Simple theory for the Levitron
Simple theory for the Levitron
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Levitron 的简单理论
DOI：
10.1063/1.365856
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
R. Gans
中科院分区：
文献类型：
--
作者：
T. Jones;M. Washizu;R. Gans
Levitron®是一个流行的玩具，提供了一个独特的和有趣的示范悬浮使用永磁体。它由一个小的旋转磁性顶部和一个磁性底板组成。稳定的悬浮是可能的，因为磁力和扭矩与陀螺的陀螺作用的独特耦合。它的一个简单的操作理论，使用一般轴对称形式的磁场的基础上，是基于偶极力模型。利用该模型，可以通过对陀螺方向的各种假设来研究陀螺的稳定行为。如果顶部保持与基座轴线的刚性平行，稳定性是不可能的。另一方面，如果假设在径向偏移期间，顶部保持与局部磁场平行，那么稳定性是可能的。这个简单的模型，结合磁场沿轴的测量，可以相当准确地预测稳定轨迹的上限和下限。
The Levitron® is a popular toy that provides a unique and interesting demonstration of levitation using permanent magnets. It consists of a small, spinning magnetic top and a magnetic base plate. Stable levitation is possible because of a unique coupling of the magnetic forces and torques with the gyroscopic action of the top. A simple theory of its operation, using a general axisymmetric form for the magnetic field of the base, is based on the dipole force model. With this model, the stable behavior of the spinning, levitated top may be investigated by testing various assumptions for its orientation. Stability is not possible if the top remains rigidly parallel to the axis of the base. On the other hand, if one assumes that the top remains aligned parallel to the local magnetic field during radial excursions, then stability is possible. This simple model, combined with measurements of the magnetic field along the axis, permits fairly accurate prediction of the upper and lower limits of the locus of stabl...