Multiple-gravity-assist trajectories enable adjustments of orbital energy and flight direction with relatively low propellant consumption, and thus are of significant value in the design of interplanetary missions. To address the C3 matching problem in multiple-gravity-assist trajectory optimization, which is often challenged by low computational efficiency, missing roots, and sensitivity to initial guesses, this paper develops a C3 matching function model based on Lambert transfers, analyzes its solution-space characteristics and domain variation patterns under different transfer conditions, and proposes a C3 matching algorithm that combines analytical gradients with Hermite interpolation. The proposed method reduces the dependence on dense initial guesses by partitioning the function domain, locating root intervals, and accurately computing the roots. Numerical results demonstrate that the proposed method can completely identify all matching solutions, while significantly improving computational efficiency compared with existing methods. Its effectiveness is further demonstrated through the reconstruction of the Voyager 2 trajectory, the optimization of transfer trajectories for Uranus exploration, and applications in the GTOC13 scenario.
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