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�������պ����ѧѧ�� 2001, Vol. 27 Issue (2) :233-236    DOI:
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Stability of Spinning Top Filled with Non-fully Rotating Liquid
WANG Shi-min1, LI Lei2*
1. Beijing University of Aeronautics and Astronautics, School of Science;
2. Tsinghua University, Dept. of Engineering Mechanics

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ժҪ һЩ��ת��Һϵͳ,��������������̻�Һ��ϵͳ�������ȶ�������,����Ҳ�����¶���Һ����Բ��Ĺ���������,������ʵ��ʱϵͳȴ�����˶����ȶ�.��һ�����޷���SWM(Stewartson-Wedemeyer-Murphy)�������۽���,��ʹ�ڹ�������к��ѱܿ����ȶ��IJ�������.���IJ�����ֵ����������Һ��δ��ȫ�����Ը�����ת��Һ�����ȶ��Ե�Ӱ��,��Ӧ��Lyapunov-Rumjantsev ���ֱ����ȶ�������,�ó���Һ�岻��ȫ����ʱ,��Һ�����ȶ�������.
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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.
Keywords�� gyroscopic stability   Lyapunov stability   Lyapunov's method   partial variable stability     
Received 1999-12-07;
Fund:

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��ʿ��, ����.Һ�岻��ȫ����ʱ��Һ�����ȶ����о�[J]  �������պ����ѧѧ��, 2001,V27(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 A, 2001,V27(2): 233-236
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