Analytical study of spinning solid upper stage dynamics

Analytical solutions for the spinning vehicle dynamics during the burning phase in vacuum were derived. These solutions explicity incorporate the effects of thrust misalignment, gravity gradient torques, jet damping, dynamic unbalance and spin rate variations. These expressions are useful in preliminary design studies of spinning upper stages of launch vehicles. The main advantages of this approach lies in the fact that the time required to carry out detailed parametric studies is one order lower than regular 6 DOF simulations. The application of this approach for a typical Shuttle Launched Spinning Solid Upper Stage (SSUS) mission incorporating AS-05-A payload is illustrated.