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Transfers between libration point orbits of Sun–Earth and Earth–Moon systems by using invariant manifolds

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Abstract

Single-impulse and low-thrust low-energy transfers from a Lyapunov orbit around \(L_2\) point of the Sun–Earth system to the periodic orbits around the equilibrium points \(L_i\; (i=3,4,5)\) of the Earth–Moon system are investigated. In our computation, the series expansions of invariant manifolds are used to generate the departure state, the series expansions of periodic orbits around the triangular libration points, and Lissajous orbits around the collinear libration points are used to generate the target orbits. In order to construct the first guesses for single-impulse and low-thrust low-energy transfers, we establish the corresponding optimization problems under some suitable assumptions and solve them by means of an improved cooperative evolutionary algorithm (ICEA). For computing optimal transfers, the nonlinear programming problems are established by direct description and solved by a local optimization method with the initial-guess transfers computed by ICEA. Numerical results show that the low-thrust transfers outperform the corresponding single-impulse transfers in terms of propellant mass.

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Acknowledgments

The authors are much obliged to the reviewers for their many insightful comments that substantially improved the quality of this paper. This work was carried out with financial support from the National Basic Research Program 973 of China (2013CB834103), the National High Technology Research and Development Program 863 of China (2012AA121602), the National Natural Science Foundation of China (Grant No. 11078001), and the Research and Innovation Project for College Graduates of Jiangsu Province (Grant No. CXZZ13_0042).

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  1. School of Astronomy and Space Science, Nanjing University, Nanjing, 210093, China

    Hanlun Lei & Bo Xu

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  1. Hanlun Lei
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Correspondence to Bo Xu.

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Lei, H., Xu, B. Transfers between libration point orbits of Sun–Earth and Earth–Moon systems by using invariant manifolds. J Eng Math 98, 163–186 (2016). https://doi.org/10.1007/s10665-015-9816-8

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