99-266 Heinz Han{\ss}mann
Quasi-periodic Motions of a Rigid Body II --- Implications for the Original System (208K, PostScript, gzipped and uuencoded) Jul 12, 99
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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.

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