Optimal Low-Thrust Orbit Transfers Connecting Gateway with Earth and Moon

The paper’s multi-arc section states and uses the implicit costate transformation (their Eq. (63)) linking adjacent costates via the Jacobians of the interface matching constraints, and explicitly notes that this allows sequential determination of later-arc costates from earlier ones so the unknown set has the same size as in a single-arc problem. This matches the candidate solution’s derivation and conclusions. The paper also presents the implicit and explicit interface maps (their Eqs. (55)–(56)) and the augmented multi-arc functional (their Eqs. (60)–(62)), which underpin the same integration-by-parts/multiplier argument used in the model solution. The model adds a standard derivation detail and gives the explicit linear covector map; both are consistent with the paper’s formulation and use. A minor note: for free interface times the jump in Hamiltonian would also include the scalar transition-function multiplier ε_j if ζ_j depends on τ_j, a term the model’s brief remark omits; this does not affect the main claims. See the paper’s statements around the implicit costate transform and unknown count and the multi-arc setup: Eq. (63) and surrounding discussion, and the explicit/implicit state map and augmented functional (55)–(56), (60)–(62) .