Simple parameters spaces analysis of roto-orbital integrable Hamiltonians for an axisymmetric rigid body

The present work presents a test of two Hamiltonians that produce integrable models recently proposed to study the roto-orbital motion of an axisymmetric rigid body in motion under a central gravitational field. The dynamics assumed here is approached by the motion of an axisymmetric rigid body orbiting another massive spherical one. Based on the concept of intermediary, both models are treated in Hamiltonian formalism, as perturbation of the Keplerian-Eulerian motion, using canonical variables associated to the total angular momentum. An analysis of parameters introduced to visualize possible different applications are made, in this case with special focus in binary asteroid type dynamics. The parameters space analysis present comparisons of two recently proposed intermediaries with respect to the original non-analytically integrable model and with respect to each other. In conclusion, both models behave well in regions of the parameters space where they were proposed to be valid.