一类轴对称充液陀螺系统自旋运动稳定性研究

ON THE STABILITY OF A SPINNING, ROTATIONALLY SYMMETRIC TOP CONTAINING LIQUIDS

研究了一类复杂充液旋转对称陀螺（其圆柱形容腔充有互不相溶的双元液体，且带充液圆柱中心杆）的章动振荡与其所充双元液体自由振荡之耦合问题．

The problem of coupling between the nutational oscillation of a gyro containing three component liquids and the natural oscillation of the rotating liquids themselves is investigated .The interfacial tension is considered in the free surface bounding the liquids. The linearized equations are treated analytically using the Stewartson's and Zhukovsky's theory . The stability of motion is investigated using the method of residues. It is shown theoretically that instability can occur when any of the periods of free oscillation of two immiscible liquids, which are double infinite in number, is sufficiently near to the period of nutation of the gyro with a third liquid filled column. The liquid filled gyro nutation growth rate vs. the inertia ratio is also studied in detail. The criterion has practical significance for the design of liquid filled, spinning satellite and projectiles.