Nonlinear continuous-thrust state propagation and its application in optimal orbital transfers around collinear libration points

This paper presents a semi-analytical method for propagating orbital states under continuous thrust in nonlinear motion relative to collinear libration points within the circular restricted three-body problem. The proposed approach jointly approximates higher-order nonlinear dynamics and thrust acceleration using a truncated Fourier series with respect to time, thereby transforming the governing equation into a linear-like form. This transformation enables analytical state propagation through the series expansion coefficients, reducing the problem to the determination of these coefficients via a nonlinear least-squares method. Building upon this framework, a fuel-optimal transfer method for libration point orbits is developed and reformulated as a sequential second-order cone programming problem, with the energy-optimal solution employed as the initial guess. Numerical examples in the Sun–Earth system are provided to demonstrate the accuracy of the proposed state propagation method and to validate the effectiveness of the optimal transfer approach for Halo orbits.