The role of different sets of variables in analytical or semianalytical solutions to the artificial satellite theory is reviewed. In particular, it is shown that using polar-nodal variables or non-singular variables based on them is clearly advantageous in the evaluation of the transformation from mean to osculating elements.
Lara, M. (2016). Analytical and semianalytical propagation of space orbits: The role of polar-nodal variables. In Astrophysics and Space Science Proceedings (Vol. 44, pp. 151–166). Kluwer Academic Publishers. https://doi.org/10.1007/978-3-319-23986-6_11