Dinâmica de halteres e teoria de marés

Abstract

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.