A Novel Formulation of Point Vortex Dynamics on the Sphere: Geometrical and Numerical Aspects

被引：0
作者：
Joris Vankerschaver
Melvin Leok
机构：
[1] University of California,Department of Mathematics
[2] San Diego,Department of Mathematics
[3] Imperial College London,undefined
来源：
Journal of Nonlinear Science | 2014年 / 24卷
关键词：
Point vortices; Hopf fibration; Symplectic integration; Variational methods; 37M15; 76B47; 70H03;
D O I：
暂无
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学科分类号：
摘要：
In this paper, we present a novel Lagrangian formulation of the equations of motion for point vortices on the unit 2-sphere. We show first that no linear Lagrangian formulation exists directly on the 2-sphere but that a Lagrangian may be constructed by pulling back the dynamics to the 3-sphere by means of the Hopf fibration. We then use the isomorphism of the 3-sphere with the Lie group SU(2) to derive a variational Lie group integrator for point vortices which is symplectic, second-order, and preserves the unit-length constraint. At the end of the paper, we compare our integrator with classical fourth-order Runge–Kutta, the second-order midpoint method, and a standard Lie group Munthe-Kaas method.
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页码：1 / 37
页数：36
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