In this Wolfram blog post the bizarre behavior of rotating bodies was illustrated with some simulations. When I was writing the post I ended up simulating and replaying animations one time after another. It was almost addictive to watch what was going on, so I thought perhaps others would like to try it too.
In this post I have added the CAD files, as well as an additional model library so you can easily test the different objects yourself.
Running in Mathematica
Note that System Modeler is used for the animations, so when you evaluate these commands it will only work if you have System Modeler installed (otherwise you will get a message with a link to a page with info about System Modeler).
Running in System Modeler
If you would like to simulate other objects you can change that in the model:
Note that gravity is set to 0. If you want to change that or the initial velocities you can see how to do that in the video. For the satellite you probably want to change simulation time.
Have fun exploring!
If I change the 'g' from 0 to 9.8. I still see this effect. Shouldn't it is possible only when g =0.
I think you should still see it, even though it will be a disturbed version (as illustrated in the tennis racket example) where you add a constant acceleration in the direction of the gravity.
In a realistic case the object fall to the ground before you have time to see any pattern for it. By removing gravity you just make it a lot easier to observe the phenomena.