Partial stabilization of fixed motions of a satellite with gyrodins

1Gladun, AV, 2Kovalev, AM
1Institute of Informatics and Artificial Intelligence DonNTU, Donetsk, Ukraine
2Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine, Slavyansk, Donetsk region, Ukraine
Kosm. nauka tehnol. 2005, 11 ;(Supplement1):011-017
https://doi.org/10.15407/knit2005.01s.011
Publication Language: Russian
Abstract: 
We consider the problem of stabilization of a rotatory movement of a satellite with one or two gyrodins. Present results touch upon the stability of dynamical systems with respect to part of the variables. The controls are obtained to which the fixed solutions of the system rigid body-gyrodins correspond. The solutions are positions of relative equilibriums and uniform rotations of a satellite. The cases of a controllability of a system are chosen on a linear approximation irf a neighbourhood of the fixed motions derived. In this case we construct the controls to provide stabilization of angular velocity and stabilization of uniform rotation of a satellite.
References: 

1. Gladun A. V. On the Relative Controllability of Dynamical Systems in Linear Approximation. Trudy Inst. of Applied Mathematics and Mechanics, 2, 21-31 (1998) [in Russian].
2. Krasovsky N. N. Theory of Motion Control, 476 p. (Nauka, Moscow, 1968) [in Russian].
3. Pontryagin L. S. Ordinary Differential Equations, 332 p. (Nauka, Moscow, 1974) [in Russian].
4. Smirnov E. Ya., Pavlinov V. Yu., Shcherbakov P. P., Yurkov A. V. Motion control of mechanical systems, 313 p. (Izdatel'stvo Leningradskogo Universiteta, Leningrad, 1985) [in Russian].
5. Kharlamov P. V., Kovalev A. M. Invariant relations method in multibody dynamics. Nonlinear Analysis, Theory, Methods and Applications, 30 (6), 3817-3828 (1997).
https://doi.org//10.1016/S0362-546X(97)00206-X