THE STABILITY OF A TIPPE TOP ON A SLIGHTLY ROUGH HORIZONTAL PLANE
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摘要: 本文讨论微粗糙平面上翻身陀螺绕直立的极轴永久转动的稳定性。应用关于部分变量的稳定性定理,导出在粘性和库仑两种摩擦条件下的解析形式稳定性判据。该判据用永久转动角速度的大小而不是进动角速度的大小作为判别准则,较为合理。Abstract: The stability of a tippe top rotating on a slightly rough horizontal plane is considered in this paper. The stability criterion of the permanent rotation about the vertical polar axis not only with low viscous friction but also with low dry friction is derived by using Rumiantsev's theorem of partial stability. This criterion is reasonable because it is not expressed in terms of the precessional velocity, but the angular velocity of the permanent rotation.
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Key words:
- slightly rough horizontal plane /
- tippe top /
- stability /
- partial stability
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