Multi-perturbation effects on Lagrangian points in the RTBP with a planetary belt

This study investigates the dynamical behavior of the restricted three-body problem with a planetary belt, focusing on the effects of four key perturbations: three-body interactions, prolate/radiation primaries, and planetary belt mass. Key results show that the prolate coefficient and three-body repulsive interaction significantly determine the existence and type of Lagrangian points, while planetary belt mass, radiation, and three-body attractive interaction only shift their positions. The zero-velocity surface exhibits a potential peak at the planetary belt and a persistent potential well near the prolate primary. All non-collinear Lagrangian points are linearly unstable, with partial collinear points stable. Around linearly stable collinear points, composite motion is quasi-periodic, prolate coefficient increase reduces long-period orbit period/semi-axes but slightly increases those of short-period orbits, and three-body attractive interaction barely impacts long-period orbits. Poincaré section analysis reveals that planetary belt and three-body interactions increase periodic islands, prolate primary suppresses nearby periodic orbits, stronger radiation shrinks orbits, and sufficient Jacobi integral is required for periodic orbits. This work elucidates the multi-perturbation coupling effects and provides a theoretical reference for orbital dynamics analysis in complex perturbation environments.