1
$\begingroup$

I've been struggling with this one for about $3$ weeks:

What is the integral of a $\mathbb{R}^3$ curve with respect to its curvature?

I though about approaching it with the Ferret-S formulas, and doing a change of variables or lookings at the curvature as a $1$-form, but I'm stumped.

  • 2
    Could you please put this question into a little more context? Your idea worries me. We integrate with respect to a parameter that parametrises the curve. What happens when $\kappa' = 0$?2012-10-28
  • 0
    @DifferentialMan: What do you mean by the integral of a vector-valued function with respect to a scalar function? I can only think of something like the Stieltjes integral, but without more context it is impossible to make sense of your question.2018-09-03

1 Answers 1