The Known is finite, the unknown infinite; intellectually we stand on an islet in the midst of an illimitable ocean of inexplicability. Our business in every generation is to reclaim a little more land.  -T.H. Huxley, 1887



This is an interesting math problem. It is something that everyone has probably done but put no thought into it. Take a book, something rectangular shaped. Tape it closed, or use a rubber band to hold the book shut. Now spin the book in the air. There are three ways to spin it. Two of the ways the book will spin just fine with a small perturbation. Another way will spin wildly. It will be impossible for you to get it to spin straight.

Why is this?

In essence, one of the rotation axis are unstable. This phenomenon applies to all spinning objects. In specific it can be applied to satellites. The math is a bit involved, I've attached a .pdf showing the math.

THE MATH [449Kb]

Now you can solve this numerically. Preferably using quaternions. This Matlab code shows this process with an animation.

rotbook.m and you'll need de.m

I'll upload a video here soon.