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Binary-Syzygy sequence of restricted few-body-few-center problem with symmetric primaries

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Abstract

Variational methods have been successfully applied to construct many different classes of periodic solution of N-body problem and N-center problem. However, until now, it is still challenging to apply variational methods to restricted \((N+1)\)-body problem. In this paper, we consider the restricted few-body-few-center problem (an intermediate problem between restricted \((N+1)\)-body problem and N-center problem) with symmetric torque-free primaries, identify its binary-syzygy sequence that can be realized by minimizers of the Lagrangian action functional, and construct its periodic solutions within certain topological classes. At the end, we further reveal similar results for restricted \((N+1)\)-body problem with the general rhomboidal primary system. In order to achieve the above aim, we also demonstrate the asymptotic behavior of the massless particle near two-body collision with a moving primary and establish partial Sundman–Sperling estimates of the massless particle near multi-body collision.

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Acknowledgements

It is a pleasure to thank K.C. Chen for discussion and Xijun Hu for his generous support. This work was supported by National Natural Science Foundation of China under Grant (Nos. 12101363, 12071255, 12171281) and Natural Science Foundation of Shandong Province, China, under Grant (ZR2020QA013).

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  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, China

    Ku-Jung Hsu

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Hsu, KJ. Binary-Syzygy sequence of restricted few-body-few-center problem with symmetric primaries. Celest Mech Dyn Astr 134, 9 (2022). https://doi.org/10.1007/s10569-022-10065-9

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