Updated rotating mass dipole with oblateness of one primary (II): out-of-plane equilibria and their stability
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Out-of-plane equilibrium points of the updated rotating mass dipole are investigated in this paper. The updated dipole system is consistent with a point mass connecting a spheroid with a massless rod in a constant distance. The oblateness of the spheroid allows the existence of out-of-plane equilibrium points. These equilibria are determined numerically based on the three dimensional dynamic equations. The influence of the system parameters on the position of these equilibria associated with the topological structure is analyzed in a parametric way. The stability of these equilibria is explored with linearized dynamic equations. Two particular cases with a prolate or an oblate spheroid of the first primary are presented to examine its influence on the distribution of the out-of-plane equilibrium points around the second primary.
KeywordsUpdated rotating mass dipole Oblateness of primary Out-of-plane Equilibria
This work was supported by the National Basic Research Program of China (973 Program, 2012CB720000) and China Postdoctoral Science Foundation (2014M560076).
- Chermnykh, S.V.: On the stability of libration points in a certain gravitational field. Vestn. Leningr. Univ. 2(8), 73–77 (1987) Google Scholar
- Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press, New York (1967) Google Scholar
- Shang, H.B., Wu, X.Y., Cui, P.Y.: Periodic orbits in the doubly synchronous binary asteroid systems and their applications in space missions. Astrophys. Space Sci. 355, 2154 (2014) Google Scholar
- Zeng, X.Y., Jiang, F.H., Li, J.F., Baoyin, H.X.: Study on the connection between the rotating mass dipole and natural elongated bodies. Astrophys. Space Sci. 355, 2187 (2015a) Google Scholar
- Zeng, X.Y., Baoyin, H.X., Li, J.F.: Updated rotating mass dipole with oblateness of one primary. I. Equilibria in the equator and their stability. Astrophy. Space Sci. (2015b) Google Scholar