Closed form perturbation solution of a fast rotating triaxial satellite under gravity-gradient torque
- 66 Downloads
The attitude dynamics of a fast rotating triaxial satellite under gravity-gradient is revisited. The essentially unique reduction of the Euler-Poinsot Hamiltonian, which can be performed in different sets of variables, provides a suitable set of canonical variables that expedites the perturbation approach. Two canonical transformations reduce the perturbed problem to its secular terms. The secular Hamiltonian and the transformation equations of the averaging are computed in closed form of the triaxiality coefficient, thus being valid for any triaxial body. The solution depends on Jacobi elliptic functions and integrals, and applies to non-resonant rotations under the assumption that the rotation rate is much higher than the orbital or precessional motion.
KeywordsCanonical Variable Cosmic Research Canonical Transformation Gravity Gradient Hamilton Jacobi Equation
Unable to display preview. Download preview PDF.
- 1.Andoyer, M.H., Cours de Mécanique Céleste, Paris: Gauthier-Villars et cie, vol. 1, p. 57.Google Scholar
- 4.Beletskii, V.V., Motion of an Artificial Satellite About Its Center of Mass, S. Monson, Jerusalem: Israel Program for Scientific Translations, 1966.Google Scholar
- 16.Goldstein, H., Poole, C.P., and Safko, J.L., Classical Mechanics, 3rd Ed., Addison-Wesley, 2001.Google Scholar
- 24.Lara, M. and Ferrer, S., Complete closed form solution of a tumbling triaxial satellite under gravity-gradient torque, American Astronautical Society, Paper AAS 12-119.Google Scholar
- 25.MacCullagh, J., On the rotation of a solid body, Proc. Royal Irish Acad., 1840, vol. 2, pp. 520–545.Google Scholar
- 27.Sadov, Yu.A., The action-angle variables in the Euler-Poinsot problem, Preprint Russian Academy of Sciences Moscow, KIAM, 1970, no. 22.Google Scholar
- 28.Sadov, Yu.A., Using action-angle variables in problems of disturbed Motion of a solid body about its center of mass, Preprint Russian Academy of Sciences Moscow, KIAM, 1984, no. 33.Google Scholar
- 30.Tchernousko, F.L. Study of satellite motion about center of mass using averaging method. Proc. XIVth International Astronautical Congress. 1963, vol. IV, pp. 143–154.Google Scholar