Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 123138, 15 pages
Research Article

Higher-Order Analytical Attitude Propagation of an Oblate Rigid Body under Gravity-Gradient Torque

1Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, Spain
2Departamento de Ingeniería Mecánica, Universidad de La Rioja, 26004 Logroño, Spain

Received 3 March 2011; Revised 25 June 2011; Accepted 3 August 2011

Academic Editor: Maria Zanardi

Copyright © 2012 Juan F. San-Juan 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.


A higher-order perturbation theory for the rotation of a uniaxial satellite under gravity-gradient torque demonstrates that known special configurations of the attitude dynamics at which the satellite rotates, on average, as in a torque-free state, are only the result of an early truncation of the secular frequencies of motion. In addition to providing a deeper insight into the dynamics, the higher order of the analytical solution makes it competitive when compared with the long-term numerical integration of the equations of motion.