Under two-body dynamics with a long enough flight time, a minimum-delta-v impulsive transfer is not a single trajectory but the seed of an infinite family of trajectories that all cost exactly the same total delta-v. The construction starts from a time-free, phase-free base solution whose impulse locations are called anchor positions; at any anchor position a single impulse can be split into several smaller ones that inject the spacecraft into intermediate phasing orbits, and the analytic delta-v-allocation problem determines the split without sacrificing optimality. This paper extends that construction from two-impulse to three-impulse base solutions, derives the relations that allocate delta-v at two or three anchor positions simultaneously, and answers the question of how many anchor positions a base solution should have by giving a selection rule - first delta-v optimality, then time feasibility for time-free maneuvers, and the reverse order for time-fixed rendezvous - that doubles as a certificate that the theoretical minimum delta-v is or is not reachable within a given mission time. All iso-impulse solutions are then classified in four layers: base solutions, feasible solution spaces (polytopes over the revolution counts at each anchor position), solution families (specific revolution-count combinations), and solution envelopes (polygons bounding the phasing-orbit periods, whose corner points are derived analytically and cross-checked by linear programming). The practical payoff is that a thruster limit delta-v less than or equal to delta-v-max can be respected by splitting impulses rather than by giving up optimality, at the cost of a longer maneuver. Interplanetary (Earth-to-Dionysus, Earth-to-Mars) and geocentric circle-to-circle examples with large inclination changes illustrate the method, including the case where neither base solution is time-feasible and a Lambert solution must be used with a known optimality gap.
In two-body dynamics, it is proven that for a sufficiently long flight time, generating infinitely many iso-impulse solutions is possible by solving a number of $Δv$-allocation problems analytically.…