Quaternion regularization and trajectory motion control in celestial mechanics and astrodynamics: II

Problems of regularization in celestial mechanics and astrodynamics are considered, and basic regular quaternion models for celestial mechanics and astrodynamics are presented. It is shown that the effectiveness of analytical studies and numerical solutions to boundary value problems of controlling the trajectory motion of spacecraft can be improved by using quaternion models of astrodynamics. In this second part of the paper, specific singularity-type features (division by zero) are considered. They result from using classical equations in angular variables (particularly in Euler variables) in celestial mechanics and astrodynamics and can be eliminated by using Euler (Rodrigues-Hamilton) parameters and Hamilton quaternions. Basic regular (in the above sense) quaternion models of celestial mechanics and astrodynamics are considered; these include equations of trajectory motion written in nonholonomic, orbital, and ideal moving trihedrals whose rotational motions are described by Euler parameters and quaternions of turn; and quaternion equations of instantaneous orbit orientation of a celestial body (spacecraft). New quaternion regular equations are derived for the perturbed three-dimensional two-body problem (spacecraft trajectory motion). These equations are constructed using ideal rectangular Hansen coordinates and quaternion variables, and they have additional advantages over those known for regular Kustaanheimo-Stiefel equations.