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Volume 27 Issue 2
Feb.  2001
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Journal of Beijing University of Aeronautics and Astronautics  > 2001  >  27(2): 233-236.
WANG Shi-min, LI Lei. Stability of Spinning Top Filled with Non-fully Rotating Liquid[J]. Journal of Beijing University of Aeronautics and Astronautics, 2001, 27(2): 233-236. (in Chinese)
Citation: WANG Shi-min, LI Lei. Stability of Spinning Top Filled with Non-fully Rotating Liquid[J]. Journal of Beijing University of Aeronautics and Astronautics, 2001, 27(2): 233-236. (in Chinese)
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Stability of Spinning Top Filled with Non-fully Rotating Liquid

  • 1.

    Beijing University of Aeronautics and Astronautics, School of Science

  • 2. Tsinghua University, Dept. of Engineering Mechanics

  • Received Date: 07 Dec 1999
  • Publish Date: 28 Feb 2001
    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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    • References(1)
  • [1] Stewartson K.On the stability of a spinning top containing liquid[J].J Fluid Mech,1959,5(4):577~592. [2] Wedemeyer E H. Viscous correction to Stewartson's stability criterion . AD-489697, 1966. [3] Murphy C H. Angular motion of a spinning projectile with a viscous liquid payload[J]. J Guidance Control and Dynamics, 1983,6(7-8):280~286. [4] D'Amico W P, Miller M C. Flight instability induced by a rapidly spinning, highly viscous liquid[J]. J Spacecraft and Rockets, 1979,16(52):62~64. [5] 李 磊,王照林,曾江红. 旋转充液系统非线性稳定性和动力学分析. 清华大学学报(自然科学版), 1995,35(2):41~47. [6] 王照林. 运动稳定性及其应用[M]. 北京:高等教育出版社,1992.
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