Heinz Han{\ss}mann
Quasi-periodic Motions of a Rigid Body II 
--- Implications for the Original System
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ABSTRACT.  This is a sequel to [Han{\ss}mann;97-261]. The original system, 
while being an $\varepsilon$-perturbation of the Euler top, is 
$\varepsilon^2$-close to its normal form approximation. The normal form 
automatically `removes the degeneracy' of the superintegrable Euler top 
and KAM-theory allows to conclude that a large part of the phase space 
is filled by Cantor families of invariant $3$-tori. The way these 
$3$-tori are distributed in phase space is determined by persisting 
invariant $2$-tori, serving as `landmarks' in the same way as the 
equilibria did for the one-degree-of-freedom systems treated in 
[Han{\ss}mann;97-261]. The rigid body motion along such $2$-tori closely 
follows the rotational-precessional motion of the Euler top.