97-261 Heinz Han{\ss}mann

Quasi-periodic Motions of a Rigid Body I --- Quadratic Hamiltonians on the Sphere with a Distinguished Parameter (328K, PostScript, gzipped and uuencoded) May 12, 97

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Abstract. The motion of a dynamically symmetric rigid body, fixed at one point and subject to an affine (constant$+$linear) force field is studied. The force being weak, the system is treated as a perturbation of the Euler top, a superintegrable system. Averaging along the invariant $2$-tori of the Euler top yields a normal form which can be reduced to one degree of freedom, parametrised by the corresponding actions. The behaviour of this family is used to identify quasi-periodic motions of the rigid body with two or three independent frequencies.

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