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Journal
2009 | 7 | 1 | 67-78
Article title

Qualitative analysis of the phase flow of an integrable approximation of a generalized roto-translatory problem

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EN
Abstracts
EN
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.
Publisher
Journal
Year
Volume
7
Issue
1
Pages
67-78
Physical description
Dates
published
1 - 3 - 2009
online
8 - 1 - 2009
References
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  • [5] E. Leimanis, The general problem of the motion of coupled rigid bodies about a fixed point (Springer Verlag, Berlin, 1965)
  • [6] J. Llibre, A. E. Teruel, C. Valls, A. de la Fuente, J. Phys. A-Math. Gen. 34, 1919 (2001) http://dx.doi.org/10.1088/0305-4470/34/9/309[Crossref]
  • [7] F. Marchis, P. Descamps, D. Hestroffer, J. Berthier, I. de Pater, American Astronomical Society 36, 1180 (2004)
  • [8] J. A. Vera and A. Vigueras, Advances in the Astronautical Sciences 123, 2775 (2005)
  • [9] J. A. Vera, A. Vigueras, Celest. Mech. Dyn. Astr 94, 289 (2006) http://dx.doi.org/10.1007/s10569-005-5910-y[Crossref]
  • [10] L. S. Wang, K. Y. Lian, P. T. Chen, IEEE. T. Automat. Contr. 40, 1732 (1995) http://dx.doi.org/10.1109/9.467678[Crossref]
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-008-0140-z
Identifiers
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