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I am looking for classical (real) functionals defined on rectifiable curves (neither necessarily simple nor closed) in either $\mathbb{R}^2$ or $\mathbb{R}^3$.

There's length, turning number, total curvature, mean curvature, ... What else?

This question is quite loosely stated, I'm sorry, but I'm just in a pre-hunting phase, looking for (real) numbers associated to curves :)

Thanks!

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Energy is pretty classical, but very similar to length though. –  wspin Dec 19 '12 at 21:28

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