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Transform vector to Cylindrical Coordinates

  1. Oct 6, 2009 #1
    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. jcsd
  3. Oct 6, 2009 #2


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    HI ph351, welcome to PF!:smile:

    The [itex]\mathbf{\hat{i}}[/itex], [itex]\mathbf{\hat{j}}[/itex], and [itex]\mathbf{\hat{k}}[/itex] are just another way of writing [itex]\mathbf{\hat{x}}[/itex], [itex]\mathbf{\hat{y}}[/itex] and [itex]\mathbf{\hat{z}}[/itex]. 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 [itex]\{\mathbf{\hat{e}}_x,\mathbf{\hat{e}}_y,\mathbf{\hat{e}}_z\}[/itex] and [itex]\{\mathbf{\hat{e}}_1,\mathbf{\hat{e}}_2,\mathbf{\hat{e}}_3\}[/itex].

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