On the Stability of a Planar Resonant Rotation of a Satellite in an Elliptic Orbit

We study the Lyapunov stability problem of the resonant rotation of a rigid body satellite about its center of mass in an elliptical orbit. The resonant rotation is a planar motion such that the satellite completes one rotation in absolute space during two orbital revolutions of its center of mass. The stability analysis of the above resonance rotation was started in [4, 6]. In the present paper, rigorous stability conclusions in the previously unstudied range of parameter values are obtained. In particular, new intervals of stability are found for eccentricity values close to 1. In addition, some special cases are studied where the stability analysis should take into account terms of degree not less than six in the expansion of the Hamiltonian of the perturbed motion. Using the technique described in [7, 8], explicit formulae are obtained, allowing one to verify the stability criterion of a time-periodic Hamiltonian system with one degree of freedom in the special cases mentioned.