Method of investigation of sharp resonance problems in celestial mechanics and cosmodynamics. T. 1: Orbital motion. (Q2717073)

The first volume of the monograph consists of three parts. The first part presents the method of investigation of stationary and conditionally-periodic solutions in the so-called sharp resonance problems of celestial mechanics and astrodynamics. The method is a generalization of KAM theory to sharp resonance cases by using Delaunay-Zeipel procedure. Here we also present necessary and sufficient conditions for existence of stationary and conditionally-periodic solutions of canonical systems of ordinary differential equations with a sharp commensurability of frequencies.NEWLINENEWLINENEWLINEIn the second part the above-mentioned method is applied to a restricted two-body problem (triaxial planet-satellite), to restricted three-body problems (an asteroidal three-body problem (Sun-Jupiter-asteroid), and a satellite three-body problem (triaxial planet-satellite-third body)). On the plane of parameters depending on the form of the planet and on the orbit orientations of the satellite and the third body (in the three-body problem) we find continuous families of stationary solutions (motions). NEWLINENEWLINENEWLINEIn the third part we determine conditionally-periodic solutions (motions) using stationary solutions (motions) for all the problems examined in the second part. The numerical investigations of analytical solutions and a comparison with pure numerical results show the effectiveness of the method proposed.NEWLINENEWLINENEWLINEThe method can be used for every resonance problem of celestial mechanics and astrodynamics described by canonical system of ordinary differential equations. The second volume of the monograph includes the problems of rotatory-translatory motions of two and three rigid bodies, and is in preparation for publishing.