MONTE CARLO PROPAGATION OF ORBITAL ELEMENTS USING MODIFIED CHEBYSHEV PICARD ITERATION
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Prior works have shown promising efficiency while propagating perturbed two-body motion using orbital elements combined with a novel integration technique. While previous studies show that Modified Chebyshev Picard Iteration (MCPI) is a powerful tool used to propagate position and velocity, instead using orbital elements to propagate the state vector reduces the number of MCPI iterations required, which is especially useful for reducing the computation time when including computationally-intensive calculations such as Spherical Harmonic gravity, and it also converges for a larger number of revolutions using a single segment (up to 17 orbits compared with 3 orbits for the cartesian, fully spherical harmonic low-Earth orbit case). Results for the Classical Orbital Elements and the Modified Equinoctial Orbital Elements (the latter provides singularity-free solutions) show that state propagation using these variables is inherently well-suited to the propagation method chosen. The present study incorporates a Monte Carlo analysis using a local Taylor Series model that reduces the computational time and provides a high-accuracy solution for propagating the Modified Equinoctial Orbital Elements both in serial and in parallel on a compute cluster. MCPI is an iterative numerical method used to solve linear and nonlinear, ordinary differential equations (ODEs). It is a fusion of orthogonal Chebyshev function approximation with Picard iteration that approximates a long-arc trajectory at every iteration. Previous studies have shown that it outperforms the state of the practice numerical integrators of ODEs in a serial computing environment; since MCPI is inherently massively parallelizable, this capability increases the computational efficiency of the method presented.