Document Type
Article
Publication Date
9-17-2026
Abstract
The spatial Circular Restricted Three-Body Problem (CR3BP) produces complex orbital dynamics that are difficult to classify at scale using traditional, manual Poincaré map analysis. A Poincaré map simplifies continuous orbital motion by recording the points where a trajectory intersects a chosen surface in phase space, converting a continuous path into a discrete set of crossings that reveal underlying topological structure. These crossings make it easier to characterize trajectory behavior, but interpreting them visually becomes impractical for large datasets and as Poincaré maps evolve from two into four dimensions. To address this challenge, an unsupervised clustering pipeline for discovering dynamical structures in four-dimensional (4D) Poincaré maps is introduced. Each trajectory’s Poincaré crossings are transformed into a compact feature representation capturing geometric dispersion, statistical, and frequency-based characteristics, enabling density-based clustering without prior labels. The method is evaluated across multiple Jacobi constants to assess robustness, and expanded to investigate chaining dynamical structures to find similar structures across different Jacobi constants. The results demonstrate that feature-based clustering can recover meaningful dynamical structures in high-dimensional trajectory data.
Source Publication
Astrophysics and Space Science (ISSN 0004-640X | eISSN 1572-946X)
Recommended Citation
Trigg, K.M., Broyles, D.J., Bettinger, R.A. et al. Application of machine learning to discover dynamical structures in 4D Poincaré maps in the circular restricted three-body problem. Astrophys Space Sci 371, 107 (2026). https://doi.org/10.1007/s10509-026-04638-5
Comments
Open Access funding provided by Air Force Research Laboratory (AFRL) Technical Libraries Consortia.
This article is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.