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IssuesArchive of Issues2011-3pp.335-347

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N.I. Amel'kin, "On Steady Motions of a Rigid Body Bearing Three-Degree-of-Freedom Control Momentum Gyroscopes and Their Stability," Mech. Solids. 46 (3), 335-347 (2011)
Year 2011 Volume 46 Number 3 Pages 335-347
DOI 10.3103/S0025654411030010
Title On Steady Motions of a Rigid Body Bearing Three-Degree-of-Freedom Control Momentum Gyroscopes and Their Stability
Author(s) N.I. Amel'kin (Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141700 Russia, namelkin@mail.ru)
Abstract Equations of motion are obtained for a rigid body bearing N three-degree-of-freedom control momentum gyroscopes in gimbals and the entire set of steady motions in a homogeneous external field is determined. The steady motion dependence on the magnitude of the system angular momentum is studied and a detailed analysis of the secular stability is performed.

In the case of dissipative forces acting in the gyroscope gimbal axes, the Barbashin-Krasovskii theorem is used to study stability in the sense of Lyapunov. It is shown that, depending on the angular momentum magnitude, either static states of the system or two motions corresponding to rotations of the bearing body about the axis of the greatest moment of inertia are asymptotically stable, while all the other stationary motions are unstable in the sense of Lyapunov.
Keywords rigid-body, control momentum gyroscope, steady motions, secular stability, stability in the sense of Lyapunov
References
1.  N. I. Amel'kin, "On the Motions of a Rigid Body Containing Two-Degree-of-Freedom Control Moment Gyros with Dissipation in Gimbal Axes," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 19-30 (2006) [Mech. Solids (Engl. Transl.) 41 (4), 12-20 (2006)].
2.  N. I. Amel'kin, "Stability Analysis of Steady Rotations of a Rigid Body Bearing Two-Degree-of-Freedom Control Moment Gyros with Dissipation in Gimbal Suspension Axes," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 26-40 (2007) [Mech. Solids (Engl. Transl.) 42 (4), 517-529 (2007)].
3.  N. I. Amel'kin, "On Limit Motions of a System of Control Moment Gyros with Intrinsic Dissipation in a Homogeneous Gravitational Field," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 23-32 (2008) [Mech. Solids (Engl. Transl.) 43 (3), 333-341 (2008)].
4.  V. V. Rumyantsev and A. S. Oziraner, Stability and Stabilization of Motion in Part of Variables (Nauka, Moscow, 1987) [in Russian].
5.  A. V. Karapetyan, Stability of Stationary Motions (Editorial URRS, Moscow, 1998) [in Russian].
6.  N. Rouché, P. Habets, and M. Lalou, Stability Theory by Liapunov's Direct Method (Springer, Berlin, 1977; Mir, Moscow, 1980).
Received 03 March 2010
Link to Fulltext http://www.springerlink.com/content/72w2737354706165/
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