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Research Article | Open Access

Applications of knot theory to the detection of heteroclinic connections between quasi-periodic orbits

Surrey Space Centre, University of Surrey, Guildford, UK
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Abstract

Heteroclinic connections represent unique opportunities for spacecraft to transfer between isoenergetic libration point orbits for zero deterministic ΔV expenditure. However, methods of detecting them can be limited, typically relying on human-in-the-loop or computationally intensive processes. In this paper we present a rapid and fully systematic method of detecting heteroclinic connections between quasi-periodic invariant tori by exploiting topological invariants found in knot theory. The approach is applied to the Earth–Moon, Sun–Earth, and Jupiter–Ganymede circular restricted three-body problems to demonstrate the robustness of this method in detecting heteroclinic connections between various quasi-periodic orbit families in restricted astrodynamical problems.

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Keywords

circular restricted three-body problem (CR3BP)quasi-periodic torusheteroclinic connectionknot theory

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Astrodynamics
Volume 8 Issue 4,
December 2024
Pages 577-595
DOI: 10.1007/s42064-024-0201-0

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Cite this article:
Owen D, Baresi N. Applications of knot theory to the detection of heteroclinic connections between quasi-periodic orbits. Astrodynamics, 2024, 8(4): 577-595. https://doi.org/10.1007/s42064-024-0201-0

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Received: 18 September 2023
Accepted: 16 January 2024
Published: 15 April 2024
© The Author(s) 2024

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