We describe the method of representation the aerodynamic torque in problems of mathematical modeling uncontrolled attitude motion of spacecraft Progress. The components of the torque are calculated in the nodes of the grid on the two-dimensional sphere. The calculations were based on the detailed geometric model of the spacecraft external surface. The found arrays of torque data were approximated by the segments of the Fourier series by spherical functions up to the order (8,8) inclusive. These approximations are used in the equations of attitude motion of the spacecraft. We describe the use of such equations in reconstruction of the motion of spacecraft Progress MS-07, MS-08 in the gravitational orientation mode by measurements of their angular rates and in the prognosis of electric charge from the solar arrays of the spacecraft in the mode of its single-axis solar orientation.

geometric model of a spacecraft, calculation of the aerodynamic torque, uncontrolled attitude motion, reconstruction of attitude motion by measurement data, prognosis of charge from the solar arrays of the spacecraft

Mathematical modelling in actual problems of science and technics

Belyaev Mikhail Yuryevich,  ,  Rocket and Space Corporation Energia

Matveeva Tatiana Vladimirovna,  ,  Rocket and Space Corporation Energia

Sazonov Vasilii Victorovich,  ,  orcid.org/0000-0002-6168-7438,  Lomonosov Moscow State University

Sazonov Victor Vasil’yevich,  ,  orcid.org/0000-0003-0032-2483,  KIAM RAS