East–west stationkeeping of satellite orbits with resonant tesseral harmonics

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Satellite orbits that are eccentric and inclined with near-repeating ground tracks can exhibit complex dynamical motions. This class of orbit is typically in resonance with multiple Earth tesseral harmonics. Depending on the selected resonance (i.e. orbits with a 24 h period, 12 h period, etc.), inclination, and eccentricity, the interaction between tesserals produces a variety of motions ranging between responses that are periodic, quasiperiodic, and chaotic. Furthermore, the type of motion encountered by a satellite can have a significant impact on the east-west stationkeeping process. Indeed, the classical stationkeeping algorithm is shown to be potentially non-convergent in regions of the phase space that possess higher order periodic, quasiperiodic, and/or chaotic motions. Poincaré sections provide insight into the location of these regions, and suggest improvements to the classical control technique. Combining this information with an asymptotic analysis, an alternative method is developed and demonstrated to remain stable in the complex regions of the phase space. The proposed method retains the ‘grazing’ strategy of the classical algorithm; however, the algorithm adapts to the dynamical environment to ensure stability of the process. Preliminary results demonstrate that the algorithm remains stable in chaotic regions of the phase space and accomplishes the primary objective of maintaining motion in a prescribed deadband region.