Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 3, pp. 395-411.
@article{AIHPC_2007__24_3_395_0,
     author = {Bonnard, Bernard and Caillau, Jean-Baptiste},
     title = {Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {395--411},
     publisher = {Elsevier},
     volume = {24},
     number = {3},
     year = {2007},
     doi = {10.1016/j.anihpc.2006.03.013},
     mrnumber = {2319940},
     zbl = {1127.49017},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2006.03.013/}
}
TY  - JOUR
AU  - Bonnard, Bernard
AU  - Caillau, Jean-Baptiste
TI  - Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2007
SP  - 395
EP  - 411
VL  - 24
IS  - 3
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2006.03.013/
DO  - 10.1016/j.anihpc.2006.03.013
LA  - en
ID  - AIHPC_2007__24_3_395_0
ER  - 
%0 Journal Article
%A Bonnard, Bernard
%A Caillau, Jean-Baptiste
%T Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust
%J Annales de l'I.H.P. Analyse non linéaire
%D 2007
%P 395-411
%V 24
%N 3
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2006.03.013/
%R 10.1016/j.anihpc.2006.03.013
%G en
%F AIHPC_2007__24_3_395_0
Bonnard, Bernard; Caillau, Jean-Baptiste. Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 3, pp. 395-411. doi : 10.1016/j.anihpc.2006.03.013. http://www.numdam.org/articles/10.1016/j.anihpc.2006.03.013/

[1] Allgower E.L., Georg K., Introduction to Numerical Continuation Methods, Classics Appl. Math., vol. 45, SIAM, Philadelphia, 2003. | MR | Zbl

[2] Arnold V.I., Mathematical Methods of Classical Mechanics, Springer-Verlag, New York, 1978. | MR | Zbl

[3] Bolsinov A., Fomenko A., Integrable Geodesics Flows on Two-Dimensional Surfaces, Kluwer, New York, 2000. | Zbl

[4] Bonnard B., Caillau J.-B., Trélat E., Geometric optimal control of elliptic Keplerian orbits, Disc. Cont. Dyn. Syst. Ser. B 5 (4) (2005) 929-956. | MR | Zbl

[5] B. Bonnard, J.-B. Caillau, E. Trélat, Second order optimality conditions in the smooth case and applications in optimal control, ESAIM Control Optim. Calc. Var., in press. | Numdam | MR | Zbl

[6] Bonnard B., Chyba M., Singular Trajectories and their Role in Optimal Control, Math. Appl., vol. 40, Springer-Verlag, Paris, 2003. | MR | Zbl

[7] J.-B. Caillau, Contribution à l'étude du contrôle en temps minimal des transferts orbitaux, PhD thesis, ENSEEIHT, Institut National Polytechnique de Toulouse, 2000.

[8] Caillau J.-B., Gergaud J., Noailles J., Minimum time control of the Kepler equation, in: Blondel V., Megretski A. (Eds.), Unsolved Problems in Mathematical Systems and Control Theory, Princeton University Press, 2004, pp. 89-92. | MR

[9] Chaplais F., Averaging and deterministic optimal control, SIAM J. Control Optim. 25 (3) (1987) 767-780. | MR | Zbl

[10] Epenoy R., Geffroy S., Optimal low-thrust transfers with constraints: generalization of averaging techniques, Acta Astronaut. 41 (3) (1997) 133-149.

[11] Françoise J.-P., Oscillations en biologie : analyse qualitative et modèles, Math. Appl., vol. 46, Springer-Verlag, Paris, 2005. | MR | Zbl

[12] S. Geffroy, Les techniques de moyennisation en contrôle optimal. Application aux transferts orbitaux à poussée continue, Master thesis, ENSEEIHT, Institut National Polytechnique de Toulouse, 1994.

[13] J. Gergaud, T. Haberkorn, Homotopy method for minimum consumption orbit transfer problem, ESAIM Control Optim. Calc. Var., in press. | Numdam | MR | Zbl

[14] Kevorkian J., Cole J.D., Perturbation Methods in Applied Mathematics, Springer-Verlag, New York, 1981. | MR | Zbl

[15] Peng S.G., Analyse asymptotique et problème homogénéisé en contrôle optimal avec vibrations rapides, SIAM J. Control Optim. 27 (4) (1989) 673-696. | MR | Zbl

[16] Pontriaguine L. et al. , Théorie mathématiques des processus optimaux, Mir, Moscou, 1974. | MR | Zbl

[17] Zarrouati O., Trajectoires Spatiales, CNES-Cepadues, Toulouse, 1987.

Cité par Sources :