This moving frame is a new contribution to the field and we expect that it will be useful in some specific applications of differential geometry and kinematics in the future.
📌 3 Key Takeaways
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Objective & Hypothesis:In this study, we introduce a new moving frame on regular surfaces for trajectories with non-vanishing angular momentum and give the angular velocity vector for this frame.
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Key Findings & Data:Then, we consider the special trajectories generated by Smarandache curves according to this frame in three-dimensional Euclidean space and investigate the Serret-Frenet apparatus of them.
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Conclusion & Impact:This moving frame is a new contribution to the field and we expect that it will be useful in some specific applications of differential geometry and kinematics in the future.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Kinematics of a particle · Moving frame · Regular surfaces
Abstract
In this study, we introduce a new moving frame on regular surfaces for trajectories with non-vanishing angular momentum and give the angular velocity vector for this frame. Then, we consider the special trajectories generated by Smarandache curves according to this frame in three-dimensional Euclidean space and investigate the Serret-Frenet apparatus of them. Moreover, we provide an illustrative example explaining how this frame is constructed and how the aforementioned special trajectories are generated. This moving frame is a new contribution to the field and we expect that it will be useful in some specific applications of differential geometry and kinematics in the future.
ÖZEN, K. E., TOSUN, M. (2021). A New Moving Frame for Trajectories on Regular Surfaces. Ikonion Journal of Mathematics, Cilt: 3 - Sayı: 1, 20–34. https://ajindex.com/articles/764538
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