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<p>This study presents a novel geometric and kinematic framework for magnetic catenary curves by integrating magnetic curve theory, dual geometry, and dual quaternion screw theory. The dual flux surfaces associated with magnetic catenary curves are constructed via the Study mapping, and the kinematic transformation between the dual flux surfaces and the corresponding magnetic surfaces is characterized by explicit screw operators in dual space. These results provide a screw-theoretic interpretation of magnetic catenary curves in dual space and establish a new link between magnetic geometry and rigid body kinematics.</p>

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Magnetic Catenary Curves and Dual Flux Surfaces via Dual Quaternion Screw Theory

  • 期刊论文

  • 发表日期：

    2026年7月25日

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  • Abdussamet Çalışkan

摘要

This study presents a novel geometric and kinematic framework for magnetic catenary curves by integrating magnetic curve theory, dual geometry, and dual quaternion screw theory. The dual flux surfaces associated with magnetic catenary curves are constructed via the Study mapping, and the kinematic transformation between the dual flux surfaces and the corresponding magnetic surfaces is characterized by explicit screw operators in dual space. These results provide a screw-theoretic interpretation of magnetic catenary curves in dual space and establish a new link between magnetic geometry and rigid body kinematics.