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| Relative equilibria of an intermediary in attitude dynamics of a generic triaxial spacecraft in a circular orbit under gravity-gradient perturbation are discussed. Intermediary defines a Poisson flow over a large parameter space: three physical parameters (moments of intertia) and three distinguished parameters, the integrals $M, G_3$ and $n$. In the case of slow motion we identify conditions under which different bifurcations of the classic unstable trajectories occur, scenario of great interest in relation to stabilization and control purposes. Our study is based on the use of the invariants defining the full reduced $\mathbb{S}^2\times \mathbb{S}^2$ space orbital space and the associated energy-momentum mapping. We identify bifurcation curves along which the system shows degeneracy, connected with the change of stability of the classic unstable equilibria of the second reduced space (Euler system). The role played by the triaxiality is illustrated with several examples. |
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