Low Thrust Minimum Time Orbit Transfer Nonlinear Optimization Using Impulse Discretization via the Modified Picard–Chebyshev Method
Darin Koblick, Shujing Xu, Joshua Fogel and Praveen Shankar

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 111, No. 1, pp. 1-27, 2016
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Keywords Low Thrust, Picard–Chebyshev, Optimization, Multi-Impulse, Boundary Value Problem.

The Modified Picard-Chebyshev Method (MPCM) is implemented as an orbit propagation solver for a numerical optimization method that determines minimum time orbit transfer trajectory of a satellite using a series of multiple impulses at intermediate waypoints. The waypoints correspond to instantaneous impulses that are determined using a nonlinear constrained optimization routine, SNOPT with numerical force models for both Two-Body and J2 perturbations. It is found that using the MPCM increases run-time performance of the discretized lowthrust optimization method when compared to other sequential numerical solvers, such as Adams-Bashforth-Moulton and Gauss-Jackson 8th order methods.

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