In this paper, we consider the rigid spacecraft with an internal rotor as a regular point of reducible regular controlled Hamiltonian (RCH) system. In the cases of coincident and non-coincident centers of buoyancy and gravity, we give explicitly the equations of motion and Hamilton-Jacobi equations of reduced spacecraft-rotor system on the symplectic leaves by calculation in detail, which show the effect on controls in regular symplectic reduction and Hamilton-Jacobi theory respectively.
Hong Wang. "Symmetric Reduction and Hamilton-Jacobi Equation of Rigid Spacecraft with a Rotor." J. Geom. Symmetry Phys. 32 87 - 111, 2013. https://doi.org/10.7546/jgsp-32-2013-87-111