Vector Calculus | Part IA, 2004

Define the curvature, κ\kappa, of a curve in R3\mathbb{R}^{3}.

The curve CC is parametrised by

x(t)=(12etcost,12etsint,12et) for <t<\mathbf{x}(t)=\left(\frac{1}{2} e^{t} \cos t, \frac{1}{2} e^{t} \sin t, \frac{1}{\sqrt{2}} e^{t}\right) \quad \text { for }-\infty<t<\infty

Obtain a parametrisation of the curve in terms of its arc length, ss, measured from the origin. Hence obtain its curvature, κ(s)\kappa(s), as a function of ss.

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