论文标题
在不可方向表面上进行点涡流的哈密顿量方法I：莫比乌斯乐队
Hamiltonian approach for point vortices on non-orientable surfaces I: the Mobius band
论文作者
论文摘要
这是两篇伴侣论文中的第一篇，其中我们研究了不可定向的二维表面上的涡旋运动。我们通过描述相位空间，汉密尔顿和局部运动方程来建立“哈密顿式”方法，以在不可方向的表面上指向涡流运动。本文主要集中于Mobius频段的动态。为此，我们将一些已知的涡流动力学概念调整为不可取向的表面。我们明确地编写了涡旋运动的汉密尔顿型方程，并通过描述相对平衡的描述以及对一个和两个涡流的运动的彻底研究，重点是运动的周期性。
This is the first of two companion papers, in which we investigate vortex motion on non-orientable two dimensional surfaces. We establish the `Hamiltonian' approach to point vortex motion on non-orientable surfaces through describing the phase space, the Hamiltonian and the local equations of motion. This paper is primarily focused on the dynamics on the Mobius band. To this end, we adapt some of the known notions of vortex dynamics to non-orientable surfaces. We write Hamiltonian-type equations of vortex motion explicitly and follow that by the description of relative equilibria and a thorough investigation of motion of one and two vortices, with emphasis on the periodicity of motion.
