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

TL;DR

This paper introduces a geometric decomposition-based analytic method for calculating the time derivatives of a rocket's instantaneous impact point, simplifying the process and improving clarity over previous methods.

Contribution

It presents a novel geometric formulation that decomposes IIP derivatives into downrange and crossrange components, making calculations more straightforward and compact.

Findings

The new formulation is easier to understand and implement.

Numerical simulations validate the accuracy of the proposed method.

Abstract

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.