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Relative equilibria of full dynamics of a rigid body with gravitational orbit-attitude coupling in a uniformly rotating second degree and order gravity field

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Abstract

The motion of a rigid body in a uniformly rotating second degree and order gravity field is a good model for the gravitationally coupled orbit-attitude motion of a spacecraft in the close proximity of an asteroid. The relative equilibria of this full dynamics model are investigated using geometric mechanics from a global point of view. Two types of relative equilibria are found based on the equilibrium conditions: one is the Lagrangian relative equilibria, at which the circular orbit of the rigid body is in the equatorial plane of the central body; the other is the non-Lagrangian relative equilibria, at which the circular orbit is parallel to but not in the equatorial plane of central body. The existences of the Lagrangian and non-Lagrangian relative equilibria are discussed numerically with respect to the parameters of the gravity field and the rigid body. The effect of the gravitational orbit-attitude coupling is especially assessed. The existence region of the Lagrangian relative equilibria is given on the plane of the system parameters. Numerical results suggest that the negative C20 with a small absolute value and a negative C22 with a large absolute value favor the existence of the non-Lagrangian relative equilibria. The effect of the gravitational orbit-attitude coupling of the rigid body on the existence of the non-Lagrangian relative equilibria can be positive or negative, which depends on the harmonics C20 and C22, and the angular velocity of the rotation of the gravity field.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant 11432001.

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Authors and Affiliations

  1. Distributed Space Systems Lab, Faculty of Aerospace Engineering, Technion—Israel Institute of Technology, Haifa, 32000, Israel

    Yue Wang

  2. School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China

    Shijie Xu

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  1. Yue Wang
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  2. Shijie Xu
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Correspondence to Yue Wang.

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Wang, Y., Xu, S. Relative equilibria of full dynamics of a rigid body with gravitational orbit-attitude coupling in a uniformly rotating second degree and order gravity field. Astrophys Space Sci 354, 339–353 (2014). https://doi.org/10.1007/s10509-014-2077-6

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  • DOI: https://doi.org/10.1007/s10509-014-2077-6

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