The strong stability of most natural motions

Problems of Hamiltonian Mechanics can generally be simplified by some Von Zeipel transformations which reduce the influence of short period parameters and lead to very slowly variable functions: the “quasi-integrals”; however these transformations are implicit and then difficult to use.An explicit construction of the quasi-integrals is presented here and is used to integrate the motion of an artificial satellite perturbed by the zonal harmonics of the Earth gravitational potential; the quasi-integrals are also used to obtain informations on the stability of natural satellites, i.e. lower bounds on the duration of escape or capture.