An exact differential form to check analytical theories

Abstract

As a result of a Von Zeipel's elimination of periodic arguments, the linear differential form ∑W i dv i , where theW i 's are the constant actions and thev i 's the mean motions of the averaged angles, is exact, because, as we prove here, it is the differential of the principal function averaged over the new angles. We propose to use this exact form to check the analytical expressions developed from an elimination of periodic arguments, and we take as an example the main problem of artificial satellites.