Study of the roto-orbital motion using intermediaries: numerical experiments

Abstract

The purpose of the present study is to test two recently proposed integrable models to study the roto-orbital motion of an axisymmetric rigid body, considering this body under the influence of a central gravitational field. Based on the concept of intermediary, both models are treated in Hamiltonian formalism, as perturbation of the Keplerian–Eulerian motion, using canonical variables associated with the total angular momentum. Parameters are introduced to visualize possibilities for different applications; nevertheless, we concentrate on the binary asteroid-type dynamics. Numerical experiments compare the two intermediaries with respect to the original model. Several values for attitude, shape, orbital eccentricity and distance are considered for systems with a slow-rotating axisymmetric rigid body in an eccentric relative orbit, i.e., with significant disturbing effects. In general, both models present good precision in wide regions of the dynamical parameters spaces defined.