Programed motion of the magnetized spacecraft

  • К. С. Жилисбаева al-Farabi Kazakh National University, Almaty, Republic of Kazakhstan
  • А. Д. Саспаева Joint stock company Joint-Stock Company “National Center of Space Research and Technology”, Almaty, Republic of Kazakhstan


This paper focuses on the problem of creation of control of the rotational motion of the magnetized dynamically symmetric Earth’s satellite in a polar circular orbit plane in the geomagnetic field. It is assumed that the permanent magnetic moment of the satellite is directed along the axis of its dynamic symmetry. The rotational motion of the satellite is caused by interaction of the magnetic moment of the satellite and the Earth’s magnetic field, which is modeled by the direct dipole. Influence of gravitational moment is not considered. The objective of the control system is to implement the required programed motion. The satellite’s rotation around its own axis is selected as the programed motion (in this case the angle deviation of the axis should be constant). Equations of programed motion of the magnetized satellite in the semi-combined coordinate system are derived. The control moments that ensure the specified programed motion are obtained. The solutions of the motion equations of the control system are found by Runge-Kutta method using the mathematical package Maple. According to the results the graphs of change of the kinematic parameters of the motion are obtained with and without control moments which demonstrate uncontrolled motion of the satellite. It is shown that the programed motion can be implemented by selection of the values of the deviation angle and the angular velocity, even when there is an asymptotic instability of Lyapunov’s programmed motion.


[1] M.J.Sidi. Spacecraft dynamics and control. Cambridge: Univercity Press, 2002. - 409p.
[2] Ivanov D.S., Ovchinnikov M.Y.,Tkachev S.S. С.С. Upravlenie orientasiei tverdogo tela, podveshannogo na strune s ispolsovaniem ventiliatornych dvigatelei //Isvestia RAN. Theory i systemy upravlenia. 2011. – No1. С.127-139 (in Russian)
[3] Hentov A.A. Passivnaya stabilisasiya iskusstvennych sputnikov po magnitnomu polu Zemli // Kosmisheskie issledovannie. - 1967. - Tom. 5, No 4. - S. 540-553.(in Russian)
[4] Appel P. Teoretisheskaya mechanika. - М.: Fizmatkis, 1960. - 487 s.(in Russian)
[5] Mukhametzyanov I.A., Mucharlyamov R.G. Uravnenie programmnych dvijeni. М.: Izd. RUDN, 1986 (in Russian)
[6] Bezglasnyi S.P. Stabilisathsya i upravleniya dvijeniem dynamisheskich system . Electronnoe ushebnoe posobie. - Samara, 2010. - 102 s.(in Russian)
[7] Zhilisbayeva K.S,Tureeva Zh.U. O beznutatsionnom dvijenii namagnishennogo dynamisheski simmetrishnogo sputnika // Vestnik KazGU, ser. matem., mechanika, informatika. - 2005. - No3(46), - С. 85-90.
[8] Zhilisbayeva K.S. O kolebanyach namagnishennogo sputnika v okrestnosti statsionarnogo dvijenia . // Sb. Methody experimentalnoi phyzyki. - 2010. - S. 49-52.(in Russian)
[9] Zhilisbayeva K.S., Ismailova A. Passive Magnetic Stabilization of the Rotational Motion of the Satellite in its Inclined Orbit // Applied Mathematical Sciences. - 2015. - Vol. 9, no. 16. - Р. 791-802.
[10] Saspayeva A.D Postoenie uravnenya dvijenia iskustvennogo sputnika Zemli v gravitatsionnych polyach Zemli i Luny // Mezhdunarodaya konferensia "Actualnye problemy matematiki i matematisheskogo modelirovanya". -Аlmaty, Kazakhstan. - 2015. - S. 352-353. (in Russian)
How to Cite
ЖИЛИСБАЕВА, К. С.; САСПАЕВА, А. Д.. Programed motion of the magnetized spacecraft. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 89, n. 2, p. 87-93, apr. 2018. ISSN 1563-0277. Available at: <>. Date accessed: 19 oct. 2018.