三维Minkowski空间中基于Killing向量场的磁力曲线

The Magnetic Curves in 3-Dimensional Minkowski Space According to Killing Vector

本文在三维Minkowski空间中,研究了基于Killing向量场的磁力曲线.首先给出了三维Minkowski空间中对应于平移和旋转的所有Killing向量场,并对不同的Killing向量所对应的磁力曲线进行了分类,最后给出了一些磁力曲线的图像.

In this paper,the magnetic curve based on killing vector field is studied in three-dimensional Minkowski space.First of all,according to the properties of killing vector field and the special measurement of three-dimensional Minkowski space,we calculate six killing vector fields corresponding to translation and rotation in three-dimensional Minkowski space.And then we classify the magnetic force curves corresponding to different killing vectors by using Lorentz force equation,and obtain five kinds of magnetic curves represented by parametric equation or Jacobian elliptic integral.Among them,two types of magnetic curves corresponding to the rotating killing vector field are represented by Jacobian elliptic integral,while the other three types of magnetic curves are represented by parametric equations.Finally,we draw the images of some magnetic curves through the MATLAB software,and simply analyze and plan the next work which we should do,in combination with the difference between four-dimensional Minkowski space measurement and three-dimensional Minkowski space measurement.