Position vectors of slant helices in Euclidean 3-space
Ali, A. (2024). Position vectors of slant helices in Euclidean 3-space. EKB Journal Management System, 20(1), 1-6. doi: 10.1016/j.joems.2011.12.005
Ahmad T. Ali. "Position vectors of slant helices in Euclidean 3-space". EKB Journal Management System, 20, 1, 2024, 1-6. doi: 10.1016/j.joems.2011.12.005
Ali, A. (2024). 'Position vectors of slant helices in Euclidean 3-space', EKB Journal Management System, 20(1), pp. 1-6. doi: 10.1016/j.joems.2011.12.005
Ali, A. Position vectors of slant helices in Euclidean 3-space. EKB Journal Management System, 2024; 20(1): 1-6. doi: 10.1016/j.joems.2011.12.005

Position vectors of slant helices in Euclidean 3-space

Journal of the Egyptian Mathematical Society
Volume 20, Issue 1, 2012, Pages 1-6    PDF (528.46 K)
DOI: 10.1016/j.joems.2011.12.005
Author
Ahmad T. Ali*
King Abdul Aziz University, Faculty of Science, Department of Mathematics, P.O. Box 80203, Jeddah 21589, Saudi Arabia Al-Azhar University, Faculty of Science, Mathematics Department, Nasr City, 11884 Cairo, Egypt
Abstract
In this paper, position vector of a slant helix with respect to standard frame in Euclidean
space E3 is studied in terms of Frenet equations. First, a vector differential equation of third order is constructed to determine a position vector of an arbitrary slant helix. In terms of solution, we determine the parametric representation of the slant helices from the intrinsic equations. Thereafter, we apply this method to find the parametric representation of a Salkowski curve, anti-Salkowski curve and a curve of constant precession, as examples of a slant helices, by means of intrinsic equations.
Keywords
Frenet equations; Slant helices; Intrinsic equations
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