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Mathematical Problems in Engineering
Volume 2012, Article ID 137672, 19 pages
Research Article

Study of Stability of Rotational Motion of Spacecraft with Canonical Variables

1Group of Orbital Dynamics and Planetology, São Paulo State University (UNESP), Guaratinguetá 12516-410, SP, Brazil
2Department of Mathematics, São Paulo Salesian University (UNISAL), Lorena 12600-100, SP, Brazil
3Space Mechanic and Control Division, National Institute for Space Research (INPE), São José dos Campos 12227-010, SP, Brazil
4Department of Aircraft Maintenance and Aeronautical Manufacturing, Faculty of Technology (FATEC), São José dos Campos 12247-004, SP, Brazil

Received 16 July 2011; Revised 10 October 2011; Accepted 23 October 2011

Academic Editor: Tadashi Yokoyama

Copyright © 2012 William Reis Silva et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This work aims to analyze the stability of the rotational motion of artificial satellites in circular orbit with the influence of gravity gradient torque, using the Andoyer variables. The used method in this paper to analyze stability is the Kovalev-Savchenko theorem. This method requires the reduction of the Hamiltonian in its normal form up to fourth order by means of canonical transformations around equilibrium points. The coefficients of the normal Hamiltonian are indispensable in the study of nonlinear stability of its equilibrium points according to the three established conditions in the theorem. Some physical and orbital data of real satellites were used in the numerical simulations. In comparison with previous work, the results show a greater number of equilibrium points and an optimization in the algorithm to determine the normal form and stability analysis. The results of this paper can directly contribute in maintaining the attitude of artificial satellites.