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All issues Volume 51 / No 3 (May-June 2017) ESAIM: M2AN, 51 3 (2017) 965-996 References
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. [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 contrle 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. [Google Scholar]
  7. Z. Chen, J.-B. Caillau and Y. Chitour, -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 contrle 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. [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 -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. [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. [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]

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