On the homogeneous form of the differential equations of relative motion of the three-body problem

Abstract

It has previously been shown (Celestial Mechanics, Vol. 6 Nº 2, September 1972) that the system of differential equations of relative motion of the three-body problem can br brought into a homogeneous form. We give here an account of some additional proofs concerning the conditions of convergence of the geometric process used to obtain the new equations as well as a theorem due to Kolmogorov to consider analytical aspects of the problem.