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

Danny Owen; Nicola Baresi

doi:10.1007/s42064-024-0201-0

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Research Article | Open Access

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

Danny Owen(), Nicola Baresi

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 $Δ V$ 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.

Keywords

circular restricted three-body problem (CR3BP)quasi-periodic torus heteroclinic connection knot theory

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Astrodynamics

Volume 8 Issue 4,
December 2024

Pages 577-595

DOI: 10.1007/s42064-024-0201-0

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

	Stable manifold	Unstable manifold
Dimension	2	2	5	Dimension, phase space
Co-dimension	3	3	6	Co-dimension, intersection
			−1	Dimension, intersection

	Stable manifold	Unstable manifold
Dimension	3	3	5	Dimension, phase space
Co-dimension	2	2	4	Co-dimension, intersection
			1	Dimension, intersection