Determination of the position vectors of general helices from intrinsic equations in \e³

2009/04/02 by Ali, Ahmad T.
#53C40 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0904.0301

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=(ψ₁,ψ₂,ψ₃) 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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