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A Symmetric Spatial Periodic Orbit in the 2n-Body Problem

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Abstract

For each given \(n \ge 2\), we study the variational existence of a new spatial periodic orbit in the 2n-body problem. Besides excluding possible collision singularities, the main challenges left are to show that the orbit is not a relative equilibrium and it is spatial. By introducing a new estimate in the collinear central configuration, we can prove that it is not a relative equilibrium in the 2n-body problem. Furthermore, with the help of numerical calculation, the orbit is spatial in the equal-mass four-body problem.

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Authors and Affiliations

  1. Department of Mathematics, Wuhan University of Technology, Wuhan, 430070, People’s Republic of China

    Wentian Kuang

  2. Department of Mathematics, Southern University of Science and Technology, Shenzhen, 518055, People’s Republic of China

    Wentian Kuang

  3. Department of Mathematics, Brigham Young University, Provo, UT, 84602, USA

    Tiancheng Ouyang

  4. School of Mathematical Sciences, Beihang University, Beijing, 100191, People’s Republic of China

    Duokui Yan

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  1. Wentian Kuang
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  2. Tiancheng Ouyang
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  3. Duokui Yan
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Correspondence to Duokui Yan.

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The research of Wentian Kuang is supported by NSFC (No. 11901279) and China Postdoctoral Science Foundation (No. 2019M660970). The research of Duokui Yan is supported by NSFC (No. 11871086)

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Kuang, W., Ouyang, T. & Yan, D. A Symmetric Spatial Periodic Orbit in the 2n-Body Problem. J Dyn Diff Equat 33, 1605–1614 (2021). https://doi.org/10.1007/s10884-020-09869-w

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  • DOI: https://doi.org/10.1007/s10884-020-09869-w

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