Stability Criteria of Slosh Motion with Periodicity in a Spinning Spacecraft

The attitude stability of a spin-stabilized thrusting spacecraft with internal mass motion has been studied for a long time. Numerous studies have analyzed coning instabilities of space vehicles, such as the Payload Assist Module and Delta Class upper stages, and based on the analyses of telemetries, several mechanisms have been proposed to account for the instability of a spinning spacecraft. After much speculation, the list has been narrowed to several leading destabilizing mechanisms. One of these is the liquid pool theory based on mechanical and fluid interaction.` Most studies based on this theory adopted rotor-pendulum models to describe the mechanical and fluid interaction and tried to show the appropriateness and usefulness of the proposed physical and mathematical models to explain the observed motion. Accordingly, many analyses were done for fixed parameters, that is, real flown vehicle data rather than for a wider parameter space. However, for the design and manufacture of new vehicles, it is important to do an analysis for a wider parameter range. With consideration of such aspects, a closer look is taken at the stability of internal mass motion over a wider range of parameters. Because this study is complementary to previous work,4 it uses the same physical and mathematical models. To determine the stable-unstable regions of the internal mass motion of a spinning space vehicle, a Strutt diagram is constructed by using an analytical method. Furthermore, numerical simulations are performed at various points in the unstable and stable regions of the stability diagram to verify the analytical results. Because the internal mass in the spinning body has a motion with a periodically time-dependent coefficient and is subject to periodic external excitation, the multiple scales method is used to solve the system.