Nonlinear Equilibrium Analysis and Codimension-One Bifurcation of a Three-State Rear-Wheel-Drive Vehicle Model with Combined-Slip Tire Forces

Nonlinear Equilibrium Analysis and Codimension-One Bifurcation of a Three-State Rear-Wheel-Drive Vehicle Model with Combined-Slip Tire Forces | 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 Nonlinear Equilibrium Analysis and Codimension-One Bifurcation of a Three-State Rear-Wheel-Drive Vehicle Model with Combined-Slip Tire Forces Javad Zolfaghari, A.S.M. Harithuddin, A.A. Nuraini, Raja Kamil, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9400923/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 3 You are reading this latest preprint version Abstract Accurate identification of equilibrium points and bifurcation boundaries is fundamental to understanding the nonlinear lateral dynamics of rear-wheel-drive (RWD) vehicles, particularly during aggressive maneuvers such as drifting. Existing studies predominantly adopt simplified two-state formulations or neglect the influence of longitudinal acceleration on normal load transfer, which can produce qualitatively incorrect stability predictions. This work addresses these limitations by developing a comprehensive three-state bicycle model — retaining longitudinal velocity, lateral velocity, and yaw rate as independent state variables — and coupling it with the Modified Elliptical Method (MEM) for combined-slip tire forces. A hybrid computational framework is proposed that combines a Genetic Algorithm (GA) for global search with the Newton–Raphson method for high-precision local refinement, enabling robust identification of all equilibrium branches across the full three-dimensional state space. The implicit structure of the equations of motion, arising from the appearance of longitudinal acceleration in the normal load expressions, is explicitly accounted for through a corrected Jacobian linearization, yielding stability predictions that differ fundamentally from those of reduced-order approaches. Codimension-one bifurcation analysis is then performed by augmenting the equilibrium conditions with algebraic bifurcation criteria, pinpointing one Hopf point and five saddle-node (fold) bifurcation points to ten or more significant figures for a fixed front steering angle of δf = 0.1 rad with varying rear slip ratio sr. The results reveal new equilibrium branches and dynamic transitions not previously reported, and provide quantitative stability boundaries that can directly inform the design of advanced traction-control and drift-stabilization systems for nonlinear automotive applications. Rear-Wheel Drive Vehicle Dynamics Hybrid Optimization Equilibrium Points Stability Analysis Bifurcation Analysis and Determination Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editor assigned by journal 16 Apr, 2026 Submission checks completed at journal 16 Apr, 2026 First submitted to journal 13 Apr, 2026 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-9400923","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":625615963,"identity":"80e35000-019e-400a-a4e1-920eb35a7120","order_by":0,"name":"Javad Zolfaghari","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEUlEQVRIiWNgGAWjYFAC5gMGCQYSciCmBEKUDZ8WtoSCDwUWxiBFQC0GxGjhUfg440NFYgPRWuT9zzBu5jGQSJ8/v8fwxscdfxgMbncnMHwoO8ygOyMBqxbDG7mHjYFacjcc4zG2nHnGgMHgztkNjDPOHWYwu4FDywy+NIgWNh4zad42oJYbuRuYedvwaOk/Y/4b5DD5NqCWvzAtf/FokWfIMTCcYSCRwHAMqIURpoURjxYDibQEgw8GEoYbjqUVW/a2GfNIAv1ysOdcOo/ZmQfYbek/DIzKP3Xy8s2HN9742SYnx3e7d+ODH2XWcmbHcdhyAE2ABxQ7B8AMARx+acAQgicbfnTjRsEoGAWjYIQCAKHwYZ8WoP5hAAAAAElFTkSuQmCC","orcid":"","institution":"Universiti Putra Malaysia","correspondingAuthor":true,"prefix":"","firstName":"Javad","middleName":"","lastName":"Zolfaghari","suffix":""},{"id":625615964,"identity":"4649ed6d-0c5c-440f-b97a-8ef841df7470","order_by":1,"name":"A.S.M. 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