Qualitative analysis of the phase flow of an integrable approximation of a generalized roto-translatory problem |
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Authors: | María del Carmen Balsas Elena S Jiménez Juan A Vera Antonio Vigueras |
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Institution: | (1) Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena (Murcia), Spain |
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Abstract: | In this paper, we consider an integrable approximation of the planar motion of a gyrostat in Newtonian interaction with a
spherical rigid body. We then describe the Hamiltonian dynamics, in the fibers of constant total angular momentum vector of
an invariant manifold of motion. Finally, using the Liouville-Arnold theorem and a particular analysis of the momentum map
in its critical points, we obtain a complete topological classification of the different invariant sets of the phase flow
of this problem. The results can be applied to study two-body roto-translatory problems where the rotation of one of them
has a strong influence on the orbital motion of the system.
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Keywords: | Liouville-Arnold theorem gyrostat invariant manifolds amended potential Hill regions |
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