<p>Based on the assumption that stable orbits in the Earth–Moon ephemeris model are quasi-periodic and can be expressed in the form of trigonometric series, an algorithm that collects frequencies that form quasi-periodic stable orbit solutions up to certain orders is developed. The algorithm is used to construct semi-analytical solutions for spatial motions around the triangular libration points in the ephemeris model. The algorithm is validated, and the precision of the solution is evaluated. Stable and unstable orbits generated from dynamical substitutes around the Earth–Moon triangular libration points are studied, and the resonances that shape the stable regions are analyzed. They are found to be related to the precession rates of both the Moon’s and the small body’s orbits, the Sun’s orbital frequency, and the libration frequency of the triangular libration point. Discussions about possible natural bodies residing in the constructed stable orbits are given taking into account astronomical observations and the influence of solar radiation pressure. The frequency tracking algorithm has shown superior efficiency and accuracy in the construction of semi-analytical solutions and may find applications in complex dynamical systems.</p>