On eulerian equilibria in K-order approximation of the gyrostat in the three-body
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AuthorVera López, Juan Antonio
Knowledge AreaMatemática Aplicada
SponsorsThe authors are grateful to the referee for his useful suggestions and comments which improved the paper. This research was partially supported by the Spanish Ministerio de Ciencia y Tecnologìa (Project BFM2003-02137) and by the Consejerìa de Educaciòn y Cultura de la Comunidad Autónoma de la Región de Murcia (Project S´eneca 2002: PCMC/ 3/00074/FS/02).
PublisherHindawi Publishing Coorporation
Bibliographic CitationVERA LÓPEZ, Juan Antonio, VIGUERAS CAMPUZANO, Antonio. On eulerian equilibria in K-order approximation of the three-body. International Journal of Mathematics and Mathematical Science, (2006): 1-17, 2006
KeywordsEquilibrio Euleriano en un orden-K
Problema de tres cuerpos
We consider the noncanonical 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 of Euler type in analogy with classic results on the topic,are considered. Necessary and sufficient conditions for their existence in an approximate dynamics of order k are obtained and we give explicit expressions of these equilibria, useful for the later study of the stability of the same ones. A complete study of the number of Eulerian equilibria is made in approximate dynamics of orders zero and one. We obtain the main result of this work, the number of Eulerian equilibria in an approximate dynamics of order k for k ≥ 1 is independent of the order of truncation of the potential if the gyrostat S0 is close to the ...
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