Stability of Spinning Top Filled with Non-fully Rotating Liquid
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摘要: 一些旋转充液系统,尽管理论上满足固化液体系统的陀螺稳定性条件,并且也不在章动与液体惯性波的共振区域内,但是在实验时系统却出现运动不稳定.这一现象无法由SWM(Stewartson-Wedemeyer-Murphy)线性理论解释,致使在工程设计中很难避开不稳定的参数区域.本文采用数值方法分析了液体未完全起旋对高速旋转充液陀螺稳定性的影响,并应用Lyapunov-Rumjantsev 部分变量稳定性理论,得出了液体不完全起旋时,充液陀螺稳定性条件.Abstract: In some liquid-filled spinning systems, although top stability conditions of frozen-liquid are satisfied theoretically, and the top nutation is not of resonant instability due to liquid inertia wave, angular motion of the rotating liquid-filled system is not stable in experiments. This phenomena can not explified by resonant instability theory of the SWM(Stewartson-Wedemeyer-Murphy). Therefore, it is very difficult to avoid the instability parameters in practice design. The influence of non-fully rotating liquid on the stability of spinning liquid-filled top is numerically analyzed, and the non-linear stability of spinning liquid-filled top is investigated using the partial stability theory of Liapunov-Rumjantsev. The stability condition of spinning liquid-filled top with non-fully rotating liquid is concluded.
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