Analytical Prediction Model of Stability Boundary for Guided Projectiles

Abstract

Aiming at the problem of projectile stability under the action of control force, this paper studied the analytical prediction model of stability boundary for guided projectiles. By linearizing the longitudinal axial angular velocity of body axis coordinate, the angular motion equation under the body axis coordinate is established. Through linearizing the roll angle between the body axis coordinate and non-rolling coordinate, a five-order equation of angular motion is proposed under the non-rolling coordinate. Using the stability theory of linear system, the analytical prediction model of stability boundary under the body axis coordinate and non-rolling coordinate are obtained. Simulations of the two models under various working conditions are conducted. Results indicate that the proposed model under the body axis coordinate can be applied in the rising arc segment and the falling arc segment, whereas the control force orientation is limited. The model under the non-rolling coordinate is not limited by the control force orientation, and the prediction accuracy is good. The drawback of this model is that it can only be used for the falling arc section, and its accuracy will be harmfully affected by excessive control force. It is suggested that the two models should be applied comprehensively in practical engineering.

Keywords

• |controllable projectiles|controllable force|angular motion|stability|body axis coordinate|non-rolling coordinate