Chris, the example of the Moon directly above the Equator was for illustrative purposes. You are correct that it's nominal plane of orbit is more aligned with the plane of the Solar System than Earth's equator.

"Chaotic" shouldn't be interpreted to mean unpredictable. Sorry for the confusion. It's orbit is subject to numerous perturbations, which cause it to wander.

Some time ago, I had made a small program plotting it's orbit based on some polynomial(?) equations I scrounged up. It wanders all over the place. It almost appears that if you were to plot it in 3D, the sum of it's orbital paths would describe a donut. That is, it's orbit wanders around anywhere inside the torus.

I'll see if I can scrounge up that code and make some images.

Brian