{"title":"Applications of knot theory to the detection of heteroclinic connections between quasi-periodic orbits","authors":"Danny Owen, Nicola Baresi","doi":"10.1007/s42064-024-0201-0","DOIUrl":null,"url":null,"abstract":"<div><p>Heteroclinic connections represent unique opportunities for spacecraft to transfer between isoenergetic libration point orbits for zero deterministic Δ<i>V</i> 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.</p><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":52291,"journal":{"name":"Astrodynamics","volume":null,"pages":null},"PeriodicalIF":2.7000,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s42064-024-0201-0.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Astrodynamics","FirstCategoryId":"1087","ListUrlMain":"https://link.springer.com/article/10.1007/s42064-024-0201-0","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Astrodynamics is a peer-reviewed international journal that is co-published by Tsinghua University Press and Springer. The high-quality peer-reviewed articles of original research, comprehensive review, mission accomplishments, and technical comments in all fields of astrodynamics will be given priorities for publication. In addition, related research in astronomy and astrophysics that takes advantages of the analytical and computational methods of astrodynamics is also welcome. Astrodynamics would like to invite all of the astrodynamics specialists to submit their research articles to this new journal. Currently, the scope of the journal includes, but is not limited to:Fundamental orbital dynamicsSpacecraft trajectory optimization and space mission designOrbit determination and prediction, autonomous orbital navigationSpacecraft attitude determination, control, and dynamicsGuidance and control of spacecraft and space robotsSpacecraft constellation design and formation flyingModelling, analysis, and optimization of innovative space systemsNovel concepts for space engineering and interdisciplinary applicationsThe effort of the Editorial Board will be ensuring the journal to publish novel researches that advance the field, and will provide authors with a productive, fair, and timely review experience. It is our sincere hope that all researchers in the field of astrodynamics will eagerly access this journal, Astrodynamics, as either authors or readers, making it an illustrious journal that will shape our future space explorations and discoveries.
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