Electron. J. Diff. Equ., Vol. 2011 (2011), No. 134, pp. 1-15.

Longitudinal librations of a satellite

Massimo Furi, Mario Martelli, Alfonso Vignoli

Furi, Martelli and Landsberg gave a theoretical explanation of the chaotic longitudinal librations of Hyperion, a satellite of Saturn. The analysis was made under the simplifying assumption that the spin axis remains perpendicular to the orbit plane. Here, under the same assumption, we investigate the behavior of the longitudinal librations of any satellite. Also we show that they are possibly chaotic depending on two parameters: a constant k related to the principal moments of inertia of the satellite, and the eccentricity e of its orbit. We prove that the plane k-e contains an open region $\Omega$ with the property that the longitudinal librations of any satellite are possibly chaotic if the point (k,e) belongs to this region. Since Hyperion's point is inside $\Omega$, the results of this paper are more general than those obtained previously.

Submitted April 18, 2011. Published October 14, 2011.
Math Subject Classifications: 34C28, 70F15.
Key Words: Ordinary differential equations; Chaotic behavior of a satellite; librations.

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Massimo Furi
Dipartimento di Matematica Applicata
Università degli Studi di Firenze
Via S. Marta 3, 50139 Firenze, Italy
email: massimo.furi@unifi.it
Mario Martelli
Department of Mathematics
Claremont Graduate University
710 N College Ave
Claremont, CA 91711, USA
email: mario.martelli@cgu.edu
Alfonso Vignoli
Dipartimento di Matematica
Università di Roma Tor Vergata
Via della Ricerca Scientifica 1, 00133, Roma, Italy
email: vignoli@mat.uniroma2.it

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