Mathematical Modeling of Engineering Problems and Solutions via Polynomial Systems Using Custom-Designed Software

Mathematical Modeling of Engineering Problems and Solutions via Polynomial Systems Using Custom-Designed Software | 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 Mathematical Modeling of Engineering Problems and Solutions via Polynomial Systems Using Custom-Designed Software Asif Nabiyev This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9568575/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 Engineering disciplines fundamentally rely on the mathematical interpretation of physical phenomena. This paper explores the integration of linear algebra and polynomial modeling in solving multifaceted engineering challenges, ranging from resource allocation and financial engineering to aerospace kinematics. A primary focus is placed on systems of linear equations (SLE) and their role in modeling real-world scenarios, such as the atmospheric reentry of spacecraft and equilibrium state analysis in networked systems. Due to the computational intensity of classical methods like Cramer’s Rule in high-dimensional systems, this study presents a specialized software solution developed to optimize these calculations. The software employs high-precision algorithms to minimize rounding errors and enhance decision-making efficiency. Five distinct case studies are analyzed: industrial resource management, interest rate optimization, price equilibrium in transport networks, constant acceleration kinematics, and cubic polynomial trajectory planning for spacecraft landing. The results demonstrate that the synergy between robust mathematical modeling and algorithmic automation significantly improves the accuracy and speed of engineering analyses. Mathematical modeling Engineering software Cramer’s Rule Polynomial trajectories Spacecraft landing simulation Linear algebra 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. 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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-9568575","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":637257285,"identity":"91ba4a4a-3a6b-48df-b44a-5558edce2086","order_by":0,"name":"Asif Nabiyev","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA40lEQVRIiWNgGAWjYHACNoYEIMkvAeYwk6BFcgZJWkDA4AaxWvhnNz978LDNJnHz7eZjEgwV1okN7Mcf4NUiceeYuUFiW1ritjvH0iQYzqQnNvAkJOC35kaCmURi22Fjsxs5ZhKMbYcTGxgSDuDVIX8j/RtQy39j4xn53yQY/wG18D9swKvFAGR4YtsBOQOJHDYJxgagFolk/O4yvJFTbpBwLlkO6Clji4Rj6cZtEs/wa5G7kb7t4Y8yOx5g0D288aHGWrafP/0Bfj0gwMgGZSQwwKKJIPhDnLJRMApGwSgYoQAAXUVHkNW+kGsAAAAASUVORK5CYII=","orcid":"","institution":"Baku Engineering University","correspondingAuthor":true,"prefix":"","firstName":"Asif","middleName":"","lastName":"Nabiyev","suffix":""}],"badges":[],"createdAt":"2026-04-29 17:08:32","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9568575/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9568575/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109040923,"identity":"8cfec2ac-c57d-4c08-a483-f696f222d817","added_by":"auto","created_at":"2026-05-12 03:47:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":421074,"visible":true,"origin":"","legend":"","description":"","filename":"articlekosmik.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9568575/v1_covered_a1aca491-ad66-4601-a71c-f83617d6e770.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Mathematical Modeling of Engineering Problems and Solutions via Polynomial Systems Using Custom-Designed Software","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Mathematical modeling, Engineering software, Cramer’s Rule, Polynomial trajectories, Spacecraft landing simulation, Linear algebra","lastPublishedDoi":"10.21203/rs.3.rs-9568575/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9568575/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eEngineering disciplines fundamentally rely on the mathematical interpretation of physical phenomena. 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