Position vectors of slant helices in Euclidean 3-space
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 deter...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2012-04-01
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| Series: | Journal of the Egyptian Mathematical Society |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X11000289 |
| _version_ | 1818176949819801600 |
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| author | Ahmad T. Ali |
| author_facet | Ahmad T. Ali |
| author_sort | Ahmad T. Ali |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T20:24:19Z |
| format | Article |
| id | doaj.art-828bc47eb95e49a69ab79e08efc9c9e8 |
| institution | Directory Open Access Journal |
| issn | 1110-256X |
| language | English |
| last_indexed | 2024-12-11T20:24:19Z |
| publishDate | 2012-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-828bc47eb95e49a69ab79e08efc9c9e82022-12-22T00:52:00ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2012-04-012011610.1016/j.joems.2011.12.005Position vectors of slant helices in Euclidean 3-spaceAhmad T. AliIn 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.http://www.sciencedirect.com/science/article/pii/S1110256X11000289Frenet equationsSlant helicesIntrinsic equations |
| spellingShingle | Ahmad T. Ali Position vectors of slant helices in Euclidean 3-space Journal of the Egyptian Mathematical Society Frenet equations Slant helices Intrinsic equations |
| title | Position vectors of slant helices in Euclidean 3-space |
| title_full | Position vectors of slant helices in Euclidean 3-space |
| title_fullStr | Position vectors of slant helices in Euclidean 3-space |
| title_full_unstemmed | Position vectors of slant helices in Euclidean 3-space |
| title_short | Position vectors of slant helices in Euclidean 3-space |
| title_sort | position vectors of slant helices in euclidean 3 space |
| topic | Frenet equations Slant helices Intrinsic equations |
| url | http://www.sciencedirect.com/science/article/pii/S1110256X11000289 |
| work_keys_str_mv | AT ahmadtali positionvectorsofslanthelicesineuclidean3space |