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]

Zhouchao Wei, Wei Zhang, Irene Moroz, Nikolay V. Kuznetsov. Codimension one and two bifurcations in Cattaneo-Christov heat flux model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020344
[2]

Meilan Cai, Maoan Han. Limit cycle bifurcations in a class of piecewise smooth cubic systems with multiple parameters. Communications on Pure & Applied Analysis, 2021, 20 (1) : 55-75. doi: 10.3934/cpaa.2020257
[3]

Javier Fernández, Cora Tori, Marcela Zuccalli. Lagrangian reduction of nonholonomic discrete mechanical systems by stages. Journal of Geometric Mechanics, 2020, 12 (4) : 607-639. doi: 10.3934/jgm.2020029
[4]

Shuang Chen, Jinqiao Duan, Ji Li. Effective reduction of a three-dimensional circadian oscillator model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020349
[5]

Annegret Glitzky, Matthias Liero, Grigor Nika. Dimension reduction of thermistor models for large-area organic light-emitting diodes. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020460
[6]

Tien-Yu Lin, Bhaba R. Sarker, Chien-Jui Lin. An optimal setup cost reduction and lot size for economic production quantity model with imperfect quality and quantity discounts. Journal of Industrial & Management Optimization, 2021, 17 (1) : 467-484. doi: 10.3934/jimo.2020043

2019 Impact Factor: 1.233

Tools

Metrics

  • PDF downloads (59)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences