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Zbl 0847.70009
Hanssmann, Heinz
Equivariant perturbations of the Euler top. (English)
[A] Broer, H. W. (ed.) et al., Nonlinear dynamical systems and chaos. Proceedings of the dynamical systems conference, held at the University of Groningen, Netherlands in Dec. 1995, in honour of Johann Bernoulli. Boston, MA: Birkhäuser. Prog. Nonlinear Differ. Equ. Appl. 19, 227-252 (1996). ISBN 3-7643-5346-5/hbk

Summary: The motion of a rigid body in a small non-constant force field is studied. A normal form approach yields a formal 2-torus symmetry, which in turn allows to reduce the system under consideration 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. \par The external force field is supposed to be invariant under two special reflections. This $\bbfZ_2 \times \bbfZ_2$-symmetry influences the distribution of invariant tori. To simplify the necessary calculations, two of the principal moments of inertia of the rigid body are set equal. Furthermore, the study is concentrated on the case of an affine (constant+linear) force field.

MSC 2000:: *70E20 Perturbation methods for Euler's equations
37J40 Perturbations, etc.

Keywords: affine force field; normal form approach; 2-torus symmetry; quasi-periodic motions; distribution of invariant tori

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Zentralblatt MATH Berlin [Germany]