A Physics-based Work-energy Formulation for Real-time Trajectory Guidance of a Lunar Lander

A Physics-based Work-energy Formulation for Real-time Trajectory Guidance of a Lunar Lander | 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 A Physics-based Work-energy Formulation for Real-time Trajectory Guidance of a Lunar Lander Jorge Manuel Munoz-Burgos, Peter James McDonough This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6522253/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Throughout the years, many researchers have calculated and optimized trajectory solutions for lunar landing systems by employing sophisticated mathematical methods, that include: Hamilton’s Principle of Variation, Pontryagin’s maximum principle, and well known convex-optimization techniques among others. Many of these approaches typically require expensive computational resources to achieve convergence in the solution. In an effort to reduce complexity and the computational load required to generate real-time guidance commands, a simple physics-based workenergy approach has been formulated. This approach is based on the dissipation of the mechanical energy of the vehicle to its final desired energy state required to achieve a safe landing. The rocket engine(s) employed during landing (among other maneuvers) dissipates mechanical energy by both doing work against the velocity vector of the vehicle (thus defining the trajectory path), and by jettisoning mass. Therefore, by solving the energy dissipation problem at every step of the maneuver, a much simpler formulation that naturally and quickly attains convergence is obtained. This formulation is not limited to approach, landing, and divert maneuvers, but in principle it can be employed during de-orbiting, braking burn, ascent, as well as orbit insertion. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted 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-6522253","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":452866814,"identity":"68932872-46c8-4a89-bf1a-0e74cb6355ab","order_by":0,"name":"Jorge Manuel Munoz-Burgos","email":"data:image/png;base64,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","orcid":"","institution":"Amentum Space Exploration Group","correspondingAuthor":true,"prefix":"","firstName":"Jorge","middleName":"Manuel","lastName":"Munoz-Burgos","suffix":""},{"id":452866815,"identity":"70fd841b-17ef-479f-b367-ffb45061eee6","order_by":1,"name":"Peter James McDonough","email":"","orcid":"","institution":"Amentum Space Exploration Group","correspondingAuthor":false,"prefix":"","firstName":"Peter","middleName":"James","lastName":"McDonough","suffix":""}],"badges":[],"createdAt":"2025-04-24 15:38:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6522253/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6522253/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":100415927,"identity":"2eded5f7-c5e8-4d67-a3a3-fbee4c512a88","added_by":"auto","created_at":"2026-01-16 13:22:38","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2049908,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6522253/v1_covered_925ad34d-988d-414d-95ab-25b270b2d1e2.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eA Physics-based Work-energy Formulation for Real-time Trajectory Guidance of a Lunar Lander\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"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":"","lastPublishedDoi":"10.21203/rs.3.rs-6522253/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6522253/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Throughout the years, many researchers have calculated and optimized trajectory\nsolutions for lunar landing systems by employing sophisticated mathematical methods,\nthat include: Hamilton’s Principle of Variation, Pontryagin’s maximum principle,\nand well known convex-optimization techniques among others. Many of these\napproaches typically require expensive computational resources to achieve convergence\nin the solution. In an effort to reduce complexity and the computational load\nrequired to generate real-time guidance commands, a simple physics-based workenergy\napproach has been formulated. This approach is based on the dissipation\nof the mechanical energy of the vehicle to its final desired energy state required to\nachieve a safe landing. The rocket engine(s) employed during landing (among other\nmaneuvers) dissipates mechanical energy by both doing work against the velocity\nvector of the vehicle (thus defining the trajectory path), and by jettisoning mass.\nTherefore, by solving the energy dissipation problem at every step of the maneuver,\na much simpler formulation that naturally and quickly attains convergence is obtained.\nThis formulation is not limited to approach, landing, and divert maneuvers,\nbut in principle it can be employed during de-orbiting, braking burn, ascent, as well\nas orbit insertion.","manuscriptTitle":"A Physics-based Work-energy Formulation for Real-time Trajectory Guidance of a Lunar Lander","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-07 06:46:50","doi":"10.21203/rs.3.rs-6522253/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":"052d775d-0680-4bbd-8985-612ac9e5e3b6","owner":[],"postedDate":"May 7th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-01-16T11:55:17+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-07 06:46:50","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6522253","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6522253","identity":"rs-6522253","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}