Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2012, Article ID 926158, 18 pages
http://dx.doi.org/10.1155/2012/926158
Research Article

Modified Chebyshev-Picard Iteration Methods for Station-Keeping of Translunar Halo Orbits

Department of Aerospace Engineering, Texas A&M University, TAMU 3141, College Station, TX 77843-3141, USA

Received 15 July 2011; Revised 7 November 2011; Accepted 14 November 2011

Academic Editor: Tadashi Yokoyama

Copyright © 2012 Xiaoli Bai and John L. Junkins. 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.

Citations to this Article [12 citations]

The following is the list of published articles that have cited the current article.

  • Gaurav Misra, Hao Peng, and Xiaoli Bai, “Halo Orbit Station-keeping using Nonlinear MPC and Polynomial Optimization,” 2018 Space Flight Mechanics Meeting, . View at Publisher · View at Google Scholar
  • Christian Circi, Daniele Romagnoli, and Federico Fumenti, “Halo orbit dynamics and properties for a lunar global positioning system design,” Monthly Notices of The Royal Astronomical Society, vol. 442, no. 4, pp. 3511–3527, 2014. View at Publisher · View at Google Scholar
  • Ben K. Bradley, Brandon A. Jones, Gregory Beylkin, Kristian Sandberg, and Penina Axelrad, “Bandlimited implicit Runge-Kutta integration for Astrodynamics,” Celestial Mechanics & Dynamical Astronomy, vol. 119, no. 2, pp. 143–168, 2014. View at Publisher · View at Google Scholar
  • Min Zhu, Hamid Reza Karimi, Hui Zhang, Qing Gao, and Yong Wang, “Active Disturbance Rejection Station-Keeping Control of Unstable Orbits around Collinear Libration Points,” Mathematical Problems in Engineering, vol. 2014, pp. 1–14, 2014. View at Publisher · View at Google Scholar
  • Donghoon Kim, John L. Junkins, and James D. Turner, “Multisegment Scheme Applications to Modified Chebyshev Picard Iteration Method for Highly Elliptical Orbits,” Mathematical Problems in Engineering, vol. 2015, pp. 1–7, 2015. View at Publisher · View at Google Scholar
  • Chang-Joo Kim, Do Hyeon Lee, Sung Wook Hur, and Sangkyung Sung, “Fast and accurate analyses of spacecraft dynamics using implicit time integration techniques,” International Journal of Control, Automation and Systems, vol. 14, no. 2, pp. 524–539, 2016. View at Publisher · View at Google Scholar
  • A. Narula, and J. D. Biggs, “Fault-Tolerant Station-Keeping on Libration Point Orbits,” Journal of Guidance, Control, and Dynamics, pp. 1–9, 2017. View at Publisher · View at Google Scholar
  • Travis Swenson, Robyn Woollands, John Junkins, and Martin Lo, “Application of Modified Chebyshev Picard Iteration to Differential Correction for Improved Robustness and Computation Time,” The Journal of the Astronautical Sciences, 2017. View at Publisher · View at Google Scholar
  • Maksim Shirobokov, Sergey Trofimov, and Mikhail Ovchinnikov, “Survey of Station-Keeping Techniques for Libration Point Orbits,” Journal of Guidance, Control, and Dynamics, pp. 1–21, 2017. View at Publisher · View at Google Scholar
  • Robyn M. Woollands, John L. Junkins, Ahmad Bani Younes, and Ahmed M. Atallah, “Tuning orthogonal polynomial degree and segment interval length to achieve prescribed precision approximation of irregular functions,” Space Flight Mechanics Meeting, 2018, no. 210009, 2018. View at Publisher · View at Google Scholar
  • Yi Qi, and Anton de Ruiter, “Station-keeping strategy for real translunar libration point orbits using continuous thrust,” Aerospace Science and Technology, pp. 105376, 2019. View at Publisher · View at Google Scholar
  • Mohammad Tafakkori‐Bafghi, Ghasem Barid Loghmani, Mohammad Heydari, and Xiaoli Bai, “Jacobi‐Picard iteration method for the numerical solution of nonlinear initial value problems,” Mathematical Methods in the Applied Sciences, 2019. View at Publisher · View at Google Scholar