A deeper look at resonance trapping

The problem of resonance trapping is further analyzed by the consideration of a quasi Hamiltonian model, which is the classical one-degree-of-freedom Hamiltonian model, modified by the inclusion of a nonconservative term for the derivative of the momentum. A new formulation to compute capture probabilities is deduced, which is a function of the particular nonconservative force involved. The new results can be quite different from those associated with the classical model, when the extra term for the variation of the momentum is not negligible in comparison with the variation of the resonance detuning parameter. This is the case of resonance trappings induced by gas drag. In this new formulation, we study all possible cases of resonance trappings as combinations of converging and diverging orbits with interior and exterior resonances. We find the possibility of resonance trapping for diverging orbits, although the cases for which they occur have not been found to be associated to any real Solar System force.