NDLI: State Transition Matrix for Perturbed Orbital Motion Using Modified Chebyshev Picard Iteration

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State Transition Matrix for Perturbed Orbital Motion Using Modified Chebyshev Picard Iteration

Content Provider	Springer Nature Link
Author	Younes, Ahmad Bani Junkins, John L. Macomber, Brent Turner, James Read, Julie L.
Copyright Year	2015
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.
Starting Page	148
Ending Page	167
Page Count	20
File Format	PDF
ISSN	00219142
Journal	The Journal of the Astronautical Sciences
Volume Number	62
Issue Number	2
e-ISSN	21950571
Language	English
Publisher	Springer US
Publisher Date	2015-08-13
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Orbital mechanics Extraterrestrial Physics, Space Sciences Numerical integration State transition matrix Mathematical Applications in the Physical Sciences Spherical harmonic gravity Aerospace Technology and Astronautics Modified Chebyshev-Picard Iteration (MCPI) Trajectory propagation Celestial mechanics
Content Type	Text
Resource Type	Article
Subject	Aerospace Engineering Space and Planetary Science

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