Stability of two groups of multi-revolution elliptic halo orbits in the elliptic restricted three-body problem

The multi-revolution elliptic halo (ME-Halo) orbit is a kind of strictly periodic orbit existing in the elliptic restricted three-body problem (ERTBP) model. Its remarkable features include that it survives the eccentricity perturbation of the primaries, it has a long period commeasurable with the primary period and that its stability property varies greatly as the eccentricity. The authors utilized continuation methods together with the multi-segment optimization method to generate two groups of ME-Halo orbits, and then systematically investigated their stability evolution with respect to the eccentricity and the mass ratio of the primaries. These parameters show complicate impacts on the stability. Some ME-Halo orbits can possess more than one pairs of real eigenvalue, some have negative real eigenvalues or complex eigenvalues out of the unit circle. For certain parameters, continuation failures are observed to be accompanied by a series of eigenvalue collision and bifurcations. The results in this paper can help to understand the nonautonomous dynamic of the ERTBP and can further aid in understanding the dynamical environment for real-world applications and, thus, contribute to the trajectory development process.