Trying again because the spam filter rejected me.
>[link to textbook pdf omitted]
So I'm reading Slotine, and he transforms this system of equations
$<br /> \dot{x}_1 = x_2 - x_1 (x_1^2+x_2^2-1)<br /> \dot{x}_2 = -x_1 - x_2 (x_1^2+x_2^2-1)<br />$
into this one
$<br /> \frac{d r}{d t} = -r (r^2 - 1)<br /> \frac{d \theta}{d t} = -1<br />$
using these coordinates:
$<br /> r = (x_1^2+x_2^2)^{1/2}<br /> \theta = tan^-1(x2/x1)<br />$
I did some of the work but found myself thinking
>hey this is tedious
and I was wondering if any of you anons see a simple way of justifying it. Modeled it in Xcos though