上海科技大学知识管理系统

We study the secular behaviour of a test particle orbiting a dominant central body and perturbed by a Miyamoto-Nagai (MN) disc eta We derive a quadrupole-level secular Hamiltonian of this system, which involves a dimensionless parameter. that is used to characterize the flattening of MN disc eta (The smaller., the flatter disc; and eta = 0 gives the infinitely thin Kuzmin disc.) We find that, in the quadrupole approximation, the perturbation of the MN disc can give rise to the von Zeipel-Lidov-Kozai (ZLK)-like dynamics and depending on the value of. the dynamics has two different manifestations: (i) when eta < 1/3, the test particle's behaviour is similar to that described in the classical ZLK problem. In particular, as eta increases from 0 to 1/3, the critical inclination for the large eccentricity oscillations decreases from 26 degrees, 56 to 0 degrees; (ii) when eta > 1/3, the orbital evolution of the test particle and the phase-space morphology are opposite to the classical ZLK case. This leads to a striking result that the test particle cannot remain on a near-coplanar orbit if its eccentricity is sufficiently large. However, as eta increases further the ZLK-like dynamics would be gradually suppressed by the spherical term in the Hamiltonian. We also survey the global secular dynamics numerically in which the quadrupole approximation is no longer valid.