A. A. Tikhonov

Electrodynamic stabilization of earth-orbiting satellites in equatorial orbits

A satellite with electrodynamic stabilization system is considered. Based on the method of Lyapunov functions, sufficient conditions of the asymptotic stability of direct equilibrium position of this satellite in the orbital coordinate system under perturbing action of a gravitational moment are obtained. These conditions allow one to ensure a rational choice of parametric control coefficients depending on parameters of the satellite and its orbit.

Monoaxial electrodynamic stabilization of earth satellite in the orbital coordinate system

Consideration was given to the Earth satellite moving along a circular arbitrarily inclined orbit. The possibility of using the electrodynamic control system for monoaxial stabilization of the satellite in an indirect position in the orbital coordinate system was analyzed. An extension of the concept of electrodynamic control including a solution of the problem of electrodynamic compensation of the perturbing moment was suggested. Conditions were established for solution of the formulated problem with the use of the electromagnetic control in the presence of perturbing action of the gravitational moment. Sufficient conditions for asymptotic stability of the satellite equilibrium were established for the nonlinear statement of problem.

Electrodynamic control for spacecraft attitude stability in the geomagnetic field

The electrodynamic method of spacecraft attitude control is studied in an octupole geomagnetic field approximation. An analytical derivation is given for refined laws of control over spacecraft electrodynamic parameters, which ensure the required spacecraft guidance. Spacecraft equilibrium position is proved to be stable under continually acting disturbances. The effectiveness and practical feasibility of the proposed spacecraft attitude control method is confirmed by numerical analysis.

Electrodynamic stabilization of artificial earth satellites in the König coordinate system

An artificial Earth satellite in a circular equatorial orbit is considered. We analyze the possibility of a satellite’s three-axis stabilization in the König coordinate system using an electrodynamic control system exploiting Lorentz and magnetic control torques. Conditions allowing the electromagnetic control to solve the problem for a gravitational torque disturbance are obtained. In the nonlinear formulation, sufficient conditions for the asymptotic stability of the satellite equilibrium position are obtained.

Attitude stabilization of a rigid body in conditions of decreasing dissipation

The paper presents the problem of triaxial stabilization of the angular position of a rigid body. The possibility of implementing a control system in which dissipative torque tends to zero over time and the restoring torque is the only remaining control torque is considered. The case of vanishing damping considered in this study is known as the most complicated one in the problem of stability analysis of mechanical systems with a nonstationary parameter at the vector of dissipative forces. The lemma of the estimate from below for the norm of the restoring torque in the neighborhood of the stabilized motion of a rigid body and two theorems on asymptotic stability of the stabilized motion of a body are proven. It is shown that the sufficient conditions of asymptotic stability found in the theorems are close to the necessary ones. The results of numerical simulation illustrating the conclusions obtained in this study are presented.

On dynamical equations in s-parameters for rigid body attitude motion

In the paper, the attitude motion of a rigid body in a potential force field is under consideration. The complete set of three modified Rodrigues-Hamilton parameters, also known as s-parameters, and corresponding three generalized momenta is used for rigid body attitude representation. A new form of canonical differential equations for rigid body attitude dynamics is constructed. Built equations are suitable for analytical and numerical studying the problem of rigid body attitude dynamics.

On electrodynamical compensation of a torque disturbing satellite orientation

A satellite with electrodynamic attitude control system is considered. The problem of compensation of an external disturbing torque is solved. The optimization of control process in vicinity of programmed motion is achieved on the basis of control system without involving additional measuring devices.

On symmetrical oscillations of gyrostat in weak elliptic orbit

A gyrostat in weak elliptical Keplerian orbit lying in geomagnetic equatorial plane is considered. The gyrostat is supplied with flywheel and possesses electrostatic charge and intrinsic magnetic moment. The gyrostat attitude motion under the action of Lorentz and magnetic torques is under consideration. It was revealed that the differential system of gyrostat attitude motion is reversible with three stationary sets. The symmetrical periodic motions of oscillatory type are analyzed. A bifurcation in the set of gyrostat symmetrical oscillations and generation of two isolated symmetrical oscillations is discovered in transition from circular orbit to elliptical one.

On a satellite stabilization in the Konig frame

A circular orbiting artificial Earth satellite is considered. The satellite is equipped with an electrodynamic attitude control system exploiting Lorentz and magnetic control torques. The perturbing influence of the gravity-gradient torque is taken into account. The problem of satellite stabilization in the Konig coordinate system with the use of electrodynamic attitude control system is investigated in nonlinear formulation. On the basis of the Lyapunov functions method, sufficient conditions for the asymptotic stability of the programmed satellite equilibrium position in the Konig frame are obtained.

On computer algebra methods and numerical simulation in the problems of charged satellite attitude dynamics

A satellite with parametric attitude control system is considered. The satellite interacts with geophysical fields by gravitational, magnetic and Lorentz torques. The control algorithms for the satellites stabilization are proposed. The correct mathematical model that ensures the prescribed accuracy is constructed with the use of computer algebra methods.