National Research University), Postgraduate Student of the Department of Theoretical Mechanics of Samara State Aerospace University named after Academician S.P. Korolev (National Research University); graduated from the Faculty of Aircrafts of Samara State Aerospace University named after Academician S.P. Korolev; an author of articles in the field of the theoretical mechanics, theory of stability and control. [email: walkthrough@mail.ru]V. Krasnikov


Stabilization of Program Motions of a Singlerotor Gyrostat With a Cavity Filled With Viscous Fluid
The asymptotically stable program motions problem of a singlerotor gyrostat with a spherical cavity entirely filled with viscous fluid is studied. The gyrostat is modeled by a system of two connected solid bodies with common axis of rotation. The first body is a carrier that has a cavity filled with highly viscous fluid. The second body is a dynamically symmetric rotor. In the paper, the gyrostat motion equations are constructed in the Lagrange equations form of the second kind. In the equations, the influence of fluid on the motion of the gyrostat is described using the kinematic characteristics of the gyrostat. The program motions realization problem is solved by the active program and stabilizing controls attached to the gyrostat. The 1 Авторы выражают искреннюю благодарность Андрееву А.С. и Перегудовой О.А. за внимание к работе и ряд ценных замечаний.active stabilizing controls are constructed by the principle of feedback. The task is solved on the basis of a direct method of Lyapunov’s functions of stability theory and a method of the limit functions and the limit systems. The results of this paper can be used for designing control systems for objects with cavities filled with fluids. Gyrostat, viscous fluid, program motion, lyapunov’s function, asymptotic stability.

