A METHOD FOR PREDICTING ENERGY-STABILIZED MOTION OF SPACECRAFT BASED ON DIFFERENTIAL TAYLOR TRANSFORMATIONS

To predict the motion of spacecrafts, a numerical-analytical method for integrating the differential equation of the orbital motion of a spacecraft stabilized by the Baumgart differential method is proposed. The stabilization of the differential equation of motion by the Baumgart method is carried out according to the energy of the spacecraft. Stabilization is carried out to reduce the influence of the Lyapunov instability on the accumulation of numerical errors in the integration of the differential equation, which is effective when conducting a long-term numerical prediction of the motion of spacecraft. Integration of the stabilized equation is based on differential Taylor transformations. Computational schemes with a constant step and an integration order are considered, as well as schemes with adaptation by an integration step and order. For adaptive schemes, the results of forecasting the motion of spacecraft according to the criterion “accuracy-computational complexity» for a given relative error of integration with respect to integration phase variables and spacecraft energy are presented. It is shown that both options require setting various internal adaptation parameters, but they have comparable efficiency. Recommendations are proposed on the use of the developed method for integrating energy-stabilized equations for predicting the motion of spacecraft in the near space in the Greenwich rectangular coordinate system.

Algorithm for Spacecraft Angular and Translational Motion Control with use of Orientation Thrusters

The paper discusses the algorithm of spacecraft orientation and docking thrusters control for simultaneous spatial and angular motion. The solution of control velocity formation problem and the problem of required engines configuration determination along with the optimization of control vector execution accuracy are considered. The formation of control velocity is carried out using a phase plane with switching lines and a zone of inactivity. The calculation of thrusters working duration time is based on the method of least squares with non-negative resulting solution vector and additional boundary conditions. In the paper, the necessary control parameters were chosen to ensure the necessary accuracy of spacecraft stabilization. To demonstrate the developed algorithm, mathematical modelling of various considered spacecraft's orbital flight stages was executed, including damping of initial angular velocities, spatial motion, and stabilization under the influence of continuous perturbations. The simulation took into account the disturbing moments acting on the spacecraft, thrusters mounting errors and the characteristics of the angular velocity meter. The elastic characteristics of the structure were not taken into account. The results of mathematical modelling showed that the proposed algorithm coped well with the task, and was able to ensure the movement of the spacecraft center of masses in a given direction and simultaneous angular stabilization with required accuracy.