Phase structure of co-orbital motion with Jupiter

In this paper, we investigate the dynamics of the inclined co-orbital motion with Jupiter through a torus phase structure in the Sun-Jupiter circular restricted three-body problem. A semi-analytical method to establish the Hamiltonian approximation for the inclined co-orbital motion is proposed. Phase structures of different kinds of co-orbital behaviours are shown in the torus space clearly. Based on numerical computation, we analyse the evolution and the connection of different co-orbital dynamics. Summarizing results and conclusions in this paper, we find two main principles throughout the investigation of the co-orbital motion: (i) the libration amplitude of the resonant angle for the co-orbital motion is bounded by the corresponding Hamiltonian isosurface in the torus space and (ii) the co-orbital behaviour is influenced by collision curves, and with the decrease of the Hamiltonian value, the influence is more significant.