Symmetric Reduction and Hamilton-Jacobi Equation of Rigid Spacecraft with a Rotor

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In this paper, we consider the rigid spacecraft with an internal rotor as a regular point reducible regular controlled Hamiltonian (RCH) system. In the cases of coincident and non-coincident centers of buoyancy and gravity, we give explicitly the motion equation and Hamilton-Jacobi equation of reduced spacecraft-rotor system on a symplectic leaf by calculation in detail, respectively, which show the effect on controls in regular symplectic reduction and Hamilton-Jacobi theory.