Hi,
I just tried the command TransformedField in Mathematica 9 because I want to convert vector fields between cartesian coordinates in 2D and polar coordinates. But I do not get the output I expect:
I want to convert the ODE $\dot{r} = 0, \dot{\theta} = 1$ into cartesian coordinates. I think it should work like this:
In[2]:=TransformedField[
"Polar" -> "Cartesian",
{0, 1},
{r, \[Theta]} -> {x, y}
]
Out[2]= {-(y/Sqrt[x^2 + y^2]), x/Sqrt[x^2 + y^2]}
I would expect { -y, x } as the output.
Because this is what I get when deriving $x(t) = r(t) \cos ( \theta(t) )$ with respect to t by hand -- the same for $y(t) = r(t) \sin ( \theta(t) ) ).
My question: Did I misunderstood the functionality of TransformedField? Or is this some kind of bug (I run Mathematica 9.0.1.0 on a 64-bit Linux).
I hope someone can resolve my confusion.
Frank
