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Applying data mining techniques to higher-dimensional Poincaré maps in the circular restricted three-body problem. (English) Zbl 1482.70009

Summary: Poincaré maps are regularly used to facilitate rapid and informed trajectory design within multi-body systems. However, maps that capture a general set of spatial trajectories are often higher-dimensional and, as a result, challenging for a human to analyze. This paper addresses this challenge by employing techniques from data mining. Specifically, distributed clustering, dimension reduction and classification are used in combination to construct a data-driven approach to autonomously group higher-dimensional crossings on a Poincaré map according to the geometry of the associated trajectories generated over a short time interval. This procedure is demonstrated using a periapsis map that captures spatial trajectories at a single energy level in the Sun-Earth circular restricted three-body problem. Arcs along hyperbolic invariant manifolds associated with families of tori in the \(L_1\) and \(L_2\) gateways are also projected onto this clustering result to rapidly extract their fundamental geometries. Together, these examples demonstrate the potential for the presented data-driven approach to facilitate analysis of a complex solution space reflected on a higher-dimensional Poincaré map.

MSC:

70F07 Three-body problems

Software:

Matlab; hdbscan; UMAP; AstroML
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Full Text: DOI

References:

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