Abstract
Attitude dynamics of perturbed triaxial rigid bodies is a rather involved problem, due to the presence of elliptic functions even in the Euler equations for the free rotation of a triaxial rigid body. With the solution of the Euler—Poinsot problem, that will be taken as the unperturbed part, we expand the perturbation in Fourier series, which coefficients are rational functions of the Jacobian nome. These series converge very fast, and thus, with only few terms a good approximation is obtained. Once the expansion is performed, it is possible to apply to it a Lie-transformation. An application to a tri-axial rigid body moving in a Keplerian orbit is made.
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References
Abad, A., Elipe, A. and Vallejo, M.: 1994, ‘Automated Fourier series expansions for elliptic functions’, Mech. Res. Commun. 21, 361–366.
Abad, A., Elipe, A. and Vallejo, M.: 1997, ‘Normalization of perturbed non-linear Hamiltonian oscillators’, Int. J. Non-lin. Mech. 32, 443–453.
Andoyer, H.: 1923, Cours de mécanique céleste, Paris, Gauthier-Villars et Cie
Arribas, M. and Elipe, A.: 1993, ‘Attitude dynamics of a rigid body on a Keplerian orbit: a simplification’, Celest. Mech. & Dyn. Astr. 55, 243–247.
Barkin, Y. A.: 1992, Lecture notes Universidad de Zaragoza (unpublished).
Brumberg, V. A.: 1995, Analytical Techniques of Celestial Mechanics. Springer, Berlin.
Deprit, A.: 1967, ‘Free rotation of a rigid body studied in the phase plane’, Am. J. Phy. 35, 424–428.
Deprit, A.: 1969, ‘Canonical transformation depending on a small parameter’, Celestial Mechanics, 1, 12–30.
Deprit, A. and Elipe, A.: 1993, ‘Complete reduction of the Euler—Poinsot problem’, J. Astronaut. Sci. 41, 603–628.
Elipe, A., Abad, A. and Arribas, M.: 1992, ‘Scaling Hamiltonians in attitude dynamics of two rigid bodies’, Rev. Acad. Ciencias de Zaragoza 47, 137–154.
Ferrândiz, J. M. and Sansaturio, M. E.: 1989, ‘Elimination of the nodes when the satellite is a non-spherical rigid body’, Celest. Mech. & Dyn. Astr. 46, 307–320.
Galgani, L., Giorgilli, A. and Strelcyn, J. M.: 1981, ‘Chaotic motion and transition to stochasticity in the classical problem of a heavy rigid body with a fixed point’, Il Nuovo Cimento B, 61, 1–20.
Kinoshita, H.: 1972, ‘First-order perturbations of the two finite body problem’, Publ. Astron. Soc. Japan 24, 423–457.
Sadov, Yu. A.: 1970, ‘The Action-Angles Variables in the Euler-Poinsot Problem’, Akad. Nauk SSSR, Prep. 22.
Serret, J. A.: 1866, ‘Mémoire sur l’emploi de la méthode de la variation des arbitraires dans la théorie des mouvements de rotation’, Mémoi. Acad. Sci. Paris 35, 585–616.
Shuster, M.: 1993, ‘A survey on attitude representations’, J. Astronaut. Sci. 41, 439–517.
Wisdom, J.: 1987, ‘Rotational dynamics of irregularly shaped natural satellites’, Astron. J. 94, 1350–1360.
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© 2001 Springer Science+Business Media Dordrecht
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Elipe, A., Vallejo, M. (2001). On the Attitude Dynamics of Perturbed Triaxial Rigid Bodies. In: Pretka-Ziomek, H., Wnuk, E., Seidelmann, P.K., Richardson, D.L. (eds) Dynamics of Natural and Artificial Celestial Bodies. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1327-6_1
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DOI: https://doi.org/10.1007/978-94-017-1327-6_1
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