Efficient Orbit Propagation of Orbital Elements Using Modified Chebyshev Picard Iteration Method
J.L. Read, A. Bani Younes and J.L. Junkins

doi:10.3970/cmes.2016.111.065
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 111, No. 1, pp. 65-81, 2016
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Keywords Propagation, Integration, Orbital Mechanics, Classical Orbital Elements, Modified Equinoctial Orbital Elements, Modified Chebyshev Picard Iteration, MCPI, Chebyshev Polynomials, Initial Value Problem, IVP.
Abstract

This paper focuses on 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, the present results show that using orbital elements to propagate the state vector reduces the number of MCPI iterations and nodes 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 > 5.5x as many revolutions using a single segment when compared with cartesian propagation. 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. Additional benefits are achieved using a segmentation scheme, while future expansion to the two-point boundary value problem is expected to increase the domain of convergence compared with the cartesian case. 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 is expected to increase the computational efficiency of the method presented.

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