Massimo Furi, Mario Martelli, Alfonso Vignoli
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
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
,
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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