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A modified Chebyshev Picard iteration method is proposed for solving orbit propagation initial/boundary value problems. Cosine sampling techniques, known as Chebyshev-Gauss-Lobatto (CGL) nodes, are used to reduce Runge’s phenomenon that plagues many series approximations. The key benefit of using the CGL data sampling is that the nodal points are distributed nonuniformly, with dense sampling at the beginning and ending times. This problem can be addressed by a nonlinear time transformation and/or by utilizing multiple time segments over an orbit. This paper suggests a method, called a multisegment method, to obtain accurate solutions overall regardless of initial states and albeit eccentricity by dividing the given orbit into two or more segments based on the true anomaly. [ABSTRACT FROM AUTHOR]

The halo orbits around the Earth-Moon L2 libration point provide a great candidate orbit for a lunar communication satellite, where the satellite remains above the horizon on the far side of the Moon being visible from the Earth at all times. Such orbits are generally unstable, and station-keeping strategies are required to control the satellite to remain close to the reference orbit. A recently developed Modified Chebyshev-Picard Iteration method is used to compute corrective maneuvers at discrete time intervals for station-keeping of halo orbit satellite, and several key parameters affecting the mission performance are analyzed through numerical simulations. Compared with previously published results, the presented method provides a computationally efficient station- keeping approach which has a simple control structure that does not require weight turning and, most importantly, does not need state transition matrix or gradient information computation. The performance of the presented approach is shown to be comparable with published methods. [ABSTRACT FROM AUTHOR]