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Zbl 0935.70006
Hanssmann, Heinz
Quasi-periodic motions of a rigid body. I: Quadratic Hamiltonians on the sphere with a distinguished parameter. (English)
[J] Regul. Khaoticheskaya Din. 2, No.2, 41-57 (1997). ISSN 1560-3547

Summary: We study the motion of a dynamically symmetric rigid body, fixed at one point and subject to an affine (constant+linear) force field. 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, parametrized by the corresponding actions. We use the behaviour of this family 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
70H05 Hamilton's equations
34C27 Almost periodic solutions of ODE

Keywords: averaging procedure; affine force field; perturbation of Euler top; dynamically symmetric rigid body; superintegrable system; invariant 2-tori; normal form; quasi-periodic motions

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