Analysis of stability and dynamical behavior near triangular libration points in the restricted five-body problem
摘要
The paper is an investigation of the motion of a spacecraft around triangular libration points of the restricted five-body problem (R5BP) and its stability. With the assumption that the spacecraft moves in gravitational environments of four primaries, the configuration is such that the first primary is located at the origin of the coordinate system, while the second primary is collinear with the first primary, and the third and fourth are located above and below, on the left of the first primary. The equations of motion are established, and the locations of the libration points, zero velocity curve, stability of the libration points, and the Poincaré surfaces of sections are thoroughly investigated analytically and numerically when the mass of the first primary is varied. It is observed that when the mass of the first primary is increasing, the position of the spacecraft drifts away from the first primary. Further, it is seen that the increasing mass of the first primary reduces the region where motion of the spacecraft is allowed around the triangular points. Finally, the Poincaré Surface of section was explored, and it was seen that as the mass of the first primary is increasing, more clusters were noticed around the primaries, and this shows the presence of stable or quasi-periodic orbits, which correspond to regular motion. Consequently, the orbits are stable. The problem can be applied to study the motion of a spacecraft in the environments of Jupiter and its three Moons.