Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How to find the arc length parametrization of the Archimedean spiral?

I know the curve is defined in the complex nubmer like this: $c(t)=e^{it} - ite^{it}$

and $|\frac{d}{dt}(c(t))|= te^{it}$ (is this correct?)

now I should find $\int te^{it} dt$ (the integration from 0 to t ,,,I am stuck here)

share|improve this question
1  

1 Answer 1

up vote 2 down vote accepted

It is easier to use the polar formula for the Archimedean spiral: $r=a+b\theta$. The arc length in polar coordinates is $ds=\sqrt{dr^2 +r^2 d\theta^2}$ or $\frac {ds}{d\theta}=\sqrt{r^2+\frac {dr^2}{d\theta^2}}=\sqrt{(a+b\theta)^2+b^2}$ and integrate that.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.