Publishing house Radiotekhnika

"Publishing house Radiotekhnika":
scientific and technical literature.
Books and journals of publishing houses: IPRZHR, RS-PRESS, SCIENCE-PRESS

Тел.: +7 (495) 625-9241


Theoretical aspects of mathematical modeling of the large sized spacecraft dynamics


I.I. Dementyev – Quality Engineer, «CB «Arsenal» (SPb). E-mail:

The paper presents new theoretical aspects of the development of mathematical models describing the motion of the spacecrafts (SC) with large-sized composite and metal detachable components: solar panels, reflector withdrawal rods, telescopes with long-focus lenses, etc. The solutions and proposals outlined in the paper are aimed at improving the efficiency of the control of elastic spacecrafts (SC). In particular, the method we propose is based on the combination of the centralized control system (CCS) and local oscillation damping systems (LODS). This method, together with the stated theoretical aspects of mathematical modeling of the dynamics of space vehicles samples, is the basis for the effective management of the spacecraft centre of mass position, of the angular positions of the machines and of the orientation of their detachable components. As a consequence, using LODS in combination with CMS improves the performance of large-sized spacecrafts which experience oscillations of their elastic elements during flight operations. In this paper the mathematical models and the classification of external influences affecting the changes of spacecraft positions in outer space are outlined. They form the foundation for the further development of the systems of equations describing the motion of a spacecraft, followed by the development of the algorithms of their dynamics management. The paper contains a rationale for the choice of the Lagrange equations of the second kind which are the basis for mathematical modelling of spacecraft motion. The results of the paper identify perspective research areas related to the generation of the control actions and the calculation of their quantities for producing high-quality solutions to the target tasks of a spacecraft performed by it in space and from space in minimum time under the combined effect of the disturbing loads with mechanical, thermal and radiative or other background. When designing the sample space vehicles for the development of near-space, for the flight operations to space objects of the solar system, for the procedure of landing on the surface of these objects and for the creation of manned bases on the Moon and on Mars, much attention is paid to the motion control system (MCS). The novel theoretical aspects and the method of large-sized spacecrafts control presented in the paper provide the ability to create a MCS which meets the requirements for spacecraft motion control systems, and the purpose of spacecrafts is to solve the tasks set to the cosmonautics in the XXI century.


  1. Artjukhin JU.P., Kargu L.I., Simaev V.L. Sistemy upravlenija kosmicheskikh apparatov, stabilizirovannykh vrashheniem. M.: Nauka. 1979. 295 s.
  2. Atamasov V.D., Dementev I.I. Metod reshenija zadachi upravlenija orientaciejj sovremennykh kosmicheskikh apparatov // Trudy IVnauchno-tekhnich. konf. molodykh uchenykh i specialistov FGUP «KB «Arsenal». 2013. S. 34−36.
  3. Goldstejjn G. Klassicheskaja mekhanika. M.: Gostekhizdat. 1957. 413 s.
  4. Gorshkov A.G., Starovojjtov EH.I., JArovaja A.V. Mekhanika sloistykh vjazkouprugoplasticheskikh ehlementov konstrukcijj. M.: FIZMATLIT. 2005. 576 s.
  5. Degtjarev G.L., Sirazetdinov T.K. Teoreticheskie osnovy optimalnogo upravlenija uprugimi kosmicheskimi apparatami. M.: Mashinostroenie. 1986. 216 s.
  6. Dementev I.I. Uravnenie dlja rascheta parametrov i opredelenija form kolebatelnykh processov konstruktivnykh ehlementov kosmicheskikh apparatov, geometricheskaja forma kotorykh otvechaet forme prjamougolnykh plastin // Trudy IIInauchno-tekhnich. konf. molodykh uchenykh i specialistov OAO «KBSM». 2013. S. 78−81.
  7. Ivanov N.M., Lysenko L.N. Ballistika i navigacija kosmicheskikh apparatov. M.: Drofa. 2004. 544 s.
  8. Kovalenko A.D. Vvedenie v termouprugost. Kiev: Naukova Dumka. 1965. 204 s.
  9. Popov V.I. Sistemy orientacii i stabilizacii kosmicheskikh apparatov. M.: Mashinostroenie. 1986. 184 s.
  10. Sapego M.K., Testoedov N.A., Atamasov V.D., Babuk V.A., Belov V.P., Burylov L.S., Romanov A.V. Teorija proektirovanija slozhnykh tekhnicheskikh sistem kosmicheskogo bazirovanija. SPb.: NPO «Professional». 2012. 560 s.


© Издательство «РАДИОТЕХНИКА», 2004-2017            Тел.: (495) 625-9241                   Designed by [SWAP]Studio