Resumo:
The objective of this work is to present a model in tidal theory using what is known
in the literature as the gravitational dumbbell model. To this end, we initially study in
detail the foundations of the problem, such as the solutions to the two-body problem,
Kepler’s Laws, and the perturbative formalism of Delaunay variables. The equations
of motion for the model are based on the Lagrangian formalism of Classical Mechanics,
coupled with dissipative forces through a dissipation function. The obtained results
focus on the stability of the relative equilibria, which depend on the considered level of
angular momentum. We propose an analysis of the model alternative to that found in
the literature, using tools from the qualitative theory of ordinary differential equations,
providing a more precise and detailed description of the dynamics involved.