%0 Journal Article 
%A Vera López, Juan Antonio
%T On eulerian equilibria in K-order approximation  of the gyrostat in the three-body
%D 2006
%@ 1978-9999
%U http://hdl.handle.net/10317/455
%X 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 sphere. The instability of Eulerian equilibria is proven for any approximate dynamics if the gyrostat is close to the sphere. In this way, we generalize
the classical results on equilibria of the three-body problem and many of those obtained
by other authors using more classic techniques for the case of rigid bodies.
%K Matemática Aplicada
%K Equilibrio Euleriano en un orden-K
%K Problema de tres cuerpos
%K Giróstato
%~ GOEDOC, SUB GOETTINGEN