Why does the spinning book have an unstable axis?

[jpswensen]

I searched through the forums and couldn't find a topic or answer, so I will pose it (possibly again). I can work through deriving the equations of motion (either through Euler-Lagrange methods or Hamilton methods) for the spinning book problem and it is obvious that there *is* an unstable axis, but I am wondering if there is a more fundamental explanation as to *why* this occurs. I guess I can see that it happens in the equations and experiments, but don't have any intuition or understanding as to why this occurs.

I have searched the internet and various mechanics books that show derivations of this problem, but haven't seen an explanation of why. If someone could point me to a good book or article that tries to explain it, I would appreciate it.

 

[K^2]

Because moment of inertia is a tensor, so angular momentum and angular velocity are not co-linear in general. Angular momentum is conserved, which forces angular velocity vector to precess.

 

[Bob S]

There is a comprehensive discussion in Goldstein's book on Classical Mechanics. If an object has three unequal principal moments of inertia, spinning about the intermediate axis is unstable. Look up polhode in Google. There are some Youtube videos that demonstrate the rolling of the polhode on the invariable plane. See

http://www.google.com/url?sa=t&sour...g5ywCw&usg=AFQjCNFWuUf34mlgPymTSWQ5gdCwf552bw

http://www.google.com/url?sa=t&sour...pbCwCw&usg=AFQjCNF3ti1bv9375jQT-cFre4XXoNOyyg

Bob S

 

[Studiot]

Will this do?

(after Acheson)