Quaternion-Based Coordinates for Nonsingular Modeling of High-Inclination Orbital Transfer

Abstract

A study to conducted to present the new coordinates and equations of motion, and to validate the formulation on the low-thrust orbit-raising problem. The equations of motion for a single particle in orbit about the Earth were presented for conducting the investigations. The previous formulation was reviewed using spherical coordinates to show how singularities could be removed by introducing quaternions to replace the usual two angle coordinates. It was demonstrated that this formulation had the added benefit of keeping all variables of order unity in addition to removing the singularity. It was also demonstrated that a nonsingular formulation of the equations of motion needed to be provided to investigate high-inclination orbits. Two main alternatives were available for this purpose, such as applying variation of parameters or changing coordinate system.