The integrability of various schemes for averaging the differential equations of translational - rotational motion of a rigid body in the field of attraction of a sphere, stated in Delaunay - Andoyer canonical variables, is investigated. The Gauss and Moiseev averaging schemes give rise to equations integrable in the case of three - dimensional motion of rigid bodies. The Fatou and Delaunay - Hill averaging schemes are integrable solely in the case of translational - rotational motion of bodies in the plane. The operation of inversion of the first integrals is carried out for each averaging scheme to be integrated.
Department of Celestial Mechanics and Gravimetry
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