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New quaternion models of spaceflight regular mechanics and their applications in the problems of motion prediction for cosmic bodies and in inertial navigation in space

This report considers the problems of regularizing the models of spaceflight mechanics, inertial navigation in space, motion prediction for cosmic bodies and spacecrafts. Our report shows the results of comparing the accuracy of numerical integration of the classical Newtonian differential equations (DE) of the spatial restricted three-body problem (the Earth, the Moon and a spacecraft) in Cartesian coordinates and the regular quaternion DE in four-dimensional Kustaanheimo-Stiefel variables (KS-variables) for the same problem, which were derived by the authors of this report.