Calculation of a Dynamical Substitute for the Real Earth–Moon System Based on Hamiltonian Analysis

Abstract The Earth–Moon libration points no longer exhibit the dynamical characteristics of “equilibrium points” due to perturbation effects when applying the ephemeris model. By decoupling the forced motions within the ephemeris model and computing the dynamical substitute trajectories, we can reconstruct a dynamical system that recovers the “equilibrium points” feature. Diverging from the conventional analytical approach rooted in the framework of Newtonian mechanics, this paper presents a novel method for calculating dynamical substitute based on the Hamiltonian mechanics framework. First, the Hamiltonian equations for the ephemeris model are formulated. Subsequently, the problem of decoupling forced motions is reformulated as solving a nonautonomous differential equation through canonical transformations. Then, an iterative method based on frequency analysis is employed for the computation. Eventually, approximate analytical solutions for five libration points over a 360 yr period are provided. Simulation results demonstrate that the computed approximate analytical solutions are in excellent agreement with the numerical integration results derived from the ephemeris model, thereby validating the efficacy of the proposed method. The Hamiltonian dynamical system derived herein enables the analysis of nonlinear central manifold motions via canonical transformations, facilitating the construction of higher-order analytical solutions for libration point orbits. This framework also provides a robust foundation for exploring characterization parameters of libration point orbits within the real Earth–Moon system.