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!