The gravitational influence of a second satellite on the rotation of an oblate moon is numerically examined .
A simplified model , assuming the axis of rotation perpendicular to the ( Keplerian ) orbit plane , is derived .
The differences between the two models , i.e .
in the absence and presence of the second satellite , are investigated via bifurcation diagrams and by evolving compact sets of initial conditions in the phase space .
It turns out that the presence of another satellite causes some trajectories , that were regular in its absence , to become chaotic .
Moreover , the highly structured picture revealed by the bifurcation diagrams in dependence on the eccentricity of the oblate body ’ s orbit is destroyed when the gravitational influence is included , and the periodicities and critical curves are destroyed as well .
For demonstrative purposes , focus is laid on parameters of the Saturn-Titan-Hyperion system , and on oblate satellites on low-eccentric orbits , i.e . e \approx 0.005 .