Revisiting Vinti Theory for the Main Problem
The Vinti model is a intermediary dynamical model that approximates the two-body plus J2 model, but has a closed form solution when solved in oblate spheroidal coordinates.
Biria, A. D. and Russell, R. P., “A Satellite Relative Motion Model Including J2 and J3 via Vinti’s Intermediary,” Celestial Mechanics and Dynamical Astronomy, Vol. 130, Article 23. doi: 10.1007/s10569-017-9806-4, https://doi.org/10.1007/s10569-017-9806-4; http://rdcu.be/HGId
link to .m code
Biria, A., Russell, R.P., “Equinoctial Elements for Vinti Theory: Generalizations to an Oblate Spheroidal Geometry,” Acta Astronautica, Vol. 153, Dec. 2018, pp. 274-288, https://doi.org/10.1016/j.actaastro.2017.11.013
link to .m code
Also see Biria, A. D. and Russell, R. P., “Analytical Solution to the Vinti Problem in Oblate Spheroidal Equinoctial Orbital Elements,” The Journal of the Astronautical Sciences (2019), https://doi.org/10.1007/s40295-019-00179-y.
link to .m code