Alexey Alexandrovich Tikhonov

A satellite with an electrodynamic attitude control system is considered. The problem of stabilization of the programmed motion in which the axis of the satellite’s dynamic symmetry is stabilized along the local vertical, and the satellite rotates around this axis is solved. On the basis of the Lyapunov function method, sufficient conditions for asymptotic stability of the stabilized programmed motion in the presence of the perturbing gravitational torque are obtained. These conditions allow a rational choice of the coefficients of parametric control depending on the parameters of the satellite and its orbit.

The study of the motion of spacecraft with a solar sail is related to the projects that have been actively developed recently for flights to the borders of the solar system and their use for maneuvering in the vicinity of libration points. When planning and im- plementing these projects, it is necessary to take into account the change in the properties of the sail surface during flight. In particular, as shown earlier, the electric charge induced on the surface of the sail leads to deformation of its surface. The present work is devoted to the study of the effect of deformation of the sail surface on its dynamics. For certainty, the movement along the Tsander trajectory of the flight from Earth’s orbit to Mars’ orbit is chosen. It is shown that even for small relative deformations of the sail surface, the trajectory deviation from the calculated one can exceed the radius of Mars. The results obtained make it possible to determine the optimal parameters of the transverse stiffeners of the solar sail for the realization of permissible relative deformations in the Earth’s orbit.

An artificial Earth satellite (AES) with a double electric layer in a circular Keplerian orbit is considered. The interaction of the AES with Earth’s magnetic field is analyzed. The moment of Lorentz forces acting on the AES is calculated. The calculated moment is compared with the corresponding moment acting on an AES with a single electric layer. Based on this comparison, a conclusion is made about the advantages of using a double electric layer over a single one in the electrodynamic attitude control system of AESs.

A satellite with a system of three concentric shields for electrostatic protection against cosmic radiation is considered. The interaction of an electric charge with the Earth’s magnetic field leads to the emergence of a Lorentz force torque acting on the rotational motion of the satellite relative to the center of mass. The Lorentz force torque is calculated taking into account the complex shape of the electrostatic protection screens and the geomagnetic field gradient in the volume of the screen. The geomagnetic field is modeled by a direct magnetic dipole. Differential equations of the satellite’s motion about the center of mass are written out and the first integrals of these equations are constructed. Steady-state motions of the satellite are found and sufficient conditions for their stability are obtained.

A satellite moving in the gravitational and magnetic fields of Earth is considered. The possibility of designing an integrated attitude control system that combined magnetic and Lorentz control systems is being studied. The expediency of such an association is shown. The effectiveness of the constructed electrodynamic attitude control system for stabilization of different programmed motions of the satellite is confirmed. An algorithm for constructing control torques is shown for each of the considered problems. The results of the computer simulation are presented. The three-axial stabilization of a satellite in the orbital frame requires restoring and dissipative components of control torques. In general case for monoaxial stabilization of a satellite in the orbital frame the control parameters can be constructed as a sum of restoring, dissipative, and compensating components. Stabilization in two-axis programmed rotation requires one to compensate for the specified gyroscopic torque, and an additional term can be introduced into one of the control vectors. For the problem of three-axial stabilization in the Koenig frame, the gravity gradient torque can be compensated by means of the Lorentz torque. Finally, the three-axial stabilization of a satellite in the magnetoLorentz frame also involves the creation of a compensating torque.

In this paper, the orbital motion of an electrically charged spacecraft in the gravitational and magnetic fields of the Earth is investigated. A straight dipole is considered as a model of the geomagnetic field. The nonlinear autonomous system of differential equations of motion of the spacecraft center of mass in the Cartesian and spherical coordinate systems is derived. The analytical study of the influence of the Lorentz force on the orbital motion of a charged spacecraft is carried out. The approximate solution of the differential system if found, The results of numerical simulation of the spacecraft orbital motion based on the derived system of differential equations are presented. The analytical and numerical solutions are compared. The problem of stabilizing the spacecraft’s center of mass in the orbital plane is considered. Feedback control methods based on the use of jet engines are proposed. The technical justification of the proposed control methods is carried out. As a result, stabilization of an electrically charged spacecraft in a small neighborhood of the plane of the initial orbit is achieved.