American Institute of Mathematical Sciences

Advanced
2011, 2011(Special): 1196-1205. doi: 10.3934/proc.2011.2011.1196

Energy-minimal transfers in the vicinity of the lagrangian point $L_1$

Gautier Picot 1,

1. 

Mathematics Institute, Bourgogne University, 9 avenue Savary, 21078 Dijon

Received  July 2010 Revised  April 2011 Published  October 2011

This article deals with the problem of computing energy-minimal trajectories between the invariant manifolds in the neighborhood of the equilibrium point $L_1$ of the restricted 3-body problem. Initializing a simple shooting method with solutions of the corresponding linear optimal control problem, we numerically compute energy-minimal extremals from the Pontryagin's Maximum principle, whose optimality is ensured thanks to the second order optimality condition.
Keywords: 3-body problem, numerical analysis methods, Optimal control.
Mathematics Subject Classification: Primary: 49K15, 49M05; Secondary: 70F07.
Citation: Gautier Picot. Energy-minimal transfers in the vicinity of the lagrangian point $L_1$. Conference Publications, 2011, 2011 (Special) : 1196-1205. doi: 10.3934/proc.2011.2011.1196
[1]

Gianni Arioli. Branches of periodic orbits for the planar restricted 3-body problem. Discrete & Continuous Dynamical Systems - A, 2004, 11 (4) : 745-755. doi: 10.3934/dcds.2004.11.745
[2]

Alain Albouy, Holger R. Dullin. Relative equilibria of the 3-body problem in $ \mathbb{R}^4 $. Journal of Geometric Mechanics, 2020  doi: 10.3934/jgm.2020012
[3]

Z. Foroozandeh, Maria do rosário de Pinho, M. Shamsi. On numerical methods for singular optimal control problems: An application to an AUV problem. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2219-2235. doi: 10.3934/dcdsb.2019092
[4]

Holger R. Dullin, Jürgen Scheurle. Symmetry reduction of the 3-body problem in $ \mathbb{R}^4 $. Journal of Geometric Mechanics, 2020  doi: 10.3934/jgm.2020011
[5]

Giovanni F. Gronchi, Chiara Tardioli. The evolution of the orbit distance in the double averaged restricted 3-body problem with crossing singularities. Discrete & Continuous Dynamical Systems - B, 2013, 18 (5) : 1323-1344. doi: 10.3934/dcdsb.2013.18.1323
[6]

Alain Chenciner, Jacques Féjoz. The flow of the equal-mass spatial 3-body problem in the neighborhood of the equilateral relative equilibrium. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 421-438. doi: 10.3934/dcdsb.2008.10.421
[7]

Qunyao Yin, Shiqing Zhang. New periodic solutions for the circular restricted 3-body and 4-body problems. Communications on Pure & Applied Analysis, 2010, 9 (1) : 249-260. doi: 10.3934/cpaa.2010.9.249
[8]

Martin Benning, Elena Celledoni, Matthias J. Ehrhardt, Brynjulf Owren, Carola-Bibiane Schönlieb. Deep learning as optimal control problems: Models and numerical methods. Journal of Computational Dynamics, 2019, 6 (2) : 171-198. doi: 10.3934/jcd.2019009
[9]

Xiaowei Pang, Haiming Song, Xiaoshen Wang, Jiachuan Zhang. Efficient numerical methods for elliptic optimal control problems with random coefficient. Electronic Research Archive, 2020, 28 (2) : 1001-1022. doi: 10.3934/era.2020053
[10]

Krzysztof Bartosz. Numerical analysis of a nonmonotone dynamic contact problem of a non-clamped piezoelectric viscoelastic body. Evolution Equations & Control Theory, 2020, 9 (4) : 961-980. doi: 10.3934/eect.2020059
[11]

Térence Bayen, Marc Mazade, Francis Mairet. Analysis of an optimal control problem connected to bioprocesses involving a saturated singular arc. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 39-58. doi: 10.3934/dcdsb.2015.20.39
[12]

Max Gunzburger, Sung-Dae Yang, Wenxiang Zhu. Analysis and discretization of an optimal control problem for the forced Fisher equation. Discrete & Continuous Dynamical Systems - B, 2007, 8 (3) : 569-587. doi: 10.3934/dcdsb.2007.8.569
[13]

Florin Diacu, Shuqiang Zhu. Almost all 3-body relative equilibria on $ \mathbb S^2 $ and $ \mathbb H^2 $ are inclined. Discrete & Continuous Dynamical Systems - S, 2020, 13 (4) : 1131-1143. doi: 10.3934/dcdss.2020067
[14]

Radouen Ghanem, Billel Zireg. Numerical solution of bilateral obstacle optimal control problem, where the controls and the obstacles coincide. Numerical Algebra, Control & Optimization, 2020, 10 (3) : 275-300. doi: 10.3934/naco.2020002
[15]

Elbaz I. Abouelmagd, Juan Luis García Guirao, Jaume Llibre. Periodic orbits for the perturbed planar circular restricted 3–body problem. Discrete & Continuous Dynamical Systems - B, 2019, 24 (3) : 1007-1020. doi: 10.3934/dcdsb.2019003
[16]

Martha Alvarez-Ramírez, Joaquín Delgado. Blow up of the isosceles 3--body problem with an infinitesimal mass. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1149-1173. doi: 10.3934/dcds.2003.9.1149
[17]

Samuel R. Kaplan, Ernesto A. Lacomba, Jaume Llibre. Symbolic dynamics of the elliptic rectilinear restricted 3--body problem. Discrete & Continuous Dynamical Systems - S, 2008, 1 (4) : 541-555. doi: 10.3934/dcdss.2008.1.541
[18]

Sergey V. Bolotin, Piero Negrini. Variational approach to second species periodic solutions of Poincaré of the 3 body problem. Discrete & Continuous Dynamical Systems - A, 2013, 33 (3) : 1009-1032. doi: 10.3934/dcds.2013.33.1009
[19]

Hang-Chin Lai, Jin-Chirng Lee, Shuh-Jye Chern. A variational problem and optimal control. Journal of Industrial & Management Optimization, 2011, 7 (4) : 967-975. doi: 10.3934/jimo.2011.7.967
[20]

Zahra Al Helal, Volker Rehbock, Ryan Loxton. Modelling and optimal control of blood glucose levels in the human body. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1149-1164. doi: 10.3934/jimo.2015.11.1149

 Impact Factor: 

Tools

Metrics

  • PDF downloads (14)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences