Abstract The Modified Chebyshev Picard Iteration (MCPI) method has recently proven to be highly efficient for a given accuracy compared to several commonly adopted numerical integration methods, as a means to solve for perturbed orbital motion. This method utilizes Picard iteration, which generates a sequence of path approximations, and Chebyshev Polynomials, which are orthogonal and also enable both efficient and accurate function approximation. The nodes consistent with discrete Chebyshev orthogonality are generated using cosine sampling; this strategy also reduces the Runge effect and as a consequence of orthogonality, there is no matrix inversion required to find the basis function coefficients. The MCPI algorithms considered herein are parallel-structured so that they are immediately well-suited for massively parallel implementation with additional speedup. MCPI has a wide range of applications beyond ephemeris propagation, including the propagation of the State Transition Matrix (STM) for perturbed two-body motion. A solution is achieved for a spherical harmonic series representation of earth gravity (EGM2008), although the methodology is suitable for application to any gravity model. Included in this representation the normalized, Associated Legendre Functions are given and verified numerically. Modifications of the classical algorithm techniques, such as rewriting the STM equations in a second-order cascade formulation, gives rise to additional speedup. Timing results for the baseline formulation and this second-order formulation are given.
State Transition Matrix for Perturbed Orbital Motion Using Modified Chebyshev Picard Iteration
The Journal of the Astronautical Sciences ; 62 , 2 ; 148-167
2015-06-01
20 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
Modified Chebyshev-Picard Iteration (MCPI) , Orbital mechanics , Celestial mechanics , State transition matrix , Spherical harmonic gravity , Numerical integration , Trajectory propagation Engineering , Aerospace Technology and Astronautics , Mathematical Applications in the Physical Sciences , Extraterrestrial Physics, Space Sciences
State Transition Matrix for Perturbed Orbital Motion Using Modified Chebyshev Picard Iteration
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