Equations of satellite motion about the center of mass

Matrix equations of motion about the center of mass are derived in quasi-coordinates in the Euler-Lagrange form for satellites with various damping devices. These include a satellite treated as a solid body; a satellite with one damping rotor and several rotors rotating at a constant (with respect to the satellite) rate; a satellite/stabilizer system with rotors mounted on the satellite and the stabilizer; a satellite/stabilizer system in a three-degrees-of freedom gimbal mounting; a satellite/stabilizer system with a one-degree-of freedom pin-connection between the satellite and each of the stabilizers; a satellite/stabilizer system with a two-degrees-of-freedom suspension; and a satellite with several gimbal-mounted gyroscopes. Necessary and sufficient conditions are obtained for the asymptotic stability of the steady-state solutions of the equations derived.