Planar rotations for a gyrostat in the three-body problem
Knowledge 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
2007-11-15Publisher
Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de ZaragozaBibliographic Citation
VERA LÓPEZ, Juan Antonio, VIGUERAS CAMPUZANO, Antonio. Planar rotations for gyrostat in the three-body problem. En: Jornadas de trabajo en Mecánica Celeste( 9.2006.Jaca ). Zaragoza: Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, 2007. pp.67-78. ISBN 1132-6360Keywords
Equilibrio relativoProblemas de tres cuerpos
Plano de rotación
Relative balance
Gyrostat
Three body problems
Rotation plan
Giróstato
Abstract
We consider the non-canonical Hamiltonian dynamics of a gyrostat in the three
body problem. By means of geometric-mechanics methods we study the approximate Poisson dynamics that arises when we develop the potential in series of Legendre and truncate this in an arbitrary order k. Working in the reduced problem,the existence and number of equilibria, that we denominate planar rotation type in analogy with classic results on the topic, is considered. Necessary and sufficient conditions for their existence in a approximate dynamics of order k is obtained and we give explicit expressions of this equilibria, useful for the later study of the stability of the same ones. A complete study of the planar rotation type equilibria is
made in approximate dynamics or order zero and one.
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