Linear stability of inner case of double averaged spatial restricted elliptic three-body problem

We study the secular effects in the motion of an asteroid with negligible mass in a spatially restricted elliptic three-body problem with arbitrary inclination. Averaging over mean anomalies of the asteroid and the planet is applied to obtain the double-averaged Hamiltonian system. It admits a two-parameter family of orbits corresponding to the motion of the asteroid. Our investigation aims to analyze the stability of these orbits in the inner case. We show that these orbits are stable in the linear approximation with spatial perturbation. Numerical simulations of different types of orbits are performed as well.