Helpful Pictures for the Project

Some pictures which might be of some aid.

First are annoying animated drawings which run forever and will suck up all of your available cpu cycles so they are not directly on this page. The animated gif is huge (4 MB), but should work in all browsers. The other is a flash animation which is much smaller (4 KB) but if your browser is old, it might require a plugin. After the class was over, a 3rd format, SVG was added (3 KB). Adobe has a free SVG plugin.

Maple hint: Maple does not have a planecurve analog to spacecurve, instead there is a variation on the plot command which will plot the parametric equations x=f(t), y=g(t). For example

> f:=cos(t);g:=sin(t);
> plot([f, g, t=Pi/4..7*Pi/4],x=-1..1);

will plot a circular arc starting at 45 degrees and going around to -45 degrees.

Although these images are for the Juliet problems the first image is more general. We show a planet and a moon's orbit. The north pole is blue and is perpendicular to the moon's orbit. Note that the moon is going counter-clockwise as we view the orbit from the North. For the Juliet-Uranus problem the North pole of Uranus is always in the xy-plane, the red arrow is always in the positive z-direction and the green arrow coming out of Uranus is also in the xy-plane.

The three models for how the North pole moves as Uranus orbits the sun.

The first keeps the North pole always pointed in the same direction.

The next is Run Howbackward's toral system.

The next is Kevin Brocolli's south is towards the Sun system.