# Transform vector to Cylindrical Coordinates

1. Oct 6, 2009

### ph351

i need help transforming this equation into cylindrical coordinates...

w = omega
i = i hat
j = j hat
k = k hat
r is a vector

r(t) = Asin(wt)i + Bsin(wt)j + (Ct - D)k where w, A, B, C and D are constants.

i, j, and k are throwing me off...i know they are components of x, y and z...and i know xhat = cos(phi ro{hat}) - sin(phi phi{hat} likewise for yhat swapping sin and cos...

Last edited: Oct 6, 2009
2. Oct 6, 2009

### gabbagabbahey

HI ph351, welcome to PF!

The $\mathbf{\hat{i}}$, $\mathbf{\hat{j}}$, and $\mathbf{\hat{k}}$ are just another way of writing $\mathbf{\hat{x}}$, $\mathbf{\hat{y}}$ and $\mathbf{\hat{z}}$. Different authors use different notations, and it is usually a good idea to familiarize yourself with the notation of a text before attempting to solve problems from it, or apply equation found in it. Other common notations for the Cartesian unit vectors are $\{\mathbf{\hat{e}}_x,\mathbf{\hat{e}}_y,\mathbf{\hat{e}}_z\}$ and $\{\mathbf{\hat{e}}_1,\mathbf{\hat{e}}_2,\mathbf{\hat{e}}_3\}$.

So basically, you have $\textbf{r}(t)=A\sin(\omega t)\mathbf{\hat{x}}+B\sin(\omega t)\mathbf{\hat{y}}+(Ct-D)\mathbf{\hat{z}}$...and you can just make your substitutions for $\mathbf{\hat{x}}$ and $\mathbf{\hat{y}}$ in cylindrical coordinates.