Determination of the position vectors of general helices from intrinsic equations in $\e^3$
| dc.creator | Ali, Ahmad T. | |
| dc.date | 2009-04-02 | |
| dc.date.accessioned | 2026-07-07T12:59:31Z | |
| dc.date.available | 2026-07-07T12:59:31Z | |
| dc.description | In this paper, we prove that the position vector of every space curve satisfies a vector differential equation of fourth order. Also, we determine the parametric representation of the position vector $ψ=\Big(ψ_1,ψ_2,ψ_3\Big)$ of general helices from the intrinsic equations $κ=κ(s)$ and $τ=τ(s)$ where $κ$ and $τ$ are the curvature and torsion of the space curve $ψ$, respectively. Our result extends some knwown results. Moreover, we give four examples to illustrate how to find the position vector from the intrinsic equations of general helices. | |
| dc.description | 10 pages only | |
| dc.identifier | https://arxiv.org/abs/0904.0301 | |
| dc.identifier | http://arxiv.org/abs/0904.0301 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225599 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C40, 53C50 | |
| dc.title | Determination of the position vectors of general helices from intrinsic equations in $\e^3$ | |
| dc.type | text |