Deployable antennas, as the core content of national defense technology research at this stage, have the advantages of large flexibility and light weight in practical applications, so this type of antenna can also be called a rigid-flexible hybrid structure. According to the theoretical analysis of the dynamics of flexible multi-body systems, it can be seen that effective control of unfolding antennas is a basic requirement for practical applications. Due to the instability of the specific numerical solution of the static Lagrangian function, it is difficult to completely meet the constraint equation, which is also the main factor affecting the steady development of flexible multibody dynamics. Therefore, in-depth discussion of the numerical calculation method of the static Lagrangian function, obtaining efficient and stable numerical methods from it, and providing effective information for the process control of the deployment of the antenna, is the focus of scientific research scholars at this stage. Based on the understanding of the flexible multi-body dynamics modeling method, this paper systematically analyzes the calculation method of the differential equations, and combines the direct modification method of the constraint violation of the augmentation method to propose the simulation calculation of the model. The final results prove that the dynamics of flexible multi-body systems have a positive effect on the application analysis of deployable antennas.