Prediction and Correction of Spacecraft Motion Based on the Solutions of Regular Quaternion Equations in KS-Variables and Isochronous Derivatives

This report considers the problems of prediction and correction of motion of a spacecraft using the solutions of regular quaternion equations in four-dimensional Kustaanheimo-Stiefel variables (KS-variables), which exhibit dramatic computational advantages in the sense of accuracy over the equations in Cartesian coordinates. The new formulas are derived which interrelate the variations of the Cartesian coordinates and the projections of the velocity vector of a spacecraft with the variations of the KS-variables and their first derivatives. The variations of the KS-variables and their first derivatives, and also the matrix of isochronous derivatives of these variables are found. The new linearized regular quaternion differential equations of the perturbed orbital motion of a spacecraft are derived in variations of the KS-variables and their first derivatives.