Approximate analytical solutions to optimal reconfiguration problems in perturbed satellite relative motion

Sangjin Lee, Sang Young Park

Research output: Contribution to journalArticlepeer-review

46 Citations (Scopus)


This paper presents new analytical solutions to the optimal reconfiguration problems of formation flying using a power-limited low-thrust propulsion that includes perturbations associated with differential gravity effects, the eccentricity effects of a chief orbit, and J2 effects. The perturbation approach and the calculus of variations are applied to optimal reconfiguration problems to obtain an approximate analytical solution. Some nonlinear relative dynamics are also presented to account for the nonlinear terms generated by each perturbation. For the sake of validity, numerical simulations are performed for satellite reconfiguration cases in which the distance between the satellites is large and the chief orbit is eccentric. The improved capacity of the new analytical solutions to ensure reasonable fuel usage is confirmed, and the magnitudes of the errors caused by each perturbation are compared and analyzed. It is found that the errors caused by unperturbed analytical solutions based on only the Hill-Clohessy-Wilshire equations are reduced by the new analytical solutions by one-half to one over 500, depending on which perturbation is considered.

Original languageEnglish
Pages (from-to)1097-1111
Number of pages15
JournalJournal of Guidance, Control, and Dynamics
Issue number4
Publication statusPublished - 2011

Bibliographical note

Funding Information:
This work was supported by the Korea Science and Engineering Foundation through the National Research Laboratory Program funded by the Ministry of Science and Technology (no. M10600 000282-06J0000-28210).

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Aerospace Engineering
  • Space and Planetary Science
  • Electrical and Electronic Engineering
  • Applied Mathematics


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