The quasi discovery of planets orbiting around other stars than our Sun, in
a nebular cloud, has given a new motivation to the development of models
combining resonances and drag forces.
In this context we develop a very simplified model, similar to the second
fundamental model of resonance, but including the asymmetric equilibria present
in some of the external mean motion resonances. The calculation of critical
ares and probabilities of capture can explain how and why the orbits are
captured in resonances, and by which paths they escape.
On the other hand, on a more quantitative point of view, we use the
three-dimensional Schubart-like integrator developped by M. Moons for all the
mean motion resonances, completed by the addition of the averaged
contributions of the drag forces; following the same idea as the initial
integrator, we calculate closed forms, without any expansion in series of the
eccentricity or the inclination, for the drag terms. This integrator is
a fast tool for simulations and tests.
We compare our results (especially in two dimensions) with other papers on the
same topic, as Beaugé and Ferraz-Mello, Gomes, Liu and Jackson, etc.