Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 134, pp. 1-15.

Title: Longitudinal librations of a satellite

Authors: Massimo Furi (Univ. degli Studi di Firenze, Italy)
         Mario Martelli (Claremont Graduate Univ., CA, USA)
	 Alfonso Vignoli (Univ. di Roma Tor Vergata, Italy)

Abstract:
 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.