Effect of High-Order Dynamics on Single-Impulse Lissajous-to-Lissajous Transfers around a Collinear Libration Point

Effect of High-Order Dynamics on Single-Impulse Lissajous-to-Lissajous Transfers around 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 Effect of High-Order Dynamics on Single-Impulse Lissajous-to-Lissajous Transfers around a Collinear Libration Point Takuto Shimazaki, Nishanth Pushparaj, Elisabet Canalias, Yasuhiro Kawakatsu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7090596/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 02 Feb, 2026 Read the published version in The Journal of the Astronautical Sciences → Version 1 posted You are reading this latest preprint version Abstract Orbital transfers between libration point orbits have played a crucial role in meeting diverse mission constraints around a libration point. Existing analytical theories for such transfers, built on the linearization of the circular restricted three-body problem, have shown promising results in developing transfer strategies. However, given the large excursions of actual mission trajectories, the influence of the neglected high-order dynamics is expected to have a nontrivial effect on these transfers. This study proposes a numerical method that iteratively refines the solutions for impulsive transfers obtained from linear theory, based on the semi-analytical Lindstedt-Poincaré expansion. This method not only provides a means for refinement but also enables systematic validations of linear transfer theories within a broader dynamical framework while retaining orbital parameters. The proposed method is applied to in-plane single-impulse transfers between two Lissajous orbits around a collinear libration point in the Sun-Earth+Moon and Earth-Moon systems. The results show that while the linear solutions remain relatively accurate near optimalities, they are significantly disturbed at the two extremities of the Lissajous orbits by the the high-order dynamics. The deviation from the linear solutions exhibits a clear dependency on parameters such as the in-plane phase, transfer orbit families, and the libration point, leading to either improvements and deteriorations in the overall performance of the transfers. These results provide insights into the validity of existing linear theories and show how the nonlinearity can be leveraged to improve maneuver strategies. Orbital transfer Libration point orbit Invariant manifold Lindstedt-Poincar´e expansion Libration point Circular restricted three-body problem Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 02 Feb, 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-7090596","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":500263725,"identity":"2fd48344-e8a3-4a33-a778-8c4b353edb55","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":500263726,"identity":"a34720d7-aa4c-41ef-87a8-6e0a4c391613","order_by":1,"name":"Nishanth Pushparaj","email":"","orcid":"","institution":"University of Nottingham","correspondingAuthor":false,"prefix":"","firstName":"Nishanth","middleName":"","lastName":"Pushparaj","suffix":""},{"id":500263729,"identity":"3f127053-9817-4455-ac4a-a772d8aaad42","order_by":2,"name":"Elisabet Canalias","email":"","orcid":"","institution":"Centre National d'Études Spatiales","correspondingAuthor":false,"prefix":"","firstName":"Elisabet","middleName":"","lastName":"Canalias","suffix":""},{"id":500263730,"identity":"8b66d4f0-3a84-4457-993f-73c6d3f5ec8b","order_by":3,"name":"Yasuhiro Kawakatsu","email":"","orcid":"","institution":"Institute of Space and Astronautical Science","correspondingAuthor":false,"prefix":"","firstName":"Yasuhiro","middleName":"","lastName":"Kawakatsu","suffix":""}],"badges":[],"createdAt":"2025-07-10 08:23:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7090596/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7090596/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s40295-025-00555-x","type":"published","date":"2026-02-02T15:57:27+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":102235067,"identity":"8b57917f-f02d-4d27-97f8-bedbc6e117de","added_by":"auto","created_at":"2026-02-09 16:15:08","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":9972435,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript250604submit2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7090596/v1_covered_1e849b94-ceb4-42b4-827d-f4a96d915b26.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Effect of High-Order Dynamics on Single-Impulse Lissajous-to-Lissajous Transfers around 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, Libration point orbit, Invariant manifold, Lindstedt-Poincar´e expansion, Libration point, Circular restricted three-body problem","lastPublishedDoi":"10.21203/rs.3.rs-7090596/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7090596/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Orbital transfers between libration point orbits have played a crucial role in meeting diverse mission constraints around a libration point. Existing analytical theories for such transfers, built on the linearization of the circular restricted three-body problem, have shown promising results in developing transfer strategies. However, given the large excursions of actual mission trajectories, the influence of the neglected high-order dynamics is expected to have a nontrivial effect on these transfers. This study proposes a numerical method that iteratively refines the solutions for impulsive transfers obtained from linear theory, based on the semi-analytical Lindstedt-Poincaré expansion. This method not only provides a means for refinement but also enables systematic validations of linear transfer theories within a broader dynamical framework while retaining orbital parameters. The proposed method is applied to in-plane single-impulse transfers between two Lissajous orbits around a collinear libration point in the Sun-Earth+Moon and Earth-Moon systems. The results show that while the linear solutions remain relatively accurate near optimalities, they are significantly disturbed at the two extremities of the Lissajous orbits by the the high-order dynamics. The deviation from the linear solutions exhibits a clear dependency on parameters such as the in-plane phase, transfer orbit families, and the libration point, leading to either improvements and deteriorations in the overall performance of the transfers. These results provide insights into the validity of existing linear theories and show how the nonlinearity can be leveraged to improve maneuver strategies.","manuscriptTitle":"Effect of High-Order Dynamics on Single-Impulse Lissajous-to-Lissajous Transfers around a Collinear Libration Point","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-19 04:22:25","doi":"10.21203/rs.3.rs-7090596/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"69c7966e-8cd5-4477-87ca-f142533bf1a1","owner":[],"postedDate":"August 19th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-02-09T16:05:37+00:00","versionOfRecord":{"articleIdentity":"rs-7090596","link":"https://doi.org/10.1007/s40295-025-00555-x","journal":{"identity":"the-journal-of-the-astronautical-sciences","isVorOnly":false,"title":"The Journal of the Astronautical Sciences"},"publishedOn":"2026-02-02 15:57:27","publishedOnDateReadable":"February 2nd, 2026"},"versionCreatedAt":"2025-08-19 04:22:25","video":"","vorDoi":"10.1007/s40295-025-00555-x","vorDoiUrl":"https://doi.org/10.1007/s40295-025-00555-x","workflowStages":[]},"version":"v1","identity":"rs-7090596","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7090596","identity":"rs-7090596","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}