Uncontrolled spacecraft formations on two-dimensional invariant tori

Marcel Duering, Massimiliano Vasile, Markus Landgraf

Research output: Contribution to conferencePaper

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Within the class of natural motions near libration point regions quasi-periodic trajectories evolving on invariant tori are studied. Those orbits prove beneficial for relative spacecraft configurations with large distances among satellites. In this study properties of invariant tori are outlined, and non-resonant and resonant tori around the Sun/Earth libration point L1 are computed. A numerical approach to obtain the frequency base and to parametrize a torus in angular phase space is introduced. Initial states for spacecraft formations on the torus’ surface are defined. The formation naturally evolve along its surface such that the relative positions within a formation are unaltered and the relative distances and the orientation are closely bounded. An in-plane coordinate frame together with a modified torus motion is introduced and the inner and outer behaviour of the formation’s geometry is investigated.
Original languageEnglish
Number of pages16
Publication statusPublished - 29 Oct 2012
Event23rd International Symposium on Spaceflight Dynamics - Pasadena, United States
Duration: 29 Oct 20122 Nov 2012


Conference23rd International Symposium on Spaceflight Dynamics
Country/TerritoryUnited States


  • two-dimensional torus
  • quasi-periodic objects
  • spacecraft formations,
  • parametrization


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