# 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