Stability of a Spinning Axisymmetric Rocket with Dissipative Internal Mass Motion

One hypothesis for explaining the coning instabilities observed in certain spinning axisymmetric solid fuel rockets attributes the source of the instability to the accumulation of slag near the exit of the rocket casing. This hypothesis was explored using a particle model with elastic restoring forces to represent the slag motion, and further examined for modification results when dissipative forces are added to the model, based on the second method of Liapunov. An alternative derivation of the dissipative results is now provided, based on perturbation analysis of the undamped characteristic values; this yields additional insight into the stability results. A numerical example simulating the coning instability shows that a coning growth similar to that observed in space is possible assuming certain time histories of spacecraft parameters. The example requires the natural frequency of moving mass to be close to the nominal spacecraft spin rate to produce the coning instability. In addition to their relevance for the specific problem of spinning rocket stability, the results presented provide insight on how the maximum axis spin rule for torque free spinning bodies is modified in the presence of thrust. (Author)