Orbital oscillations of an elastic vertically-tethered satellite
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The motion of a satellite in a circular orbit with respect to its center of mass is considered. The satellite bears an elastic tether system unrolled along the local vertical. The load at the end of the tether oscillates harmonically. The satellite motion under the action of the gravitational moment and the moment due to the tether tension force is studied. The bifurcation diagram is constructed and the hetero- and homoclinic separatrix trajectories are determined. Mel'nikov's method is used to study the satellite chaotic behavior near separatrices under the action of the periodic tether tension force. The results of the present paper can be used to analyze tether systems of gravitational stabilization and to study the orbital behavior of a satellite with an unrolled tether system with respect to the satellite center of mass.
Keywordsspace tether system satellite dynamics bifurcation diagram Mel'nikov'smethod chaos
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- 1.V. V. Beletskii and E. M. Levin, Dynamics of Space Tether Systems (Nauka, Moscow, 1990) [in Russian].Google Scholar
- 2.I. M. Sidorov, “On the Use of Tether Systems to Construct a Constantly Operating Transport Channel in Space,” Polet, No. 8, 36–39 (2000).Google Scholar
- 6.V. V. Beletskii, Artificial Satellite Motion about Its Center of Mass (Nauka, Moscow, 1965) [in Russian].Google Scholar
- 9.V. K. Mel'nikov, “On the Stability of the Center for Time Periodic Perturbations,” Trudy Moskov. Mat. Obshch. No. 12, 3–52 (1963) [Trans. Moscow Math. Soc. (Engl. Transl.) No. 12, 1–57 (1963)].Google Scholar
- 10.V. S. Aslanov, “Chaotic Behavior of the Biharmonic Dynamics System,” Int. J. Math. Math. Sci. (IJMMS), 2009, Article ID 319179 (2009).Google Scholar
- 11.J. Guckenheimer and Ph. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, New York, 1997; In-t Komput. Issled., Moscow-Izhevsk, 2002).Google Scholar