Stability of a Spinning Axisymmetric Rocket with Dissipative Internal Mass Motion

Abstract

Onehypothesisforexplainingtheconinginstabilitiesobservedincertainspinningaxisymmetricsolidfuelrockets attributes the source of the instability to the accumulation of slag near the exit of the rocket casing. Previously this hypothesis was explored using a particle model with elastic restoring forces to represent the slag motion. A recent paper further examines how the results are modie ed when dissipative forces are added to the model. The work is based on the second method of Lyapunov. An alternative derivation of the dissipative results is now provided. The new derivation is based on perturbation analysis of the undamped characteristic values and yields additional insight into the stability results. A numerical example simulating the coning instability is also given. It 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 beclose to thenominal spacecraft spin rate to produce the coning instability. In addition to their relevance for the specie c problem of spinning rocket stability, the results presented provide insight on how the maximum axis spin rule for torque free spinning bodies is modie ed in the presence of thrust.