Abstract
In this paper we consider the translational and rotational motion of satellites around the Earth. First, we study the motion of an arrow-type satellite. We consider the system of equations of motion in the first approximation. We consider the linear Hamiltonian systems of differential equations. The Hamiltonian systems arise in transportation problems. We consider the normalization of Hamiltonian matrix. We solve the system of matrix equations to find the generating function of the canonical transformation. We obtain stability criterion in several cases. Further, we study the motion of a spoke-type satellite. We consider eigenvalues of characteristic equation corresponding to the motion equations. We get the normal form of the Hamiltonian matrix. We obtain the stability criterion.
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