轴对称外场中对称陀螺的哈密顿动力学。悬浮轨道管
Hamiltonian dynamics of a symmetric top in external fields having axial symmetry. Levitating Orbitron
摘要：
对称顶是一般顶的一种特殊情况，$T^*SE(3)$上的正则Poisson结构是描述对称顶的常用方法。这种结构在$SO(3)$的右作用下是不变的，但是对称顶的哈密顿量仅在子群$S^1$的右作用下是不变的，该子群对应于对称顶的对称轴的旋转。因此，它的泊松结构作为约简$T^*SE(3)/S^1$得到。其次，我们提出了描述对称顶场和轴对称外场相互作用模型的哈密顿量。证明了悬浮轨道电子在相对平衡状态下的稳定性。
英文摘要：
The symmetric top is a special case of the general top, and canonical Poisson structure on $T^*SE(3)$ is the common method of its description. This structure is invariant under the right action of $SO(3)$, but the Hamiltonian of the symmetric top is invariant only under the right action of subgroup $S^1$ that corresponds to the rotation around the symmetry axis of the symmetric top. So, its Poisson structure was obtained as the reduction $T^*SE(3)/S^1$. Next we propose the Hamiltonian that describes the wide class of the interaction models of symmetric top and axially-symmetric external field. The stability of the levitating Orbitron in relative equilibrium was proved.
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