Reduced expansion of the perturbating function

Let us consider the first order secular Hamiltonian for the 3-body problem, i.e., the perturbating function averaged with respect to the mean anomalie s. We exhibit two sets of variables, quadratic with respect to the usual os culating elements and isometry-invariant. In each of them this function may be expanded in a neighborhood of the circular coplanar point. Each set con tains six variable, linked by a relation. We give the first terms of the ex pansion in the second set. (C) 2001 Academie des sciences/Editions scientif iques et medicales Elsevier SAS.