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arXiv · 0904.0301

Determination of the position vectors of general helices from intrinsic equations in $\e^3$

Ahmad T. Ali
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Abstract

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.

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Ahmad T. Ali. 2009-04-02. Determination of the position vectors of general helices from intrinsic equations in $\e^3$. https://arxiv.org/abs/0904.0301

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