Finding Curvature

1. Jun 24, 2013

Bashyboy

1. The problem statement, all variables and given/known data
Find the curvature K of the curve, where s is the arc length parameter:

$\vec{r}(t) = \langle 2 \cos t , 2 \sin t, t \rangle$

2. Relevant equations

$s(t) = \int_a ^t ||\vec{r}'(u)||du$

3. The attempt at a solution

I know I need to find the arc length function, in order to find the curvature function; however, I am unsure as to what I should choose a to be for the lower limit of the integral.

Last edited: Jun 24, 2013
2. Jun 24, 2013

pasmith

You need to use the Frenet-Serret formulae and the chain rule.

You should not need to perform any integrations.

Last edited: Jun 24, 2013
3. Jun 24, 2013

ehild

Choose it so that s(0)=0.

4. Jun 24, 2013

Bashyboy

So, the choice is arbitrary? If so, why?

5. Jun 24, 2013

ehild

Why not? Just as you can start time at any instant, you can measure an arc length from any point on a line. Usually the arc length is connected to the trajectory of an object if time is involved, that is why I suggested s(0)=0. But you also can keep "a" in the expression s(t). Solve the problem and you will see that"a" cancels.

ehild

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