Geodesic flow of the averaged controlled kepler equation

Forum Mathematicum

Volumn 21, Issue 5, 2009, Pages 797-814

  Bonnard, Bernard ^a   Caillau, Jean Baptiste ^b  

^a UNIVERSITÉ DE BOURGOGNE   (France)

^b UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67649275496     PISSN: 09337741     EISSN: 14355337     Source Type: Journal    
DOI: 10.1515/FORUM.2009.038     Document Type: Article

References (18)

1. Arnold V. I., Varchenko A. N., Gusein-Zade S.M.: Singularities of differentiable maps, Vol.1. BirkḦauser 1988.
2. Bolsinov A., Fomenko A.: Integrable Geodesic Flows on Two-Dimensional Surfaces. Kluwer 2000.
3. Bonnard B., Caillau J.-B.: Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust. Ann. Inst. H. Poincaŕe Anal. Non Lińeaire 24 (2007), 395-411.
4. Bonnard B., Caillau J.-B., Sinclair R., Tanaka M.: Conjugate and cut loci of a two-sphere of revolution with application to optimal control. HAL preprint (2008), no.00212075, 1-20 (url: hal.archives-ouvertes.fr/hal-00212075).
5. Bonnard B., Caillau J.-B., Tŕelat E.: Geometric optimal control of elliptic Keplerian orbits. Disc. Contin. Dyn. Syst. Ser. B 5 (2005), 929-956.
6. Chang D. E., Chichka D. F., Marsden J. E.: Lyapunov-based transfer between Keplerian orbits. Disc. Contin. Dyn. Syst. Ser. B 2 (2002), 57-67.
7. Darboux G.: Lȩcons sur la Th́eorie Ǵeńerale des Surfaces, Tome III. Gauthiers-Villars 1914.
8. do Carmo M. P.: Riemannian Geometry. BirkḦauser 1992.
9. Elerath D.: An improved Topogonov comparison theorem for non-negatively curved manifolds. J. Differential Geom. 15 (1980), 187-216.
10. Epenoy R., Geffroy S.: Optimal low-thrust transfers with constraints: generalization of averaging techniques.Acta Astronaut. 41 (1997), 133-149.
11. Gluck H., Singer D.: Scattering of geodesic fields I and II. Ann. of Math. 108 (1978), 347-372; and 110 (1979), 205-225.
12. Klingenberg W. P.A.: Riemannian Geometry. de Gruyter 1982.
13. Klingenberg W. P. A.: Poincaŕe's closed geodesic on a convex surface. Trans.Amer. Math. Soc. 356 (2004), 2545-2556.
14. von Mangoldt H.: Uber diejenigen Punkte auf positiv gekr̈ummten Flächen, welche die Eigenschaft haben, daß die von ihnen ausgehenden geoD̈atischen Linien nie aufḦ oren, K̈urzeste Linien zu sein. J. ReineAngew.Math. 91 (1881), 23-53.
15. Myers S. B.: Connections between geometry and topology I and II. Duke Math. J. 1 (1935), 376-391; and 2 (1936), 95-102.
16. Nagell T.: Introduction to Number Theory.Wiley 1951.
17. Poincaŕe H.: Sur les lignes ǵeod́esiques des surfaces convexes.Trans.Amer.Math. Soc. 5 (1905), 237-274.
18. Tanaka M.: On the cut loci of a von Mangoldt's surface of revolution. J. Math. Soc. Japan 44 (1992), 631-641.