A method of forming modes of the controlled motion of the tether systems to solve practical problems in elliptical orbits

Аuthors

Kupreev S. A.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: kupreevsa@mati.ru

Abstract

Orbital tether system (TS) is separately formed area of the promising technologies [1]. However, the consideration of the function of space bundles in the elliptical orbits is not sufficiently covered by specialized literature. In the known works [2-12] the solution of practical problems with the use of the TS is discussed in the terms of functioning bundles in the circular orbits, while a number of problems can be solved only in the elliptical orbits. The solution of problems of the dynamics of functioning of the TS in the elliptical orbits is more complicated than for the circular and requires a special theoretical study. Scientific problem, the solution of which is devoted to the work, is in full qualitative analysis of the topological structures of the dynamic system of the controlled motion of the TS and the formation of suitable modes of their movement during the operation in the elliptical orbits.

An effective method of the formation of modes of the controlled motion of the tether systems to solve practical problems in the elliptical orbits is proposed. The method is based on the mathematical apparatus of the qualitative theory of dynamical systems and the theory of bifurcations [13, 14].

All types of quality structures of a dynamic system of the controlled motion of related objects are set, all bifurcations of the system under study and the bifurcation values of parameters that define the totality of characteristics of the controlled movement in elliptical orbits are identified. It gives you the opportunity to have a clear picture of the characterization of possible trajectories of the controlled motion under all values of the control parameters, under any initial conditions of motion and at any period of time.

As a result of the analysis of all types of the qualitative structures of the phase trajectories, a set of implemented modes of the controlled motion is defined and the regions of initial conditions where they are implemented are set. The modes should correspond to particular steady phase trajectories of the system and the set of orbito-resistant non-singular phase trajectories that fill the fixed region of the phase surface.

Keywords:

tethered system, modes of relative motion, controlled motion

References

1. Danilenko A.V., Elkin K.A., Lyagushina S.Ts. Doklady Vos’mogo mezhdunarodnogo aerokosmicheskogo kongressa IAC’15, Moscow, 2015, pp. 289-294.

2. Alpatov A.P., Beletskii V.V., Dranovskii V.I., Zakrzhevskii A.E., Pirozhenko A.V., Troger G., Khoroshilov V.S. Dinamika kosmicheskikh sistem s trosovymi i sharnirnymi soedineniyami (Dynamics of space systems with cable and pivot connection), Izhevsk, Institut komp’yuternykh issledovanii, 2007, 559 р.

3. Beletskii V.V., Levin E.M. Dinamika kosmicheskikh trosovykh sistem (Dynamics of space tether systems), Moscow, Nauka, 1990, 336 p.

4. 4 Ivanov V.A., Kupreev S.A., Liberzon M.R. Sblizhenie v kosmose s ispol’zovaniem trosovykh sistem (The convergence in space with the using of tethered systems), Мoscow, Khoruzhevskii, 2010, 360 p.

5. Ivanov V.A., Kupreev S.A., Ruchinskii V.S. Kosmicheskie trosovye sistemy osobie (Space tether systems.), Moscow, Al’fa-M, 2014, 208 p.

6. Ivanov V.A., Kupreev S.A., Ruchinskii V.S. Orbital’noe funktsionirovanie svyazannykh kosmicheskikh ob«ektov (Orbital functioning of the connected space objects), Moscow, INFRA-M, 2014, 320 p.

7. Shcherbakov V.I. Mekhanika statsionarnykh dvizhenii gibko svyazannykh KA (Mechanics of steady motions of flexibly connected spacecrafts), St.Petersburg, Voenno-kosmicheskaya akademiya im. A.F. Mozhaiskogo, 2007, 106 p.

8. Kruijff M. Tethers in Space: A propellantless propulsion in-orbit demonstration. Delft University of Technology, The Netherlands, 2011, 432 p.

9. M. L. Cosmo and E. C. Lorenzini, Tethers in Space Handbook, NASA Marshall Space Flight Center, Huntsville, Ala, USA, 3rd edition, 1997, 274 p.

10. V.S. Aslanov, A.S. Ledkov, Dynamics of the Tethered Satellite Systems. Cambridge: Woodhead Publishing Limited, 2012, 331 p.

11. Ledkov A.S., Dyukov D.I., Elektronnyi zhurnal «Trudy MAI», 2012, no 61, available at: http://www.mai.ru/science/trudy/eng/published.php?ID=35644 (accessed 05.09.2015)

12. Naumov O.N. Elektronnyi zhurnal «Trudy MAI», 2011, no 43, available at: http://www.mai.ru/science/trudy/eng/published.php?ID=24767 (accessed 05.09.2015)

13. Andronov A.A., Leontovich E.A., Gordon I.I., Maier A.G. Kachestvennaya teoriya dinamicheskikh sistem vtorogo poryadka (Qualitative theory of dynamic systems of the second order), Moscow, Nauka, 1960, 568 p.

14. Andronov A.A., Leontovich E.A., Gordon I.I., Maier A.G. Teoriya bifurkatsii dinamicheskikh sistem na ploskosti (The theory of bifurcations of dynamic systems on plane), Moscow, Nauka, 1967, 488 p.

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