On nonlinear stability of the regular vortex systems on a sphere.
On nonlinear stability of the regular vortex systems on a sphere.
复制标题
球面上规则涡系统的非线性稳定性。
作者：
L. Kurakin
我们提出了位于正n边形顶点球体上同一纬度的n个相同点涡旋系统的静止旋转稳定性和不稳定性的充分必要条件。我们还检查了位于正多面体顶点的相同点涡旋的平衡配置的稳定性。证明了涡旋四面体、八面体和二十面体是稳定的，而涡旋立方体和十二面体是不稳定的。
We present the necessary and sufficient conditions for stability and instability of the stationary rotation of a system of n identical point vortices located at the same latitude on a sphere at vertices of a regular n-gon. We also examine stability of the equilibrium configuration of identical point vortices, situated at the vertices of a regular polyhedra. It is proved that vortex tetrahedron, octahedron, and icosahedron are stable, while vortex cube and dodecahedron are unstable.