Canonical solution of the critical inclination problem taking into account PN-corrections

The critical inclination problem in artificial satellite theory and the post-Newtonian (PN) effects on it are discussed. The Hamiltonian is constructed and is expressed in terms of the Delaunay variables containing the zonal harmonics up to <f>J4</f> and the PN contributions up to order <f>J2/cl2</f>. The Hamiltonian is ordered out such that the PN terms are of order <f>J2</f>. Two successive canonical transformations based on Lie series and transform are carried out to remove short- and long-period terms from the Hamiltonian, respectively. Terms are retained up to third order in the secular and to the second order in the periodic terms, where <f>J2</f> is considered of first order. [Copyright &y& Elsevier]