First- and Second-Order Partial Derivatives of Free-Flight Range and Time Equations for Impact Accuracy of Ballistic Missiles

摘要

Calculation of the impact error of a ballistic missile as a result of perturbation in the cutoff conditions can be accomplished by use of a Taylor Series. This requires the determination of the partial derivatives of the free-flight range and time-of-flight equations. First- and second-order partial range and time derivatives were obtained for several coordinate systems. These derivatives are plotted against cutoff conditions for a wide range of minimum energy (maximum range) trajectories. Several special conditions are noted. (Author)