Application of Modified Chebyshev Picard Iteration to Differential Correction for Improved Robustness and Computation Time
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2017, American Astronautical Society. A novel application of Modified Chebyshev Picard Iteration (MCPI) to differential correction is presented. By leveraging the Chebyshev basis functions of MCPI, interpolation in 1 dimension may be used to target plane crossing events, instead of integrating the 42 dimensional variational equation required for standard step integrators. This results in dramatically improved performance over traditional differential correctors. MCPI was tested against the Runge-Kutta 7/8 integrator on over 45,000 halo orbits in three different three-body problems, and was found to be up to an order of magnitude faster, while simultaneously increasing robustness.