Spacecraft trajectory design is evolving and innovation is increasingly driven by computational methods. As new regimes are explored, numerical techniques are most often developed to cope with undesirable behavior in sensitive dynamical systems. Nonlinear systems with sensitive dynamics are ubiquitous spacecraft trajectory modeling, where the models include, for example, perturbations due to an aspherical central body, multi-body perturbations, and solar wind.;Numerical techniques are particularly useful in designing trajectories for lunar south pole coverage. Dual-spacecraft constellations include either two spacecraft in lunar "frozen" orbits or in multi-body orbits near the libration points of the Earth-Moon Restricted 3-Body Problem (R3BP). Alternatively, single spacecraft constellations, or "pole-sitters," require only one spacecraft for continuous surveillance and a control source for displacing the vehicle below the trans- or cis-lunar libration point. The control source might originate from a solar sail or an electric thruster. A spacecraft equipped with an electric thruster has an added advantage in that it can be deployed immediately and is eventually inserted into a larger constellation for continued surveillance.;The following investigation includes many numerical techniques that are useful for trajectory design. The methods are applied for a thorough analysis of motion in the Earth-Moon R3BP, including dual-spacecraft and pole-sitter missions for lunar south pole coverage, where continuous line-of-sight access between a lunar ground station and the Earth is required. The various options for coverage are explored in higher-fidelity models and evaluated in terms of elevation angle and altitude from the Shackleton crater near the lunar south pole. The choice of constellation is driven by the mission requirements.
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