http://arxiv.org/abs/1403.0405
The order and chaos of the motion near equilibrium points in the potential of a rotating highly irregular-shaped celestial body are investigated from point of view of the dynamical system theory. The non-degenerate equilibrium point is continuous with continuous parameter changes. The topological structure in the vicinity of equilibrium points has 6 ordinary cases, 3 resonant cases, 3 degenerate real saddle cases, 1 degenerate-equilibrium and resonant case, as well as 1 degenerate-equilibrium and degenerate real saddle case. A minimum estimate for the number of periodic orbits on a fixed energy hypersurface is presented. Resonant equilibrium points are found to be Hopf branching points and lead to the appearing and disappearing of periodic orbits and tori. The possible topological transfer between different cases for equilibrium points is discovered. The conclusions are suitable for all kinds of rotating celestial bodies, simple-shaped or highly irregular-shaped, including asteroids, comets, planets and satellites of planets. Applications to asteroids 216 Kleopatra, 2063 Bacchus and 25143 Itokawa are amazing and interesting: eigenvalues affiliated to the equilibrium point E3 for the asteroid 216 Kleopatra move and always belong to Case O4; while eigenvalues affiliated to the equilibrium point E3 for the asteroid 2063 Bacchus and 25143 Itokawa move though the resonant cases and collision of eigenvalues occurs. Poincar\’e sections in the potential of the asteroid 216 Kleopatra showed the chaos behaviors of the large scale orbits.
Y. Jiang, H. Baoyin, X. Wang, et. al.
Tue, 4 Mar 14
12/61