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Zbl 0970.70008
Hanssmann, Heinz
Quasi-periodic motion of a rigid body under weak forces. (English)
[A] Simó, Carles (ed.), Hamiltonian systems with three or more degrees of freedom. Proceedings of the NATO Advanced Study Institute, S'Agaró, Spain, June 19-30, 1995. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 533, 398-402 (1999). ISBN 0-7923-5710-8/hbk

Summary: We study the motion of a dynamically symmetric rigid body, fixed at one point and subject to an affine (i.e. constant and linear) force field. The force being weak, and the system is treated as a perturbation of Euler top, i.e. as a superintegrable system. A normal form approach yields a formal 2-torus symmetry, which in turn allows to reduce the problem to the study of a one-degree-of-freedom system. We use the behaviour of this system in order to identify quasi-periodic motions of the rigid body with two or three independent frequencies.

MSC 2000:: *70E17 Motion of a rigid body with a fixed point
70E20 Perturbation methods for Euler's equations
70E40 Integrable cases of motion

Keywords: weak force; affine force field; dynamically symmetric rigid body; perturbation of Euler top; superintegrable system; normal form approach; 2-torus symmetry; quasi-periodic motions

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