Geometric Decomposition-Based Formulation for Time Derivatives of Instantaneous Impact Point

A new analytic formulation to express the time derivatives of the instantaneous impact point (IIP) of a rocket is proposed. The geometric relationship on a plane tangential to the IIP is utilized to decompose the inertial IIP rate vector into the downrange and crossrange components, and a systematic procedure to determine the component values is presented. The new formulation shows significant advantages over the existing formulation such that the procedure and final expressions for the IIP derivatives are easy to understand and more compact. The validity of the proposed formulation was demonstrated through numerical simulation.