Celestial Mechanics and Dynamical Astronomy

, Volume 107, Issue 4, pp 471–485 | Cite as

The use of invariant manifolds for transfers between unstable periodic orbits of different energies

  • Kathryn E. DavisEmail author
  • Rodney L. Anderson
  • Daniel J. Scheeres
  • George H. Born
Original Article


Techniques from dynamical systems theory have been applied to the construction of transfers between unstable periodic orbits that have different energies. Invariant manifolds, trajectories that asymptotically depart or approach unstable periodic orbits, are used to connect the initial and final orbits. The transfer asymptotically departs the initial orbit on a trajectory contained within the initial orbit’s unstable manifold and later asymptotically approaches the final orbit on a trajectory contained within the stable manifold of the final orbit. The manifold trajectories are connected by the execution of impulsive maneuvers. Two-body parameters dictate the selection of the individual manifold trajectories used to construct efficient transfers. A bounding sphere centered on the secondary, with a radius less than the sphere of influence of the secondary, is used to study the manifold trajectories. A two-body parameter, κ, is computed within the bounding sphere, where the gravitational effects of the secondary dominate. The parameter κ is defined as the sum of two quantities: the difference in the normalized angular momentum vectors and eccentricity vectors between a point on the unstable manifold and a point on the stable manifold. It is numerically demonstrated that as the κ parameter decreases, the total cost to complete the transfer decreases. Preliminary results indicate that this method of constructing transfers produces a significant cost savings over methods that do not employ the use of invariant manifolds.


Circular restricted three-body problem Unstable periodic orbits Invariant manifolds Dynamical systems theory Transfer trajectories Libration point orbits 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Kathryn E. Davis
    • 1
    Email author
  • Rodney L. Anderson
    • 1
  • Daniel J. Scheeres
    • 1
  • George H. Born
    • 1
  1. 1.Colorado Center for Astrodynamics ResearchUniversity of Colorado at BoulderBoulderUSA

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