The use of invariant manifolds for transfers （利用不变流形进行转移）.pdf

Celest Mech Dyn Astr (2010) 107:471–485 DOI 10.1007/s10569-010-9285-3 ORIGINAL ARTICLE The use of invariant manifolds for transfers between unstable periodic orbits of different energies Kathryn E. Davis · Rodney L. Anderson · Daniel J. Scheeres · George H. Born Received: 16 November 2009 / Revised: 13 April 2010 / Accepted: 3 May 2010 / Published online: 5 June 2010 © Springer Science+Business Media B.V. 2010 Abstract Techniques from dynamical systems theory have been applied to the construc- tion of transfers between unstable periodic orbits that have different energies. Invariant man- ifolds, 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, , is computed within the bounding sphere, where the gravitational effects of the secondary dominate. The parameter 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 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 manifold