I am trying to understand how to describe the rotation of a solid body flying in 3D space. From physics forums, I understand that the rotation of any solid object in space, is around 2 axes simultaneously.
Can someone help me understand what it means and how can I describe this kind of rotation by Euler angles, axis-angle or with quaternions?
Look here for my previous question in this area, which includes videos of an actual asteroid movement: Aren't asteroids contradicting Euler's rotation theorem?
I would like to describe that movement using one of the above mentioned representations. Is it possible in an easy way? What I had in mind, is that I can write an algorithm like
1. rotates an object around axis A by n degrees 2. rotates axis B around axis A by n degrees 3. rotates the object around axis B by n degrees 4. rotates axis A around axis B by n degrees
And run it in a loop with small n. But I don't know if it would give the above described rotation movement. Is there any literature in mathematics which would describe this "2 axis" rotation?
I asked the previous question in Physics forum here, and I got the following response, what I don't know what to do with.
You might also want to google the phrase "The polhode rolls without slipping on the herpolhode lying in the invariable plane."
together with 2 youtube videos showing objects producing this rotation:
an animation: http://www.youtube.com/watch?v=zmXpSL91fzk
a book on space station: http://www.youtube.com/watch?v=GgVpOorcKqc
Can you tell me where should I start reading and where can I find a method or an algorithm to describe that movement with a common rotation representation? Also, can someone shed some light on what does that polhode statement mean?