In addition, a functional measuring the deviation from the helical structure is introduced, and its behavior is analyzed numerically on selected example curves and visualized through the corresponding graphs.
📌 3 Key Takeaways
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Objective & Hypothesis:In this study, space curves are investigated under a curvature-based reparametrization.
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Key Findings & Data:Within this framework, it is shown that the Frenet–Serret system for generalized helices can be reduced to a simpler form, and that the tangent vector can be expressed through a third-order linear differential equation.
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Conclusion & Impact:In addition, a functional measuring the deviation from the helical structure is introduced, and its behavior is analyzed numerically on selected example curves and visualized through the corresponding graphs.
In this study, space curves are investigated under a curvature-based reparametrization. Within this framework, it is shown that the Frenet–Serret system for generalized helices can be reduced to a simpler form, and that the tangent vector can be expressed through a third-order linear differential equation. Furthermore, this approach is shown to provide a characterization of helices. An associated energy conservation is established, and the results are interpreted via the spherical image of the tangent indicatrix. In addition, a functional measuring the deviation from the helical structure is introduced, and its behavior is analyzed numerically on selected example curves and visualized through the corresponding graphs.
Suroğlu, G. A., Hızal, Ş. F., Bulut, H. (2026). A Third-Order Tangent Characterization of Helices under Curvature-Based Reparametrization. Cankaya University Journal of Science and Engineering, Volume: 23 Issue: 1. https://ajindex.com/articles/1468612
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