论文标题
在革命旋转表面和kasamawashi艺术的旋转表面上的动态的某些方面
On some aspects of the dynamics of a ball in a rotating surface of revolution and of the kasamawashi art
论文作者
论文摘要
我们研究了由重型均匀的球形成的非体力学系统动力学的某些方面，这些球被约束，而无需在稳定旋转的革命表面上滑动。首先，在表面的图形轴为垂直的情况下（因此，系统为$ \ textrm {so（3）} \ times \ textrm {so（2）$ - 对称），并且表面在其顶点（非键音）最大值，我们显示出对验证的可能性。这是完成到5维$ \ textrm {so（3）} $ - 还原系统的过程中完成的。当$ \ textrm {so（3）} $ - 对称性持续存在时，当表面的图形倾斜相对于垂直行业而言 - 可以将系统视为日本kasamawashi（turn umbrella）性能艺术的简单模型 - 在这种情况下，我们研究了5二维系统的（稳定性）的（稳定性）。
We study some aspects of the dynamics of the nonholonomic system formed by a heavy homogeneous ball constrained to roll without sliding on a steadily rotating surface of revolution. First, in the case in which the figure axis of the surface is vertical (and hence the system is $\textrm{SO(3)}\times\textrm{SO(2)}$-symmetric) and the surface has a (nondegenerate) maximum at its vertex, we show the existence of motions asymptotic to the vertex and rule out the possibility of blow up. This is done passing to the 5-dimensional $\textrm{SO(3)}$-reduced system. The $\textrm{SO(3)}$-symmetry persists when the figure axis of the surface is inclined with respect to the vertical -- and the system can be viewed as a simple model for the Japanese kasamawashi (turning umbrella) performance art -- and in that case we study the (stability of the) equilibria of the 5-dimensional reduced system.
