Heavy symmetric tops and the Hannay angle

被引:1
|
作者
Park, Changsoo [1 ]
机构
[1] Dankook Univ, Dept Phys, Cheonan 31116, South Korea
关键词
FOUCAULT PENDULUM; PHASE;
D O I
10.1119/5.0101149
中图分类号
G40 [教育学];
学科分类号
040101 ; 120403 ;
摘要
The dynamics of a heavy symmetric top are studied in connection with the Hannay angle. When the top undergoes a steady precession due to gravity without nutation, the Hannay angle has a geometric nature such that it is identical to the solid angle subtended by the loop swept out by the symmetry axis of the top. Here, we show that the Hannay angle can also be described by the angle between two radial vectors on the disk of the top corresponding to the pure spinning motion and the coupled motion of spin and precession for one period of the precession. The geometric nature of the angle between the two radial vectors is verified by demonstrating, via parallel transport, that the magnitude of the angle is the same as that of the solid angle. In the presence of nutation, the path constructed by the symmetry axis is not closed, and the steady precession appears in the limit of infinite initial spin angular velocity. As a consequence, in an ideal situation of no friction, the Hannay angle as a pure geometric effect does not exist in the superposed motion of precession and nutation.
引用
收藏
页码:357 / 365
页数:9
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