Order and chaos near equilibrium points in the potential of rotating highly irregular-shaped celestial bodies

Abstract

Abstract. 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 positions of the non-degenerate equilibrium points vary continuously when the parameter changes. The topological structures in the vicinity of equilibrium points are classified into several different cases.Bifurcations at equilibrium points and the topological transfers between different cases for equilibrium points are also discussed. The conclusions can be applied to all kinds of rotating celestial bodies, simple-shaped or highly irregular-shaped, including asteroids, comets, planets and satellites of planets to help one to understand the dynamical behaviors around them. Applications to asteroids 216 Kleopatra, 2063 Bacchus, and 25143 Itokawa are significant and interesting: eigenvalues affiliated to the equilibrium points for the asteroid 216 Kleopatra move and always belong to the same topological cases; while eigenvalues affiliated to two different equilibrium points for the asteroid 2063 Bacchus and 25143 Itokawa move through the resonant cases of equilibrium points, and the collision of eigenvalues in the complex plane occurs. Poincaré sections in the potential of the asteroid 216 Kleopatra show the chaos behaviors of the orbits in large scale.

Equilibrium points and orbits around asteroid with the full gravitational potential caused by the 3D irregular shape

“…Case O1 is linearly stable, and both of the Case O2 and O4 are unstable. More detailed topological cases of the equilibrium points can be found in Jiang et al [30]. One can use equilibria of the large-size-ratio binary asteroid system to derive the equilibria of a single asteroid.…”

Dynamical configurations of celestial systems comprised of multiple irregular bodies

“…1  and 2  , and 1  is a massless body, then the relative equilibria of the system are equilibrium points for 1  in the body-fixed frame of 2  . More details in similar types of problems about the stability, topological classifications, and bifurcations of relative equilibria can be found in Jiang et al (2015aJiang et al ( , 2015bJiang et al ( , 2015cJiang et al ( , 2016.…”

Spacecraft motion around artificial equilibrium points

“…This is specially true during the times that they are closer to this point. The instability problem exists not only for the point itself, but also for the motion around this point [3]. This instability is also present in the other two collinear equilibrium points, called L 1 and L 2 , but many real applications are considered for these two points [4][5][6][7][8].…”