We investigate the secular dynamics of a planetary system composed of the parent star and two massive planets in mutually inclined orbits .
The dynamics are investigated in wide ranges of semi-major axes ratios ( 0.1–0.667 ) , and planetary masses ratios ( 0.25–2 ) as well as in the whole permitted ranges of the energy and total angular momentum .
The secular model is constructed by semi-analytic averaging of the three-body system .
We focus on equilibria of the secular Hamiltonian ( periodic solutions of the full system ) , and we analyze their stability .
We attempt to classify families of these solutions in terms of the angular momentum integral .
We identified new equilibria , yet unknown in the literature .
Our results are general and may be applied to a wide class of three-body systems , including configurations with a star and brown dwarfs and sub-stellar objects .
We also describe some technical aspects of the semi-numerical averaging .
The HD 12661 planetary system is investigated as an example configuration .