ISSN 1991-2927

## Author: "Sergei Pavlovich Bezglasny"

 S. Bezglasnyi, V. Krasnikov
 Stabilization of Program Motions of a Single-rotor Gyrostat With a Cavity Filled With Viscous Fluid The asymptotically stable program motions problem of a single-rotor 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.
 2016_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling, Architecture of ship's system.

 S. Bezglasnyi, A. Mukhametzyanova
 Gravitational Stabilization and Reorientation of a Dumbbell Satellite in a Circular Orbit Due to the Swing Principle A dumbsell satellite plane motion along the circular orbit is considered in the article. The motion is modeled by a weight rod with two masses fixed on the rod’s ends. A third mass can move along the rod. The control is realized by the law of moving seismic mass along the rod. The new bounded control laws solving the tasks of gravitational stability in relation to the satellite balancing state radial location flat rebellions and the tasks of dyametrical reorientation on orbit are obtained due to the swing principle. The problem is solved on the basis of the second method of the classical instability theory; the corresponding Lyapunov functions are plotted. The theoretical results are illustrated by the graphical representation of the system motion numerical simulation.Dumbbell satellite, seismicmass, gravitational torque, lyapunov function, asymptotic stability.
 2016_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 S. Bezglasnyi, E. Piiakina, A. Talipova
 Limited Control of Dual-mass Pendulum Motion A problem of parametric control of plane motions of a dual-mass pendulum (swing) with the control constraints is considered. The swing model is a weightless rod with two lumped masses one of which is fixed on the rod and the other slides along it. The control is implemented by continuously varying the length from the suspension point to the moving mass depending on the phase state. A law of swings excitation and damping control suggesting the restrictions on the moving mass displacement is proposed. The Lyapunov’s functions proving the asymptotic stability and instability of the lower pendulum position in the respective cases of the pendulum damping and excitation are chosen for the proposed law control. Theoretical results are confirmed by a graphical representation of the numerical results.Dual-mass pendulum, control, lyapunov’s function, asymptotical stability.
 2013_ 4

Sections: Mathematical modeling, calculi of approximation and software systems

Subjects: Mathematical modeling.

 S. Bezglasny, M. Khudiakova
 Gyrostat Orientation With Variable Moment of Inertia The article examines a problem of a single-axis and a triaxial orientations of the gyrostat system with inertia moment of carrier wich depend on time (a variable structure). The orientation is researched relatively Koenig’s coordinate system and a random non-inertial coordinate system. The problem is solved analytically by the active control construction applied to the system of bodies on the principle of feedback. The stabilizing control and conditions providing a possibility of desired orientation are obtained. This orientation has a property of an asymptotic stability. The assigned task was being solved on the basis of the Lyapunov’s functions method and a method of limit equations and systems which enable to use the Lyapunov’s functions which possess constant signs derivatives.Gyrostat, program motion, functions with a constant signs, lyapunov's function, asymptotic stability.
 2013_ 2

Sections: Mathematical modeling, calculi of approximations and software systems

Subjects: Mathematical modeling, Electrical engineering and electronics.

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