Perturbed Spatial Two-Body Problem: Regular Quaternion Equations of Relative Motion

Within the perturbed spatial two-body problem, the regular quaternion differential equations are proposed for the perturbed motion of the second (studied) body relative to a coordinate system rotating in an inertial coordinate system obeying an arbitrarily set law, and relative to the coordinate system associated with the Earth taken to be the first (central) body. The first integrals and the solution of the regular quaternion differential equations of the unperturbed motion of the studied body relative to the Earth are obtained using the Stumpf functions.