论文标题
电磁建模和仿真中的四元数学
Quaternion Mathematics in Electromagnetic Modeling and Simulation
论文作者
论文摘要
这项工作的目的是研究是否可以使用Quaternion数学来更好地模型并模拟通过移动电磁电荷而发生的电磁场。一个常用的麦克斯韦方程式观察到的缺陷是极性和轴向向量的问题。电磁场E是极性载体，而磁场B是轴向矢量，即使轴向向量倒置后，旋转方向也保持不变。这项工作首先得出了四个几何形状的旋转矩阵。然后将此旋转矩阵应用于与源距离的磁场建模，并将其与传统的麦克斯韦方程进行比较。这项工作是为了建模一系列移动费用，这是一架观察飞机，观察一艘潜艇以及涡流动态制动器。可以清楚地观察到，当移动观察者正在研究移动目标时，可以观察到磁性方向和幅度的差异，这证明了四局数学在此类应用中的有效性。
The purpose of this effort is to investigate if the use of quaternion mathematics can be used to better model and simulate the electromagnetic fields that occur from moving electromagnetic charges. One observed deficiency with the commonly used Maxwell's equations is the issue of polar versus axial vectors; the electromagnetic field E is a polar vector, whereas the magnetic field B is an axial vector, where the direction of rotation remains the same even after the axial vector is inverted. This effort first derived the rotation matrix for quaternion geometry. This rotation matrix was then applied to modeling the magnetic fields at a distance from a source, and comparing it to traditional Maxwell's equations. This effort was taken to model a series of moving charges, an observation aircraft observing a submarine, as well as an eddy current dynamic brake. It was clearly observed that when a moving observer is studying a moving target, differences in the magnetic direction and magnitude can be observed, demonstrating the effectiveness of quaternion mathematics in such applications.
