An Analytical Approach to In-Plane Asymptotic Three-Impulse Transfers between Lissajous Orbits near a Collinear Libration Point

An Analytical Approach to In-Plane Asymptotic Three-Impulse Transfers between Lissajous Orbits near a Collinear Libration Point | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article An Analytical Approach to In-Plane Asymptotic Three-Impulse Transfers between Lissajous Orbits near a Collinear Libration Point Takuto Shimazaki, Yasuhiro Kawakatsu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6142163/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 08 Jan, 2026 Read the published version in The Journal of the Astronautical Sciences → Version 1 posted You are reading this latest preprint version Abstract In this study, we present an analytical framework for in-plane three-impulse transfers between Lissajous orbits near a collinear libration point that have asymptotic invariant manifolds at both ends. The solutions for this type of three-impulse transfer are derived explicitly utilizing existing results on two-impulse transfers as a building block, which approximate bounded single-impulse-like transfers with asymptotic invariant manifolds at one end. The asymptotic property of these invariant manifolds not only reduces the maneuver cost compared to single-impulse and two-impulse transfers but also eliminates the large degree of freedom associated with the problem, enabling a more systematic analysis of the transfer. The proposed analytical framework is applied to the orbital transfer problem between two Lissajous orbits, and the resulting performance and key characteristics are investigated. Our numerical analysis shows that this type of transfer achieves approximately an 11% reduction in the maneuver cost across all amplitude ranges, compared to transfers with fewer maneuvers. Additionally, a linear scaling law for the optimal maneuver cost, similar to the one found in existing single-impulse transfer theory, is also identified. Orbital transfer Impulsive transfer Libration point Libration point orbit Invariant manifold Circular restricted three-body problem Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 08 Jan, 2026 Read the published version in The Journal of the Astronautical Sciences → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6142163","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":423827362,"identity":"475e72e3-0e72-4880-b384-ce68d9a963f6","order_by":0,"name":"Takuto Shimazaki","email":"data:image/png;base64,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","orcid":"","institution":"The University of Tokyo","correspondingAuthor":true,"prefix":"","firstName":"Takuto","middleName":"","lastName":"Shimazaki","suffix":""},{"id":423827364,"identity":"4e7b319c-885b-4708-94d1-99778bbce04e","order_by":1,"name":"Yasuhiro Kawakatsu","email":"","orcid":"","institution":"Institute of Space and Astronautical Science","correspondingAuthor":false,"prefix":"","firstName":"Yasuhiro","middleName":"","lastName":"Kawakatsu","suffix":""}],"badges":[],"createdAt":"2025-03-03 03:08:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6142163/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6142163/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s40295-025-00559-7","type":"published","date":"2026-01-08T15:57:01+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":100069090,"identity":"a4d17a77-4667-4df6-bc72-1f8b757d8481","added_by":"auto","created_at":"2026-01-12 16:08:53","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2230986,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript250303submissionver2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6142163/v1_covered_a1bcdd7d-7972-43d6-846d-3e7eb6c1d20a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"An Analytical Approach to In-Plane Asymptotic Three-Impulse Transfers between Lissajous Orbits near a Collinear Libration Point","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Orbital transfer, Impulsive transfer, Libration point, Libration point orbit, Invariant manifold, Circular restricted three-body problem","lastPublishedDoi":"10.21203/rs.3.rs-6142163/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6142163/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this study, we present an analytical framework for in-plane three-impulse transfers between Lissajous orbits near a collinear libration point that have asymptotic invariant manifolds at both ends. The solutions for this type of three-impulse transfer are derived explicitly utilizing existing results on two-impulse transfers as a building block, which approximate bounded single-impulse-like transfers with asymptotic invariant manifolds at one end. The asymptotic property of these invariant manifolds not only reduces the maneuver cost compared to single-impulse and two-impulse transfers but also eliminates the large degree of freedom associated with the problem, enabling a more systematic analysis of the transfer. The proposed analytical framework is applied to the orbital transfer problem between two Lissajous orbits, and the resulting performance and key characteristics are investigated. Our numerical analysis shows that this type of transfer achieves approximately an 11\\% reduction in the maneuver cost across all amplitude ranges, compared to transfers with fewer maneuvers. 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