Local Coordinates on Lie Groups for Half-Explicit Time Integration of Cosserat Rod Models with Constraints

Local Coordinates on Lie Groups for Half-Explicit Time Integration of Cosserat Rod Models with Constraints | 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 Local Coordinates on Lie Groups for Half-Explicit Time Integration of Cosserat Rod Models with Constraints Denise Tumiotto, Martin Arnold This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3909329/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Jun, 2024 Read the published version in Multibody System Dynamics → Version 1 posted 10 You are reading this latest preprint version Abstract Explicit Runge-Kutta methods are the gold standard of time integration methods for non-stiff problems in system dynamics since they combine a small numerical effort per time step with high accuracy, error control and straightforward implementation. For the analysis of beam dynamics, we couple them with a local coordinates approach in a Lie group setting to address large rotations. Stiff shear forces and inextensibility conditions are enforced by internal constraints in a coarse grid discretization of a geometrically exact beam model. The resulting non-stiff constrained systems are handled by a half-explicit approach that relies on the constraints at velocity level and avoids all kinds of Newton-Raphson iteration. We construct half-explicit Runge-Kutta Lie group methods of order up to five that are equipped with an adaptive step size strategy using embedded Runge-Kutta pairs for error estimation. The methods are tested successfully for a roll-up maneuver of a flexible beam and for the classical flying spaghetti benchmark. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 20 Jun, 2024 Read the published version in Multibody System Dynamics → Version 1 posted Editorial decision: Revision requested 03 May, 2024 Reviews received at journal 17 Mar, 2024 Reviews received at journal 08 Mar, 2024 Reviewers agreed at journal 09 Feb, 2024 Reviewers agreed at journal 09 Feb, 2024 Reviewers agreed at journal 09 Feb, 2024 Reviewers invited by journal 07 Feb, 2024 Editor assigned by journal 02 Feb, 2024 Submission checks completed at journal 31 Jan, 2024 First submitted to journal 29 Jan, 2024 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. 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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-3909329","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":270367387,"identity":"9ce613f7-19f5-4031-9753-5419a34e9030","order_by":0,"name":"Denise Tumiotto","email":"data:image/png;base64,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","orcid":"","institution":"Martin Luther University Halle-Wittenberg","correspondingAuthor":true,"prefix":"","firstName":"Denise","middleName":"","lastName":"Tumiotto","suffix":""},{"id":270367388,"identity":"a800509e-e97e-4b64-b3c0-5f373f00867e","order_by":1,"name":"Martin Arnold","email":"","orcid":"","institution":"Martin Luther University Halle-Wittenberg","correspondingAuthor":false,"prefix":"","firstName":"Martin","middleName":"","lastName":"Arnold","suffix":""}],"badges":[],"createdAt":"2024-01-29 18:19:50","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3909329/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3909329/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11044-024-10002-8","type":"published","date":"2024-06-20T16:00:43+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":58823922,"identity":"065c2094-8a9b-4e03-9be4-702c76c25610","added_by":"auto","created_at":"2024-06-21 17:10:51","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":477193,"visible":true,"origin":"","legend":"","description":"","filename":"TumiottoArnold.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3909329/v1_covered_2fe6b870-d0ce-499c-a128-c40e8faa343c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Local Coordinates on Lie Groups for Half-Explicit Time Integration of Cosserat Rod Models with Constraints","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"multibody-system-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mubo","sideBox":"Learn more about [Multibody System Dynamics](http://link.springer.com/journal/11044)","snPcode":"11044","submissionUrl":"https://submission.nature.com/new-submission/11044/3","title":"Multibody System Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-3909329/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3909329/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Explicit Runge-Kutta methods are the gold standard of time integration methods for non-stiff problems in system dynamics since they combine a small numerical effort per time step with high accuracy, error control and straightforward implementation. 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