相似扁球坐标系的单位向量及向量变换
Unit Vectors for Similar Oblate Spheroidal Coordinates and Vector Transformation
AI总结：
本文推导了笛卡尔坐标系与相似扁球坐标系间的单位向量双向变换关系，给出适用的广义正弦、余弦函数，通过算例验证其可简化扁球几何相关问题的向量场求解。
摘要：
本文推导了笛卡尔坐标系与新型相似扁球（Similar Oblate Spheroidal）坐标系之间的单位向量双向变换公式。该变换可在两类正交坐标系间转换向量场，有助于简化具有扁球几何特征的问题求解。文中通过多个算例演示了推导关系式的用法，并引入了适用于相似扁球坐标系的广义正弦与广义余弦函数。
英文摘要：
The unit vectors transformation between the Cartesian and the novel Similar Oblate Spheroidal coordinates, and vice versa, is derived. It can help to transform vector fields between these two types of orthogonal coordinates which can advantageously simplify solutions of problems exhibiting oblate spheroidal geometry. Several examples demonstrate the use of the derived relations. Generalized sine and cosine applicable in Similar Oblate Spheroidal coordinate system are introduced.
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。
