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Say I have a curve $$r(t)=\left(t + \sqrt3\sin t\;,\;\; 2\cos t\;,\;\; \sqrt3t-\sin t\right)$$

I have discovered it is a helix and I want to reparameterize the curve in terms of the standard helix form (r(t)=(acost, asint, bt)).

I need to find a rigid motion to transform the curves, I'm just not sure where to start.

Timbuc
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erika
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2 Answers2

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HINT: I'm not sure how you discovered it was a helix. But once you know that it has constant curvature and torsion ($\kappa=1/4$, $\tau=-1/4$), the standard formulas for the curvature and torsion of a (circular) helix will tell you what $a$ and $b$ have to be.

Ted Shifrin
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enter image description here The equation of the green line is given by: $$l(t)=\left(t ,0, \sqrt3t\right)$$

This is actually an elliptical helix, not a circular helix.

Alan
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