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Nonlinear Dynamics of a Two-Chain, Three-Body Formation System

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Abstract

Multibody formation constitutes a new architecture wherein the functional capabilities of a monolithic satellite are distributed, and some planned missions have begun to take advantage of the benefits offered by the use of satellite formations. The nonlinear dynamics of a two-chain, three-body formation system located on a circular orbit on the Earth is presented in this paper with the assist of nonlinear theory in astrodynamics. Different from only five libration points solved from the circular restricted three-body system, there exist sixteen equilibria for the chain system yielded by its geometry of the pseudo-potential function. For some hyperbolic equilibria, an iterative procedure is developed to correct numerically periodic orbits near them, which are referred as Lyapunov orbits in this paper. The invariant manifolds originating from those orbits are employed by Poincaré mapping to create the heteroclinic or homoclinic trajectories, and some non-transversal intersections between them are addressed in this paper.

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Acknowledgment

The authors are very grateful to the associate editor and two anonymous reviewers for their helpful comments and suggestions on revising the manuscript. The research is supported by the National Natural Science Foundation of China (11172020), and Talent Foundation supported by the Fundamental Research Funds for the Central Universities. The authors wish to thank Shijie Xu for the many useful discussions.

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Authors and Affiliations

  1. Beihang University, Beijing, 100191, China

    Ming Xu & Yan Wei

  2. China Satellite Co., Ltd., Beijing, 100096, China

    Shengli Liu

Authors
  1. Ming Xu
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  2. Yan Wei
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  3. Shengli Liu
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Correspondence to Ming Xu.

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Xu, M., Wei, Y. & Liu, S. Nonlinear Dynamics of a Two-Chain, Three-Body Formation System. J of Astronaut Sci 59, 609–628 (2012). https://doi.org/10.1007/s40295-014-0014-0

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