Stability analysis of spherical pendulum with rotational spatial vibrating suspension point

Stability analysis of spherical pendulum with rotational spatial vibrating suspension 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 Stability analysis of spherical pendulum with rotational spatial vibrating suspension point Yan Luo, Kaicheng Sheng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3852269/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract We consider a spherical pendulum whose suspension point performs high-frequency spatial vibrations. Dynamics of this pendulum can be described by averaging of its Hamiltonian over phases of vibrations. We impose conditions on vibrations such that that the averaged Hamiltonian has a rotational symmetry. Under these conditions we present a bifurcation diagram for the phase portraits of the averaged system. We show numerical simulations of different examples of vibrations. Bifurcation of phase portraits of spherical physical pendulum with vibrating suspension point are considered as well. Mathematical Physics Spherical pendulum Vibrating suspension point Averaging Phase portraits Bifurcations Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions 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. 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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-3852269","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":266690696,"identity":"31b38188-6666-4380-aa87-2568af0debd2","order_by":0,"name":"Yan Luo","email":"","orcid":"","institution":"Shandong University","correspondingAuthor":false,"prefix":"","firstName":"Yan","middleName":"","lastName":"Luo","suffix":""},{"id":266690697,"identity":"aa29a539-dd67-4c6e-b69c-9601b6b431d5","order_by":1,"name":"Kaicheng Sheng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1klEQVRIiWNgGAWjYBACCQYGNhAtx8CQwABlE6nFmHQtiQ1Ea5FsYH/24OOO2vT57TkGDB/KDjPwz27Ar0WagcfccOaZ47kbzrwxYJxx7jCDxJ0D+LXIMfCwSfO2HcvdIJFjwMzbdpjBQCKBkBb2Z9J/246ly88AavlLjBZpBgYzaca2mgSGG0AtjMRokWzmMZPsbTtguOHMs4KDPefSeSRuENAicbz9mcTPtjp5+fbkjQ9+lFnL8c8goIWBGUweBpMHgJiHgHo4qCNW4SgYBaNgFIxEAADw+z7Qz40AQQAAAABJRU5ErkJggg==","orcid":"","institution":"Shandong University","correspondingAuthor":true,"prefix":"","firstName":"Kaicheng","middleName":"","lastName":"Sheng","suffix":""}],"badges":[],"createdAt":"2024-01-11 04:29:14","currentVersionCode":2,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-3852269/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-3852269/v2","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":51336501,"identity":"209c2043-171c-4bdb-99ba-98f8d7a5e96b","added_by":"auto","created_at":"2024-02-19 19:40:01","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1879355,"visible":true,"origin":"","legend":"","description":"","filename":"Preprint2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3852269/v2_covered_818d09d7-e9eb-42c4-9213-5f1a965caebf.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eStability analysis of spherical pendulum with rotational spatial vibrating suspension point\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":"Spherical pendulum, Vibrating suspension point, Averaging, Phase portraits, Bifurcations","lastPublishedDoi":"10.21203/rs.3.rs-3852269/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3852269/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We consider a spherical pendulum whose suspension point performs high-frequency spatial vibrations. 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