Purpose <p>The dynamic characteristics of space-based parabolic antenna structures are significantly influenced by parabolic geometric parameters such as focal length and aperture radius. Therefore, dynamic analysis of space-based parabolic antennas forms the foundation for their structural design.</p> Method <p>The structural dynamics problem of a parabolic antenna connected to a satellite body via cables is simplified into a spatial parabolic flexible damping thin plate-spring-particle dynamic model. Based on Hamilton’s variational principle, a coupled non-smooth mathematical model for the above simplified dynamic model is established. A structure-preserving iterative method coupling the symplectic precise integration method and the generalized multi-symplectic method is developed to solve the coupled mathematical model, aiming to investigate the dynamic behavior of the coupled system under different initial spring elongations and various parabolic geometric parameters.</p> Results and Conclusions <p>From the simulation results, it is found that the stable attitude of the spatial parabolic flexible damping thin plate-spring-particle model is determined by the geometric parameters of the paraboloid, while the time duration required for the model to reach a stable attitude is determined by the symmetry of the initial spring elongations. The above results provide important technical support for the structural design of space-based parabolic antennas.</p>