DYNAMICS OF AN ELASTIC SATELLITE WITH INTERNAL FRICTION. ASYMPTOTIC STABILITY VS COLLISION OR EXPULSION

In this thesis, we study the dynamics of an elastic body, whose shape and position evolve due to the gravitational forces exerted by a pointlike planet whose position is fixed in space. The first result of this thesis is that, if any internal deformation of the body dissipates some energy, then the dynamics of the system has only three possible final behaviors: (i) the satellite is expelled to infinity, (ii) the satellite falls on the planet, (iii) the satellite is captured in a synchronous orbit. By item (iii) we mean that the shape of the body reaches a final configuration, that a principal axis of inertia is directed towards the attracting planet and that the center of mass of the satellite moves on a circle of constant radius. Secondly, we study the stability of the synchronous orbit. Restricting to the quadrupole approximation and assuming that the body is very rigid, we prove that such an orbit is (locally) asymtotically stable, both in the case of a triaxial satellite and in the case of a satellite with spherical symmetry. Some additional results on the dynamics of the body close to the synchronous orbit and some new kinematical results are also present in the thesis.