On the chaotic behavior of the satellite hyperion
Journal of Difference Equations and Applications
We model the longitudinal librations of Hyperion with a second order nonlinear differential equation in which the terms of order e 2 or higher, where e is the eccentricity of the satellite's elliptical orbit, are neglected. With a suitable change of variable we transform the differential equation into an equivalent one that describes the motion of a forced pendulum with a vertically oscillating pivot. We prove that the pendulum has uncountably many chaotic orbits. Hence, the proposed model indicates, although it does not prove, that Hyperion's longitudinal librations are chaotic.
M. Furi, A.S. Landsberg AS, and M. Martelli . (2005). On the chaotic behavior of the satellite hyperion. J. of Difference Eqns. and Applications 11 (7): 635-643.