Principal Unit Normal Vector

Definition

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Suppose $\mathbf{T}$ a Unit Tangent Vector, then at a point where $\kappa \ne 0$, $\mathbf{N}=\frac{1}{\kappa }\frac{d\mathbf{T}}{ds}=\frac{d\mathbf{T}/ds}{|d\mathbf{T}/ds|}=\frac{d\mathbf{T}/dt}{|d\mathbf{T}/dt|}$ $\because$ Vector Function of Constant Length where $\kappa$ is the Curvature of Curves