电磁建模与仿真中的四元数数学
Quaternion Mathematics in Electromagnetic Modeling and Simulation
摘要：
这项工作的目的是调查，如果使用四元数数学可以用来更好地建模和模拟发生移动的电磁电荷的电磁场。通常使用的麦克斯韦方程组的一个观察到的缺陷是极向量与轴向向量的问题;电磁场E是极向量，而磁场B是轴向向量，其中旋转方向即使在轴向向量反转之后也保持相同。本文首先推导了四元数几何的旋转矩阵。然后，将该旋转矩阵应用于对距源一定距离处的磁场进行建模，并将其与传统的麦克斯韦方程组进行比较。这一努力被用来模拟一系列移动的电荷，观察飞机观察潜艇，以及涡流动态制动器。人们清楚地观察到，当一个移动的观察者正在研究一个移动的目标时，可以观察到磁场方向和大小的差异，这证明了四元数数学在这种应用中的有效性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
