Time Versus Energy in the Averaged Optimal Coplanar Kepler Transfer Towards Circular Orbits

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• 作者：Bernard Bonnard (1)
  Helen C. Henninger (2)
  Jana N臎mcov谩 (3)
  Jean-Baptiste Pomet (2)
  
  1. Institut de Math茅matiques de Bourgogne ; Universit茅 de Bourgogne ; 9 avenue Alain Savary ; 21078 ; Dijon ; France
  2. Team McTAO ; INRIA Sophia Antipolis M茅diterran茅e ; 2004 rte des lucioles ; B.P. 92 ; 06902 ; Sophia Antipolis cedex ; France
  3. Department of Mathematics ; Institute of Chemical Technology ; Technick谩 5 ; 166 28 ; Prague 6 ; Czech Republic
  
• 关键词：Averaging ; Optimal control ; Low thrust orbit transfer ; Geodesic convexity ; Riemann ; Finsler geometry
• 刊名：Acta Applicandae Mathematicae
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：135
• 期：1
• 页码：47-80
• 全文大小：1,722 KB
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  2. Bao, D., Chern, S.S., Shen, Z.: An Introduction to Riemann-Finsler Geometry. Graduate Texts in Mathematics, vol.聽200. Springer, New York (2000)
  3. Bombrun, A., Pomet, J.B.: The averaged control system of fast oscillating control systems. SIAM J. Control Optim. 51(3), 2280鈥?305 (2013). doi:10.1137/11085791X . 330/" class="a-plus-plus">http://hal.inria.fr/hal-00648330/ 37/11085791X" target="_blank" title="It opens in new window">CrossRef
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  6. Bonnard, B., Caillau, J.B., Dujol, R.: Energy minimization of single input orbit transfer by averaging and continuation. Bull. Sci. Math. 130(8), 707鈥?19 (2006) 3.005" target="_blank" title="It opens in new window">CrossRef
  7. Bonnard, B., Faubourg, L., Tr茅lat, E.: M茅canique C茅leste et Contr么le des V茅hicules Spatiaux. Math茅matiques & Applications, vol.聽51. Springer, Berlin (2006)
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  10. Filippov, A.F.: Differential Equations with Discontinuous Righthand Sides. Mathematics and Its Applications (Soviet Series), vol.聽18. Kluwer Academic, Dordrecht (1988). doi:10.1007/978-94-015-7793-9 . Translated from the Russian
  11. Geffroy, S.: G茅n茅ralisation des techniques de moyennation en contr么le optimal 鈥?Application aux probl猫mes de rendez-vous orbitaux en pouss茅e faible. Th猫se de doctorat, Institut National Polytechnique de Toulouse, Toulouse, France (1997)
  12. Geffroy, S., Epenoy, R.: Optimal low-thrust transfers with constraints鈥攇eneralization of averaging techniques. Acta Astronaut. 41(3), 133鈥?49 (1997). doi:10.1016/S0094-5765(97)00208-7 CrossRef
  13. Hartman, P.: Ordinary Differential Equations, 2nd edn. Birkh盲user, Basel (1982)
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  15. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E.F.: In: Neustadt, L.W. (ed.) The Mathematical Theory of Optimal Processes. Interscience/Wiley, New York/London (1962). Translated from the Russian by K.N.聽Trirogoff
  
• 刊物主题：Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Statistical Physics, Dynamical Systems and Complexity; Mechanics;
• 出版者：Springer Netherlands
• ISSN：1572-9036

文摘

This article makes a study of the averaged optimal coplanar transfer towards circular orbits. Our objective is to compare this problem when the cost minimized is transfer time to the same problem when the cost minimized is energy consumption. While the minimum energy case leads to the analysis of a 2D-Riemannian metric using the standard tools of Riemannian geometry, the minimum time case is associated with a Finsler metric which is not smooth. Nevertheless a qualitative analysis of the geodesic flow is given in this article to describe the optimal transfers of the time minimal case.