Abstract

  THE AVERAGING PROCEDURE FOR THE RESONANT SATELLITES ON THE HIGLY
                   ELLIPTIC ORBITS.

  I.V.Tupikova

  Institute of Theoretical Astronomy,S.-Petersburg,Russia


  The  aim of the paper is  to combine  the advantages  of the canonical
transformations  in the averaging  procedure with  the use of the series
in multiples of the elliptic anomaly  w  with the coefficients depending
on  the  Jacobi nome  q  [Brumberg,1992]  instead of the standard  (e,M)
expansions.
  The initial equations of the highly elliptic resonant satellite motion
in the Delaunay variables  have been averaged by  Lie transforms  method
up to the third order of the small parameter,the  (e.M)  expansions have
been replaced by (q,w) expansions in the right-hand sides of the averaged
Lagrange equations and in the formulae connecting  the osculating and the
mean elements.
   It is worth emphasizing that though  w' is not the "slow" variable,the
substitution  l'(w')  in the series  slowly varieng for the mean Delaunay
elements  allows  to decrease  the integration time  not only due  to the
lesser number of terms but due to the increasing of the integration steps.