메뉴 건너뛰기




Volumn 17, Issue 1, 2012, Pages 245-269

Shooting and numerical continuation methods for computing time-minimal and energy-minimal trajectories in the Earth-Moon system using low propulsion

Author keywords

3 body problem; Earth Moon transfer; Energy minimization problem; Geometric control theory; Numerical analysis method; Time minimization problem

Indexed keywords


EID: 83455163728     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2012.17.245     Document Type: Article
Times cited : (14)

References (30)
  • 1
    • 0031678073 scopus 로고    scopus 로고
    • On abnormals extremals for Lagrange variational prob- lems
    • A. A. Agrachev and A. V. Sarychev, On abnormals extremals for Lagrange variational prob- lems, J. Math. Systems Estim. Control, 8 (1998), 87-118.
    • (1998) J. Math. Systems Estim. Control , vol.8 , pp. 87-118
    • Agrachev, A.A.1    Sarychev, A.V.2
  • 3
    • 0003319234 scopus 로고
    • Mathematical methods of classical mechanics
    • Second edition, Springer-Verlag, New York
    • V. I. Arnol'd, "Mathematical Methods of Classical Mechanics," Second edition, Graduate Texts in Mathematics, 60, Springer-Verlag, New York, 1989.
    • (1989) Graduate Texts in Mathematics , vol.60
    • Arnol'd, V.I.1
  • 4
    • 1542283034 scopus 로고    scopus 로고
    • Optimal low thrust trajectories to the moon
    • J. T. Betts and S. O. Erb, Optimal low thrust trajectories to the moon, SIAM J. Appl. Dyn. Syst., 2 (2003), 144-170.
    • (2003) SIAM J. Appl. Dyn. Syst. , vol.2 , pp. 144-170
    • Betts, J.T.1    Erb, S.O.2
  • 7
    • 83455180731 scopus 로고    scopus 로고
    • Transfert Terre-Lune en poussée faible par contrôle feedback - La mission SMART-1
    • A. Bombrun, J. Chetboun and J.-B. Pomet, Transfert Terre-Lune en poussée faible par contrôle feedback - La mission SMART-1, (French) INRIA Research Report, 5955 (2006), 1-27.
    • (2006) French INRIA Research Report , vol.5955 , pp. 1-27
    • Bombrun, A.1    Chetboun, J.2    Pomet, J.-B.3
  • 8
    • 83455267576 scopus 로고    scopus 로고
    • Geometric and numerical techniques in optimal control of the two and three-body problems
    • B. Bonnard, J.-B. Caillau and G. Picot, Geometric and numerical techniques in optimal control of the two and three-body problems, Commun. Inf. Syst., 10 (2010), 239-278.
    • Commun. Inf. Syst. , vol.10 , Issue.2010 , pp. 239-278
    • Bonnard, B.1    Caillau, J.-B.2    Picot, G.3
  • 9
    • 34547510460 scopus 로고    scopus 로고
    • Second order optimality conditions in the smooth case and applications in optimal control
    • DOI 10.1051/cocv:2007012
    • B. Bonnard, J.-B. Caillau and E. Trélat, Second order optimality conditions in the smooth case and applications in optimal control, ESAIM Control Optim. and Calc. Var., 13 (2007), 207-236. (Pubitemid 47184616)
    • (2007) ESAIM - Control, Optimisation and Calculus of Variations , vol.13 , Issue.2 , pp. 207-236
    • Bonnard, B.1    Caillau, J.-B.2    Trelat, E.3
  • 11
    • 11844254028 scopus 로고    scopus 로고
    • Singular trajectories and their role in control theory
    • Springer-Verlag, Berlin
    • B. Bonnard and M. Chyba, "Singular Trajectories and Their Role in Control Theory," Math. and Applications, 40, Springer-Verlag, Berlin, 2003.
    • (2003) Math. and Applications , vol.40
    • Bonnard, B.1    Chyba, M.2
  • 12
  • 13
    • 84955868449 scopus 로고
    • Théorie des singularités de l'application entrée/sortie et opti- malité des trajectoires singuliéres dans le probléme du temps minimal French
    • B. Bonnard and I. Kupka, Théorie des singularités de l'application entrée/sortie et opti- malité des trajectoires singuliéres dans le probléme du temps minimal, (French)[Theory of the singularities of the input/output mapping and optimality of singular trajectories in the minimal-time problem], Forum Math., 5 (1993), 111-159.
    • (1993) Forum Math , vol.5 , pp. 111-159
    • Bonnard, B.1    Kupka, I.2
  • 14
    • 79951804152 scopus 로고    scopus 로고
    • The smooth continuation method in optimal control with an application to quantum systems
    • B. Bonnard, N. Shcherbakova and D. Sugny, The smooth continuation method in optimal control with an application to quantum systems, ESAIM Control Optim. and Calc. Var., 17 (2011), 267-292.
    • (2011) ESAIM Control Optim. and Calc. Var. , vol.17 , pp. 267-292
    • Bonnard, B.1    Shcherbakova, N.2    Sugny, D.3
  • 15
    • 0007889463 scopus 로고    scopus 로고
    • Contribution à l'Etude du contrôle en Temps Minimal des Transferts Or- bitaux
    • J.-B. Caillau, "Contribution à l'Etude du contrôle en Temps Minimal des Transferts Or- bitaux," Ph.D thesis, Toulouse University, 2000.
    • (2000) Ph.D thesis, Toulouse University
    • Caillau, J.-B.1
  • 17
    • 83455241729 scopus 로고    scopus 로고
    • Discrete and differential homotopy in circular re- stricted three-body control to appear
    • J.-B. Caillau, B. Daoud and J. Gergaud, Discrete and differential homotopy in circular re- stricted three-body control, to appear in AIMS Proceedings, 2010.
    • AIMS Proceedings , vol.2010
    • Caillau, J.-B.1    Daoud, B.2    Gergaud, J.3
  • 18
    • 33645788599 scopus 로고    scopus 로고
    • Homotopy method for minimum consumption orbit transfer problem
    • J. Gergaud and T. Haberkorn, Homotopy method for minimum consumption orbit transfer problem, ESAIM Control Optim. Calc. Var., 12 (2006), 294-310.
    • (2006) ESAIM Control Optim. Calc. Var. , vol.12 , pp. 294-310
    • Gergaud, J.1    Haberkorn, T.2
  • 20
    • 67349222423 scopus 로고    scopus 로고
    • Existence and Lipschitzian regularity for relaxed minimizers
    • Springer Berlin
    • M. Guerra and A. Sarychev, Existence and Lipschitzian regularity for relaxed minimizers, in "Mathematical Control Theory and Finance," Springer, Berlin, (2008), 231-250.
    • (2008) Mathematical Control Theory and Finance , pp. 231-250
    • Guerra, M.1    Sarychev, A.2
  • 21
    • 27644431998 scopus 로고    scopus 로고
    • New methods in celestial mechanics and mission design
    • DOI 10.1090/S0273-0979-05-01085-2
    • J. E. Marsden and S. D. Ross, New methods in celestial mechanics and mission design, Bull. Amer. Math. Soc. (N.S), 43 (2006), 43-73. (Pubitemid 43202397)
    • (2006) Bulletin of the American Mathematical Society , vol.43 , Issue.1 , pp. 43-73
    • Marsden, J.E.1    Ross, S.D.2
  • 22
    • 0003221080 scopus 로고
    • Introduction to hamiltonian dynamical systems and the N-body problem
    • Springer-Verlag, New York
    • K. Meyer and G. R. Hall, "Introduction to Hamiltonian Dynamical Systems and the N-Body Problem," Applied Mathematical Sciences, 90, Springer-Verlag, New York, 1992.
    • (1992) Applied Mathematical Sciences , vol.90
    • Meyer, K.1    Hall, G.R.2
  • 23
    • 0004090122 scopus 로고
    • Gauthier-Villars, Paris
    • H. Poincaré, "Oeuvres," Gauthier-Villars, Paris, 1934.
    • (1934) Oeuvres
    • Poincaré, H.1
  • 26
    • 0034762981 scopus 로고    scopus 로고
    • SMART-1: The first time of Europe to the moon
    • G. Racca, B. H. Foing and M. Coradini, SMART-1: The first time of Europe to the moon, Earth, Moon and Planets, 85-86 (2001), 379-390.
    • (2001) Earth, Moon and Planets , vol.85-86 , pp. 379-390
    • Racca, G.1    Foing, B.H.2    Coradini, M.3
  • 27
    • 0036942964 scopus 로고    scopus 로고
    • SMART-1 mission description and development status
    • G. Racca, et al., SMART-1 mission description and development status, Planetary and Space Science, 50 (2002), 1323-1337.
    • (2002) Planetary and Space Science , vol.50 , pp. 1323-1337
    • Racca, G.1
  • 28
    • 3943090734 scopus 로고
    • Index of second variation of a control system
    • 496
    • A. V. Saryčev, Index of second variation of a control system, Mat. Sb. (N.S.), 113(155) (1980), 464-486, 496.
    • (1980) Mat. Sb. N.S. , vol.113 , Issue.155 , pp. 464-486
    • Saryčev, A.V.1
  • 29
    • 0016971912 scopus 로고
    • Solving non-stiff ordinary differential equations- The state of the art
    • L. F. Shampine, H. A. Watts and S. Davenport, Solving non-stiff ordinary differential equations-the state of the art, SIAM Rev., 18 (1976), 376-411.
    • (1976) SIAM Rev. , vol.18 , pp. 376-411
    • Shampine, L.F.1    Watts, H.A.2    Davenport, S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.