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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 290781, 7 pages
Research Article

Multisegment Scheme Applications to Modified Chebyshev Picard Iteration Method for Highly Elliptical Orbits

1Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141, USA
2Royce Wisenbaker Chair in Engineering, Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141, USA

Received 10 April 2014; Accepted 22 July 2014

Academic Editor: Ker-Wei Yu

Copyright © 2015 Donghoon Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A modified Chebyshev Picard iteration method is proposed for solving orbit propagation initial/boundary value problems. Cosine sampling techniques, known as Chebyshev-Gauss-Lobatto (CGL) nodes, are used to reduce Runge’s phenomenon that plagues many series approximations. The key benefit of using the CGL data sampling is that the nodal points are distributed nonuniformly, with dense sampling at the beginning and ending times. This problem can be addressed by a nonlinear time transformation and/or by utilizing multiple time segments over an orbit. This paper suggests a method, called a multisegment method, to obtain accurate solutions overall regardless of initial states and albeit eccentricity by dividing the given orbit into two or more segments based on the true anomaly.