Stability Problems in Space Flight Mechanics

Abstract

Some classical problems in space flight mechanics are recalled and relevant examples are studied, in which stability considerations arise. The first example refers to the motion of a rigid body in orbit. For tht circular case, a simple solution is obtained, where the amplitude of the deviation from the local vertical does not exceed the initial value; for an elliptic orbit, additional accelerating terms arise, and the motion amplitude may become much larger; also, unstable positions are discussed. The second example refers to a spacecraft with flexible appendages; here, gravity gradients may have a destabilizing effect and counteract the stiffening structural effects in such a way that motions of indefinitely increasing amplitude may occur. Finally, the third example occurs in the analysis of the well-known Lagrangian points in the three-body problem, when the nonzero eccentricity of the orbits of the two main attracting bodies is taken into consideration.