On the stability of the rotational motion of nonspherical natural satellites in a synchronous resonance

The stability of the rotational motion of a nonspherical natural satellite in an elliptical orbit in a synchronous spin-orbital resonance is studied. The axis of rotation of a satellite is assumed to coincide with the axis of its maximum moment of inertia and to be orthogonal to the orbital plane. O n the plane of the inertial parameters (A/C, B/C), where A, B, and C (A < B < C) are the principal moments of inertia, the boundaries of regions of st ability acid instability with respect to tilting the axis of rotation are d etermined by calculating the multiplicators of linearized Hamiltonian equat ions of motion. High resolution, achieved in the determination of the bound aries of these regions, makes it possible to impose additional constraints on the values of inertial parameters for Hyperion and, in the case of Amalt hea, to draw a conclusion on the instability of its relative motion with re spect to tilting the axis of rotation in one of two possible synchronous re sonances.