At the end of the flight, the attitude motion of the Photon M-2 satellite (it was in orbit 2005.05.31-2005.06.16) can be described by a generalized conservative system of differential equations. The secular change in the own kinetic moment of this satellite is described by the so-called evolutionary equations of Beletsky, which also form a generalized conservative system. The preprint examines the relationship between these systems. The satellite motion equations are reduced to equations of the 4th order describing the motion of the satellite axis of symmetry. Beletsky's equations are of the second order and describe the secular motion of the ort of the satellite's own kinetic moment. The solutions of these systems of equations corresponding to the real movements of the satellite are, respectively, conditionally periodic and periodic. The solutions of the 4th-order system are dominated by two frequencies – high and low ones. The spectral analysis showed that the low frequency coincides with the frequency of solutions of Beletsky’s equations. And the solutions of these equations coincide with the low-frequency component in the solution of the 4th-order system with respect to the variables that determine the direction of the axis of symmetry of the satellite.

spacecraft, attitude motion, generalized conservative system, conditionally periodic and periodic motion, spectral analysis

Theoretical and applied problems of mechanics

Bulanov Denis Mikhailovich,  ,  orcid.org/0000-0001-6667-5826,  Moscow State University

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