STABILITY OF SPINNING SPACECRAFT CONTAINING SHALLOW POOL OF LIQUID UNDER THRUST

A well-known night nutation instability observed with spinning spacecr aft under the thrust of a solid rocket motor is examined. A shallow po ol of molten slag trapped in the aft motor chamber is represented by a linearized hydrodynamic coupled finite element model. The frequency o f the dominant retrograde ''swirl'' mode of the uncoupled liquid is fo und to intersect the spacecraft nutation frequency during the anomalou s flight and is the suspected cause of instability. With no effects of internal gas flow the coupled model predicts the onset of instability only at the very end of the burn. However, if the equilibrium liquid shape is deformed slightly more outboard, as suggested by a previously predicted recirculating gas now in the motor chamber, then the model is capable of matching the onset of nutation growth observed in flight . The subsequent nutation growth amplitude profile is also matched. Ho wever, the nutation frequency of the linear model deviates from the fl ight value as the burn progresses. For a prolate spinner, high spin sp eed, low thrust and large slag axial offset are the conditions for ins tability; for an oblate spinner the destabilizing conditions are oppos ite.