The HD,196885 system is composed of a binary star and a planet orbiting the primary. The orbit of the binary is fully constrained by astrometry, but for the planet the inclination with respect to the plane of the sky and the longitude of the node are
unknown. Here we perform a full analysis of the HD,196885 system by exploring the two free parameters of the planet and choosing different sets of angular variables. We find that the most likely configurations for the planet is either nearly coplanar orbits (prograde and retrograde), or highly inclined orbits near the Lidov-Kozai equilibrium points, i = 44^{circ} or i = 137^{circ} . Among coplanar orbits, the retrograde ones appear to be less chaotic, while for the orbits near the Lidov-Kozai equilibria, those around omega= 270^{circ} are more reliable, where omega_k is the argument of pericenter of the planets orbit with respect to the binarys orbit. From the observers point of view (plane of the sky) stable areas are restricted to (I1, Omega_1) sim (65^{circ}, 80^{circ}), (65^{circ},260^{circ}), (115^{circ},80^{circ}), and (115^{circ},260^{circ}), where I1 is the inclination of the planet and Omega_1 is the longitude of ascending node.
We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities, also we assume that both planets share the same orbital p
lane. Initially we perform numerical simulations over a grid of osculating initial conditions to map the regions of stable/chaotic motion and identify equilibrium solutions. These results are later analyzed in more detail using a semi-analytical model. Apart from the well known quasi-satellite (QS) orbits and the classical equilibrium Lagrangian points L4 and L5, we also find a new regime of asymmetric periodic solutions. For low eccentricities these are located at $(sigma,Deltaomega) = (pm 60deg, mp 120deg)$, where sigma is the difference in mean longitudes and Deltaomega is the difference in longitudes of pericenter. The position of these Anti-Lagrangian solutions changes with the mass ratio and the orbital eccentricities, and are found for eccentricities as high as ~ 0.7. Finally, we also applied a slow mass variation to one of the planets, and analyzed its effect on an initially asymmetric periodic orbit. We found that the resonant solution is preserved as long as the mass variation is adiabatic, with practically no change in the equilibrium values of the angles.
