Exploring the solution space of indirect methods can provide initial guesses and evaluate the solutions with arbitrary design parameters. In this article, the solution space of the minimum-time low-thrust rephasing in an elliptical orbit is explored by reducing the number of design parameters to two and depicting the solution space on a set of contour maps. First, considering that the spacecraft in a general elliptical orbit rendezvous with a target at a different along-track position, the scaling and linearizing techniques are employed to obtain a set of unified linearized equations of motion. Analytical integrals of Euler–Lagrange equations are derived. Then, the boundary condition with free initial true longitude ($L_{0}$) is focused on, and some symmetry properties can be applied to simplify the high-dimensional shooting function and to obtain two locally optimal solutions. Finally, the solution space of free-$L_{0}$ problem is sufficiently explored by solving univariate monotone shooting functions with high efficiency and global optimality, and the nonlinear solutions are numerically obtained and compared with the linear solutions. A cubic interpolation method is proposed to provide initial guesses for the general fixed-$L_{0}$ problem. Numerical tests show the applications of the proposed solution space for solving nonlinear problems in two-body and high-fidelity dynamic models.
Solution Space of Minimum-Time Low-Thrust Rephasing in Elliptical Orbit
IEEE Transactions on Aerospace and Electronic Systems ; 61 , 1 ; 568-581
2025-02-01
4747617 byte
Article (Journal)
Electronic Resource
English
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