Singular fuel-optimal space trajectories based on linearization about a point in circular orbit

Singular solutions of a linearized problem of determining fuel-optimal trajectories of a spacecraft with bounded thrust near a satellite in circular orbit are investigated in detail. Mathematical results are presented which classify and discuss degeneracy of the singular solutions and which show that strictly singular and nonsingular solutions are mutually exclusive for fixed-end conditions. These results are consistent with those found using other approaches for other linear models, but they are not characteristic of the type of results obtained without linearization.

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