On an attitude stabilizing condition for a launch vehicle

Conventional closed-loop guidance commands are usually generated from a simplified point mass model. In real situations including computer simulations, however, the generated guidance commands are applied to a full rigid body model. This can cause attitude instability of the vehicle. In this paper, the effect of the guidance commands, generated from a point mass model, on the full rigid body model is analyzed quantitatively, and an attitude stabilizing strategy is proposed. An attitude stabilizing condition for the rigid body model is derived by using the Lyapunov stability theorem. The stabilizing condition derived can be used to stabilize the attitude of a launch vehicle by applying the corresponding feedforward guidance commands when the commands generated from a point mass model destabilize or undetermine the attitude of a launch vehicle. Computer simulations have been performed to verify our conjecture for the second stage of the Japanese N-I launch vehicle.