On the stability of a satellite cylindrical precession in an elliptic orbit : PMM vol. 40, n 6, 1976, pp. 1040–1047

The stability of motion of a dynamically symmetric satellite with respect to its center of mass in a central Newtonian gravitational field is investigated. The satellite is a solid body whose center of mass moves on an elliptic orbit. The particular case in which the satellite axis of symmetry is normal to the orbit plane (the so-called cylindrical precession [1, 2]) and its absolute angular velocity projection on the axis of symmetry is zero, is examined. Analytical and numerical methods are used. Regions of Liapunov instability and of stability in the first approximation are. obtained in the parameter space of the problem (the inertial parameter and the orbit eccentricity). Detailed nonlinear analysis is carried out in the latter, and the formal stability of the satellite cylindrical precession is proved. The question of stability for the majority of intial conditions is also considered [4].