The process of capture into a mean motion resonance induced by a non conservative force has been studied by many authors (Henrard, 1982); Peale, 1986). Capture probabilities have been established through the use of an analytical model based on averaged Hamiltonian systems, with an adiabatic varying parameter (Henrard, 1982; Lemaitre, 1984). For each resonance, these probabilities are basically function of the orbital element involved (eccentricity and/or orbital inclination) far from the resonance and the perturber's mass, there being no dependence on the dissipation rate. However when the process is not adiabatic, the dissipation rate has a fundamental importance for capture probabilities (Gomes, 1995). For these processes, an analytical association of orbital elements far from the resonance with capture probabilities is still an open question. Association of orbital elements just before resonance with the process of capture is presented in (Marzari and Vanzani, 1994) and (Lazzaro et al, 1994). In these works the eccentricity and longitude of the perihelion are checked for in respect with capture into resonance. Here we aim at verifying how the trapping process changes with orbital elements just before resonance, but not restricting ourselves to the pair eccentricity-perihelion.
Numerical analysis of degenerate Kolmogorov equations of constrained stochastic Hamiltonian systems
