American Institute of Mathematical Sciences

Advanced
June  2008, 1(2): 293-302. doi: 10.3934/dcdss.2008.1.293

Computing long-lifetime science orbits around natural satellites

Martin Lara 1, and  Sebastián Ferrer 2,

1. 

Real Observatorio de la Armada, ES-11 110 San Fernando, Spain
2. 

University of Murcia, ES-30 071 Murcia, Spain

Received  September 2006 Revised  February 2007 Published  March 2008

Science missions around natural satellites require low eccentricity and high inclination orbits. These orbits are unstable because of the planetary perturbations, making control necessary to reach the required mission lifetime. Dynamical systems theory helps in improving lifetimes reducing fuel consumption. After a double averaging of the 3-DOF model, the initial conditions are chosen so that the orbit follows the stable-unstable manifold path of an equilibria of the 1-DOF reduced problem. Corresponding initial conditions in the non-averaged problem are easily computed from the explicit transformations provided by the Lie-Deprit perturbation method.
Keywords: Astrodynamics, toral reduction, bifurcations..
Mathematics Subject Classification: 70F15, 70K65, Secondary: 70H0.
Citation: Martin Lara, Sebastián Ferrer. Computing long-lifetime science orbits around natural satellites. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 293-302. doi: 10.3934/dcdss.2008.1.293
[1]

Hayato Chiba, Georgi S. Medvedev. The mean field analysis of the kuramoto model on graphs Ⅱ. asymptotic stability of the incoherent state, center manifold reduction, and bifurcations. Discrete & Continuous Dynamical Systems, 2019, 39 (7) : 3897-3921. doi: 10.3934/dcds.2019157
[2]

Arvind Ayyer, Carlangelo Liverani, Mikko Stenlund. Quenched CLT for random toral automorphism. Discrete & Continuous Dynamical Systems, 2009, 24 (2) : 331-348. doi: 10.3934/dcds.2009.24.331
[3]

Jean-Pierre Conze, Stéphane Le Borgne, Mikaël Roger. Central limit theorem for stationary products of toral automorphisms. Discrete & Continuous Dynamical Systems, 2012, 32 (5) : 1597-1626. doi: 10.3934/dcds.2012.32.1597
[4]

Federico Rodriguez Hertz. Global rigidity of certain Abelian actions by toral automorphisms. Journal of Modern Dynamics, 2007, 1 (3) : 425-442. doi: 10.3934/jmd.2007.1.425
[5]

Lennard F. Bakker, Pedro Martins Rodrigues. A profinite group invariant for hyperbolic toral automorphisms. Discrete & Continuous Dynamical Systems, 2012, 32 (6) : 1965-1976. doi: 10.3934/dcds.2012.32.1965
[6]

Michael Baake, Natascha Neumärker, John A. G. Roberts. Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices. Discrete & Continuous Dynamical Systems, 2013, 33 (2) : 527-553. doi: 10.3934/dcds.2013.33.527
[7]

Hiroaki Yoshimura, Jerrold E. Marsden. Dirac cotangent bundle reduction. Journal of Geometric Mechanics, 2009, 1 (1) : 87-158. doi: 10.3934/jgm.2009.1.87
[8]

Katarzyna Grabowska, Paweƚ Urbański. Geometry of Routh reduction. Journal of Geometric Mechanics, 2019, 11 (1) : 23-44. doi: 10.3934/jgm.2019002
[9]

Inês Cruz, M. Esmeralda Sousa-Dias. Reduction of cluster iteration maps. Journal of Geometric Mechanics, 2014, 6 (3) : 297-318. doi: 10.3934/jgm.2014.6.297
[10]

Laura Luzzi, Ghaya Rekaya-Ben Othman, Jean-Claude Belfiore. Algebraic reduction for the Golden Code. Advances in Mathematics of Communications, 2012, 6 (1) : 1-26. doi: 10.3934/amc.2012.6.1
[11]

Jean-François Babadjian, Francesca Prinari, Elvira Zappale. Dimensional reduction for supremal functionals. Discrete & Continuous Dynamical Systems, 2012, 32 (5) : 1503-1535. doi: 10.3934/dcds.2012.32.1503
[12]

Martins Bruveris, David C. P. Ellis, Darryl D. Holm, François Gay-Balmaz. Un-reduction. Journal of Geometric Mechanics, 2011, 3 (4) : 363-387. doi: 10.3934/jgm.2011.3.363
[13]

Thomas Espitau, Antoine Joux. Certified lattice reduction. Advances in Mathematics of Communications, 2020, 14 (1) : 137-159. doi: 10.3934/amc.2020011
[14]

Ian Melbourne, Dalia Terhesiu. Mixing properties for toral extensions of slowly mixing dynamical systems with finite and infinite measure. Journal of Modern Dynamics, 2018, 12: 285-313. doi: 10.3934/jmd.2018011
[15]

Kengo Matsumoto. $ C^* $-algebras associated with asymptotic equivalence relations defined by hyperbolic toral automorphisms. Electronic Research Archive, 2021, 29 (4) : 2645-2656. doi: 10.3934/era.2021006
[16]

Ning Zhang, Qiang Wu. Online learning for supervised dimension reduction. Mathematical Foundations of Computing, 2019, 2 (2) : 95-106. doi: 10.3934/mfc.2019008
[17]

Joshua Cape, Hans-Christian Herbig, Christopher Seaton. Symplectic reduction at zero angular momentum. Journal of Geometric Mechanics, 2016, 8 (1) : 13-34. doi: 10.3934/jgm.2016.8.13
[18]

Paul Glendinning. Non-smooth pitchfork bifurcations. Discrete & Continuous Dynamical Systems - B, 2004, 4 (2) : 457-464. doi: 10.3934/dcdsb.2004.4.457
[19]

Anatoly Neishtadt. On stability loss delay for dynamical bifurcations. Discrete & Continuous Dynamical Systems - S, 2009, 2 (4) : 897-909. doi: 10.3934/dcdss.2009.2.897
[20]

Maria Conceição A. Leite, Yunjiao Wang. Multistability, oscillations and bifurcations in feedback loops. Mathematical Biosciences & Engineering, 2010, 7 (1) : 83-97. doi: 10.3934/mbe.2010.7.83

2020 Impact Factor: 2.425

Tools

Metrics

  • PDF downloads (135)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences