236
Views
31
CrossRef citations to date
0
Altmetric
Original Articles

The invariant manifold structure of the spatial Hill's problem

, &
Pages 115-147 | Received 01 Jun 2004, Accepted 03 Jan 2004, Published online: 01 Oct 2010

References

  • Conley , CC . 1968 . Low energy transit orbits in the restricted three-body problem . SIAM Journal on Applied Mathematics , 16 ( 4 ) : 732 – 746 .
  • Gómez , G and Masdemont , JJ . 2000 . Some zero cost transfers between halo orbits . Advances in the Astronautical Sciences , 115 : 1199 – 1216 .
  • Koon , WS , Lo , MW , Marsden , JE and Ross , SD . 2000 . Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics . Chaos , 10 : 427 – 496 .
  • Gómez , G , Koon , WS , Lo , MW , Marsden , JE , Masdemont , JJ and Ross , SD . 2004 . Connecting orbits and invariant manifolds in the spatial restricted three-body problem . Nonlinearity , 17 : 1571 – 1606 .
  • Gómez , G , Jorba , À. , Masdemont , JJ and Simó , C . 1993 . Study of the transfer from the earth to a halo orbit around the equilibrium point L 1 . Celestial Mechanics and Dynamical Astronomy , 56 : 541 – 562 .
  • Gómez , G , Jorba , À. , Masdemont , JJ and Simó , C . 1998 . Study of the transfer between halo aorbits . Acta Astronautica , 43 : 493 – 520 .
  • Koon WS Lo MW Marsden JE Ross SD 1999 The genesis trajectory and heteroclinic connections AAS Paper 99-451, AAS/AIAA Astrodynamics Specialist Conference Girdwood Alaska
  • Hénon , M . 1969 . Numerical exploration of the restricted problem. V. Hill's case: periodic orbits and their stability . Astronomy & Astrophysics , 1 : 223 – 238 .
  • Simó , C and Stuchi , T . 2000 . Central stable/unstable manifolds and the destruction of KAM tori in the planar Hill problem . Physica D , 140 : 1 – 32 .
  • Szebehely V 1967 Theory of Orbits New York Academic Press
  • Hill , GW . 1878 . Researches in the lunar theory . American Journal of Mathematics , 1 : 5–26, 129–147, 245–260
  • Wintner A 1941 Analytical Foundations of Celestial Mechanics Princeton NJ Princeton University Press
  • Stiefel EL Scheifele G 1971 Linear and Regular Celestial Mechanics Berlin Springer-Verlag
  • Meletlidou , E , Ichtiaroglou , S and Winterberg , J . 2001 . Non-integrability of Hill's lunar problem . Celestial Mechanics and Dynamical Astronomy , 80 : 145 – 156 .
  • Winterberg , J and Meletlidou , E . 2004 . Non-continuation of integrals of the rotating two-body problem in Hill's lunar problem . Celestial Mechanics and Dynamical Astronomy , 88 : 37 – 49 .
  • Jorba , A and Masdemont , JJ . 1999 . Dynamics in the center manifold of the restricted three-body problem . Physica D , 132 : 189 – 213 .
  • Gómez G Jorba À. Masdemont JJ Simó C 2000 Dynamics and Mission Design Near Libration Point Orbits—Volume 3: Advanced Methods for Collinear Points Singapore World Scientific
  • Dichmann DJ Doedel EJ Paffenroth RC 2003 The computation of periodic solutions of the 3-body problem using the numerical continuation software AUTO In: G. Gómez, M.W. Lo and J.J. Masdemont (Eds.) Libration Point Orbits and Applications pp. 489–528 Singapore World Scientific
  • Gómez , G and Mondelo , JM . 2001 . The dynamics around the collinear equilibrium points of the RTBP . Physica D , 157 : 283 – 321 .
  • Siegel CL Moser JK 1971 Lectures on Celestial Mechanics Berlin Springer-Verlag
  • Hénon , M . 1973 . Vertical stability of periodic orbits in the restricted problem . Astronomy and Astrophysics , 28 : 415 – 426 .
  • Marcote M 2005 PhD Universitat de Barcelona (in preparation)
  • Castellà , E and Jorba , À . 2000 . On the vertical families of two-dimensional tori near the triangular points of the bicircular problem . Celestial Mechanics and Dynamical Astronomy , 76 : 35 – 54 .
  • Anderson E Bai Z Bischof C Demmel J Dongarra J Croz D Greenbaum A Hammarling S McKenney A Ostrouchov S Sorensen D 1995 LAPACK Users’ Guide 22nd Edn., (SIAM)
  • Golub GH Van Loani CR 1996 Matrix Computations 3rd Edn Baltimore MD The Johns Hopkins University Press
  • Mondelo JM 2001 Contribution to the study of Fourier methods for quasi-periodic functions and the vicinity of the collinear librations points PhD thesis Universitat de Barcelona
  • Hénon , M . 2003 . New families of periodic orbits in Hill's problem of three bodies . Celestial Mechanics and Dynamical Astronomy , 85 : 223 – 246 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.