Spacecraft attitude control with simultaneous unloading of the angular momentum of inertial actuators

A method is proposed for solving the problem of controlling finite eigenvalues of a descriptor linear dynamic system, which is based on the original decomposition of the model of the initial system that is unsolved for the derivatives and is defined in the space of states. This method has no restrictions on the algebraic and geometric multiplicity of the finite eigenvalues and enables analytical synthesis of control laws. Using the proposed method in the case of circular orbits, we obtain the analytical solution for the problem of spacecraft attitude control with simultaneous unloading of the angular momentum of the inertial actuators. The results of the mathematical modeling are presented.