Stability of Spinning Satellite Under Axial Thrust, Internal Mass Motion, and Damping

The paper extends and clarifies the stability results for a spinning satellite under axial thrust in the presence of internal damped mass motion. It is known that prolate and oblate satellite configurations can be stabilized by damped mass motion. Here, the stability boundaries are established by exploiting the properties of the complex characteristic equation and the results are interpreted in terms of the physical system parameters. When the thrust level is the only free parameter, both prolate and oblate satellites can be stabilized provided that the thrust is within a specified range. This result is in contrast to the well-known maximum-axis rule for a free spinner where damping is always stabilizing (destabilizing) for an oblate (prolate) satellite. When adding a suitable spring-mass system, the minimum value of the spring constant that stabilizes the configuration can be established. In practice, however, the damping may well be too weak to be effective. Numerical illustrations are presented for the actual parameters of the Ulysses prolate configuration at orbit injection as well as for a fictitious oblate system. Finally, a new derivation of a previously established first integral for the undamped system is offered and its properties as a Lyapunov function are discussed.