Poisson Series Algebra in the Problem of Celestial Body Rotation around its Mass Center

The perturbed canonical equations of the problem of celestial body rotation about its center of mass are considered. Solutions are constructed via Hori's method [1]. All the operations of the method mentioned are prepared as simple action over Poisson's series depending on several variables which are based on Andoyer's angles and integrals of the unperturbed problem. Such variables are defined for a nonsymmetric rigid body and for a symmetric magnetised satellite of the Earth. In the first case variables mentioned are constructed by means of Poinsot's geometrical interpretation of the motion. In the second case these are built through intermediate canonical transformations that transfer the top of some hyperbolid to a point that corresponds to a regular precession of the satellite.