Qualitative analysis of the phase flow of an integrable approximation of a generalized roto-translatory problem
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AbstractIn 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.
2010 ◽
Vol 20
(09)
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pp. 2809-2821
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2000 ◽
Vol 20
(2)
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pp. 611-626
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1991 ◽
Vol 24
(1)
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pp. L31-L34
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2021 ◽
Vol 29
(6)
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pp. 835-850
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2018 ◽
Vol 20
(4)
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pp. 408-418