J2 Dynamics and Formation Flight

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W. S. Koon, J. E. Marsden, J. Masdemont and R. M. Murray
Submitted, 2001 AIAA Guidance, Navigation and Control Conference

We study the dynamics of the relative motion of satellites in the gravitational field of the Earth, including the effects of the bulge of the Earth (the $J_2$ effect). Using Routh reduction and dynamical systems ideas, a method is found that locates orbits such that the cluster of satellites remains close with very little dispersing, even with no controls. The use of controls in the context of this natural dynamics is studied to maintain and achieve precision formations.

  • Conference
 Paper: http://www.cds.caltech.edu/~murray/preprints/kmmm01-gnc.pdf