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Evolution of Space Curves Using Type-3 Bishop Frame | ||
| Caspian Journal of Mathematical Sciences | ||
| مقاله 7، دوره 8، شماره 1، 2019، صفحه 58-73 اصل مقاله (1.56 M) | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2018.14455.1344 | ||
| نویسنده | ||
| Taha Youssef Shaker* | ||
| Department of Mathematics Faculty of Science, Assiut University, Assiut, Egypt | ||
| تاریخ دریافت: 22 تیر 1397، تاریخ پذیرش: 21 مرداد 1397 | ||
| چکیده | ||
| In this paper, Firstly, we introduce a new version of Bishop frame using a common vector field as normal vector field of a regular curve and call this frame as type-3 Bishop frame. Geometric visualization for both Frenet frame and type-3 Bishop frame are plotted. Secondly, time evolution equation for type-3 Bishop frame and type three bishop curvatures are obtained and we plotted the evolving curve via the numerical integration of type-3 Bishop Serret Frenet equations. Finally, surfaces generated by evolving a regular space curve in $\mathbb{R}^3$ as it evolves over time with arbitrary velocities attached to type-3 Bishop frame are obtained. We plotted these surfaces via numerical integration of Gauss-Weingarten equations. | ||
| کلیدواژه‌ها | ||
| type-3 Bishop frame؛ Serret Frenet equations؛ time evolution equation | ||
| عنوان مقاله [English] | ||
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| چکیده [English] | ||
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آمار تعداد مشاهده مقاله: 577 تعداد دریافت فایل اصل مقاله: 893 |
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