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<p>In this note, we study existence of infinitely many trajectories <i>bi-normal</i> (i.e. normal at initial and final times) to the <i>xz</i>-plane in the Spatial Circular Restricted Three-Body problem, in the convexity range and near the primaries, under the assumption of the twist condition as defined by Moreno–van-Koert in [<CitationRef CitationID="CR10">10</CitationRef>]. Modulo our assumptions, this is an expected application of the relative Poincaré–Birkhoff theorem for Lagrangians in Liouville domains, as proven by the authors in [<CitationRef CitationID="CR8">8</CitationRef>].</p>

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Bi-normal trajectories in the circular restricted three-body problem

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月26日

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  • Agustin Moreno,
  • Arthur Limoge

摘要

In this note, we study existence of infinitely many trajectories bi-normal (i.e. normal at initial and final times) to the xz-plane in the Spatial Circular Restricted Three-Body problem, in the convexity range and near the primaries, under the assumption of the twist condition as defined by Moreno–van-Koert in [10]. Modulo our assumptions, this is an expected application of the relative Poincaré–Birkhoff theorem for Lagrangians in Liouville domains, as proven by the authors in [8].