Periodic motion near non-principal-axis rotation asteroids

The periodic motion near non-principal-axis (NPA) rotation asteroids is proved to be markedly different from that near uniformly rotating bodies due to the complex spin statewith precession, raising challenges in terms of the theoretical implications of dynamical systems. This paper investigates the various periodic motions near the typical NPA asteroid 4179 Toutatis, which will contribute to the understanding of the dynamical environments near the widespread asteroids in the Solar system. A novel method with the incorporation of the ellipsoid-mascon gravitational field model and global optimization is developed to efficiently locate periodic solutions in the system. The numerical results indicate that abundant periodic orbits appear near the NPA asteroids. These various orbits are theoretically classified into five topological types with special attention paid to the cycle stability. Although the concept of classical family disappears in our results, some orbits with the same topological structure constitute various generalized 'families' as the period increases. Among these 'families' a total of 4 kinds of relationships between orbits, including rotation, evolution, distortion and quasi-symmetry, are found to construct the global mapping of these types. To cover the rotation statuses of various NPA asteroids, this paper also discusses the variation of periodic orbits with diverse asteroid spin rates, showing that the scales of some orbits expand, shrink or almost annihilate as the system period changes; meanwhile, their morphology and topology remain unchanged.