Reduction, relative equilibria and stability for a gyrostat in the N-Body problem
Author
Vera López, Juan AntonioKnowledge Area
Matemática AplicadaSponsors
This research was partially supported by the Spanish Ministerio de Ciencia y Tecnología (Project BFM2003-02137) and by the Consejería de Educación y Cultura de la Comunidad Autónoma de la Región de Murcia (Project Séneca 2002: PC-MC/3/00074/FS/02).Publication date
2004-10-01Publisher
Prensas Universitarias de ZaragozaBibliographic Citation
VERA LÓPEZ, Juan Antonio, VIGUERAS CAMPUZANO, Antonio. Reduction, relative equilibria and stability for a gyrostat in the N-Body problem . En:Monografías del Seminario Matemático García de Galdeano. ed. Zaragoza: Prensas Universitarias de Zaragoza, 2003. pp.257-271. ISBN 84-7733-720-9Keywords
Sistema Lie-PoissonReducción
Equilibrio relativo
Problemas en n-cuerpos
Lie-Poisson System
Reduction
Relative balance
N-body problems
Gyrostat
Giróstato
Abstract
We consider the non-canonical Hamiltonian dynamics of a gyrostat in the nbody
problem. Using the symmetries of the system we carry out a reduction process in two steps, giving explicitly at each step the Poisson structure of the reduced system. Next,we obtain general properties of the relative equilibria of the problem and if we restrict to different approximations of the gravitational potential function, some particular cases are studied and, by means of energy-Casimir and spectral methods, sufficient and necessary conditions of stability can be obtained. We extend some results by Fanny and Badaoui (1998) and by Mondéjar, Vigueras and Ferrer (2001). In the case of a rigid body in the three-body problem, in terms of the global variables in the unreduced problem, was considered, and in the case of a gyrostat in the three-body problem was studied, but working now in the reduced system; in this way natural simplifications in the conditions
of the equilibria appear. As a particular case, ...
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