Free Access
Issue
ESAIM: M2AN
Volume 51, Number 3, May-June 2017
Page(s) 965 - 996
DOI https://doi.org/10.1051/m2an/2016044
Published online 14 April 2017
  1. E.L. Allgower and K. Georg, Introduction to numerical continuation methods, vol. 45 of Classics in Applied Mathematics. Reprint of the 1990 edition [Springer-Verlag, Berlin; MR1059455 (92a:65165)]. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2003). [Google Scholar]
  2. G. Archambeau, P. Augros and E. Trélat, Eight-shaped Lissajous orbits in the Earth-Moon system. MathS in Action 4 (2011) 1–23. [CrossRef] [MathSciNet] [Google Scholar]
  3. R. Bertrand and R. Epenoy, New smoothing techniques for solving bang–bang optimal control problems–numerical results and statistical interpretation. Optim. Control Appl. Methods 23 (2002) 171–197. [CrossRef] [Google Scholar]
  4. B. Bonnard, L. Faubourg and E. Trélat, Mécanique céleste et contrôle des véhicules spatiaux. Vol. 51 of Mathématiques & Applications (Berlin) [Mathematics & Applications]. Springer-Verlag, Berlin (2006). [Google Scholar]
  5. J.-B. Caillau, Contribution àl’étude du contrôle en temps minimal des transferts orbitaux. Ph.D. thesis, Institut National Polytechnique de Toulouse, Toulouse, France (2000). [Google Scholar]
  6. J.-B. Caillau and B. Daoud, Minimum time control of the restricted three-body problem. SIAM J. Control Optim. 50 (2012) 3178–3202. [CrossRef] [MathSciNet] [Google Scholar]
  7. Z. Chen, J.-B. Caillau and Y. Chitour, L1-minimization for mechanical systems. Available at: https://hal.archives-ouvertes.fr/hal-01136676 (2015). [Google Scholar]
  8. O. Cots, J.-B. Caillau and J. Gergaud, Differential pathfollowing for regular optimal control problems. Optim. Methods Software 27 (2012) 177–196. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  9. B. Daoud, Contribution au contrôle optimal du problème circulaire restreint des trois corps. Ph.D. thesis, Université de Bourgogne (2011). [Google Scholar]
  10. R. Epenoy, Optimal long-duration low-thrust transfers between libration point orbits. In Proc. of the 63rd International Astronautical Congress, in vol. 7. Naples, Italy (2012). [Google Scholar]
  11. L. Euler, De motu rectilineo trium corpörum se mutuo attrahentium. Oeuvres, Seria Secunda tome XXv Commentationes Astronomicae (1767) 144–151. [Google Scholar]
  12. R.W. Farquhar and A.A. Kamel, Quasi-periodic orbits about the translunar libration point. Celestial Mechanics 7 (1973) 458–473. [CrossRef] [Google Scholar]
  13. R.W. Farquhar, D.P. Muhonen, C.R. Newman and H.S. Heubergerg, Trajectories and Orbital Maneuvers for the First Libration-Point Satellite. J. Guid. Control Dynam. 3 (1980) 549–554. [CrossRef] [Google Scholar]
  14. J. Gergaud and T. Haberkorn, Homotopy method for minimum consumption orbit transfer problem. ESAIM: COCV 12 (2006) 294–310. [CrossRef] [EDP Sciences] [Google Scholar]
  15. G. Gomez and J. Masdemont, Some zero cost transfers between libration point orbits. In Point Orbits, AAS paper 00-177, AAS/AIAA Astrodynamics Specialist Conference (2000). [Google Scholar]
  16. G. Gómez, J. Masdemont, C. Simó and A. Jorba, Study refinement of semi-analytical halo orbit theory: Executive summary. [Google Scholar]
  17. G. Gómez, J. Masdemont and C. Simó, Lissajous orbits around halo orbits. Adv. Astronaut. Sci. (1997). ESOC Contract No.: 8625/89/D/MD (SC) (1991). [Google Scholar]
  18. T. Haberkorn, P. Martinon and J. Gergaud, Low thrust minimum-fuel orbital transfer: a homotopic approach. J. Guid. Control Dynam. 27 (2004) 1046–1060. [CrossRef] [Google Scholar]
  19. F. Jiang, H. Baoyin and J. Li, Practical techniques for low-thrust trajectory optimization with homotopic approach. J. Guid. Control Dynam. 35 (2012) 245–258. [CrossRef] [Google Scholar]
  20. À. Jorba and J. Masdemont, Dynamics in the center manifold of the collinear points of the restricted three body problem. Phys. D 132 (1999) 189–213. [CrossRef] [MathSciNet] [Google Scholar]
  21. W.S. Koon, M.W. Lo, J.E. Marsden and S.D. Ross, Dynamical systems, the three-body problem and space mission design. In International Conference on Differential Equations, Vols. 1, 2 (Berlin, 1999). World Sci. Publ., River Edge, NJ (2000) 1167–1181. [Google Scholar]
  22. W.S. Koon, M.W. Lo, J.E. Marsden and S.D. Ross, Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics. Chaos 10 (2000) 427–469. [NASA ADS] [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  23. J.-L. Lagrange, Essai sur le problème des trois corps. Prix de l’académie royale des Sciences de paris, tome IX, Oeuvres de Lagrange 6, Gauthier-Villars (1772) 272–282. [Google Scholar]
  24. C. Martin and B.A. Conway, Optimal low-thrust trajectories using stable manifolds. In Spacecraft Trajectory Optimization, edited by B.A. Conway. Cambridge University Press (2010) 238–262. [Google Scholar]
  25. K.R. Meyer, G.R. Hall and D. Offin, Introduction to Hamiltonian dynamical systems and the N-body problem. Vol. 90 of Appl. Math. Sci., 2nd edition. Springer, New York (2009). [Google Scholar]
  26. G. Mingotti, F. Topputo and F. Bernelli-Zazzera, Combined optimal low-thrust and stable-manifold trajectories to the Earth-Moon halo orbits. AIP Conf. Proc. 886 (2007) 100–112. [CrossRef] [Google Scholar]
  27. G. Mingotti, F. Topputo and F. Bernelli-Zazzera, Low-energy, low-thrust transfers to the Moon. Celestial Mech. Dyn. Astron. 105 (2009) 61–74. [CrossRef] [Google Scholar]
  28. G. Mingotti, F. Topputo and F. Bernelli-Zazzera, Optimal low-thrust invariant manifold trajectories via attainable sets. J. Guid. Control Dynam. 34 (2011) 1644–1655. [CrossRef] [Google Scholar]
  29. M.T. Ozimek and K.C. Howell, Low-thrust transfers in the Earth-Moon system, including applications to libration point orbits. J. Guid. Control Dynam. 33 (2010) 533–549. [CrossRef] [Google Scholar]
  30. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mishchenko, The mathematical theory of optimal processes. Translated by D.E. Brown. A Pergamon Press Book. The Macmillan Co., New York (1964). [Google Scholar]
  31. D.L. Richardson, Analytic construction of periodic orbits about the collinear points. Celestial Mech. 22 (1980) 241–253. [CrossRef] [MathSciNet] [Google Scholar]
  32. J. Senent, C. Ocampo and A. Capella, Low-thrust variable-specific-impulse transfers and guidance to unstable periodic orbits. J. Guid. Control Dynam. 28 (2005) 280–290. [CrossRef] [Google Scholar]
  33. T. Starchville and R. Melton, Optimal low-thrust trajectories to Earth-Moon L2 Halo orbits (circular problem). In Proc. of the AAS/AIAA Astrodynamics Specialists Conference. American Astro- nomical Soc. (1997) 97–714. [Google Scholar]
  34. V.G. Szebehely, Theory of Orbits – The restricted problem of three bodies. Academic Press (1967). [Google Scholar]
  35. F. Topputo, Fast numerical approximation of invariant manifolds in the circular restricted three-body problem. Commun. Nonlinear Sci. Numer. Simulat. 32 (2016) 89–98. [CrossRef] [Google Scholar]
  36. E. Trélat, Contrôle optimal. In Mathématiques Concrètes. [Concrete Mathematics]. Théorie & applications. [Theory and applications]. Vuibert, Paris (2005). [Google Scholar]
  37. E. Trélat, Optimal control and applications to aerospace: some results and challenges. J. Optim. Theory Appl. 154 (2012) 713–758. [CrossRef] [MathSciNet] [Google Scholar]
  38. E. Trélat and E. Zuazua, The turnpike property in finite-dimensional nonlinear optimal control. J. Differ. Eq. 258 (2015) 81–114. [CrossRef] [Google Scholar]
  39. L.T. Watson, HOMPACK90: FORTRAN 90 Codes for Globally Convergent Homotopy Algorithms. Department of Computer Science, Virginia Polytechnic Institute and State University (1996). [Google Scholar]
  40. F.B. Zazzera, F. Topputo and M. Massari, Assessment of mission design including utilisation of libration points and weak stability boundaries. Technical Report 03-4103b, European Space Agency, the Advanced Concepts Team. Available on line at: www.esa.int/act (2004). [Google Scholar]
  41. C. Zhang, F. Topputo, F. Bernelli-Zazzera and Y.-S. Zhao, Low-thrust minimum-fuel optimization in the circular restricted three-body problem. J. Guid. Control Dynam. 38 (2015) 1501–1510. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you