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Zbl 0831.70006
Hanssmann, Heinz
Normal forms for perturbations of the Euler top. (English)
[A] Langford, William F. (ed.) et al., Normal forms and homoclinic chaos. Proceedings of a Workshop, held at The Fields Institute for Research in Mathematical Sciences, Waterloo, Canada, November 13-16, 1992. Providence, RI: American Mathematical Society. Fields Inst. Commun. 4, 151-173 (1995). ISBN 0-8218-0326-3

Summary: A method for studying the behaviour of a rigid body in a general force field is proposed. The study is restricted to the case of a perturbation of the Euler top by a small external force. A normal form approach yields a formal 2-torus symmetry, which is turn leads to the reduction to a one- degree-of-freedom system. The behaviour of this system is used to identify quasi-periodic motions of the rigid body with two or three independent frequencies. The method is tested in the integrable cases of Lagrange and Kirchhoff. Furthermore, it is applied to other cases in which two of the principal moments of inertia of the rigid body are equal.

MSC 2000:: *70E20 Perturbation methods for Euler's equations
70E15 Motion of rigid bodies
37J99 Finite-dimensional Hamiltonian etc. systems

Keywords: equal principal moments of inertia; 2-torus symmetry; one-degree-of- freedom system; quasi-periodic motions

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