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四元数的基本概念与向量旋转的欧拉公式 |
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| 引用本文： | 张捍卫,喻铮铮,雷伟伟.
四元数的基本概念与向量旋转的欧拉公式[J].大地测量与地球动力学,2020,40(5):502-506. |
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| 作者姓名： | 张捍卫 喻铮铮 雷伟伟 |
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| 作者单位： | 河南理工大学测绘与国土信息工程学院;许昌学院城乡规划与园林学院 |
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| 基金项目： | 国家自然科学基金(41474021)。 |
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| 摘 要： | 为方便理解四元数，首先针对两个相互平行或垂直的向量，定义它们之间的一种不可交换乘积，命名为格拉斯曼乘积，同时约定这一不可交换积满足分配律。由此，进一步给出任意两个向量之间格拉斯曼积的具体表达式，并引出四元数的概念和运算法则。从理论上证明，任意四元数都可表示为两个向量之间的格拉斯曼积，并可以利用单位四元数的正交变换来表示向量旋转的欧拉公式。
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| 关 键 词： | 格拉斯曼乘积 四元数 向量旋转 正交变换 |
Study on the Basic Theory of Quaternion and Eulerian Equation of the Rotating Vector |
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| ZHANG Hanwei,YU Zhengzheng,LEI Weiwei.Study on the Basic Theory of Quaternion and Eulerian Equation of the Rotating Vector[J].Journal of Geodesy and Geodynamics,2020,40(5):502-506. |
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| Authors: | ZHANG Hanwei YU Zhengzheng LEI Weiwei |
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| Institution: | (School of Surveying and Land Information Engineering,Henan Polytechnic University,2001 Shiji Road,Jiaozuo 454000,China;School of Urban Planning and Landscape Architecture,Xuchang University,88 Bayi Road,Xuchang 461000,China) |
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| Abstract: | To understand the quaternion, this paper defines a non-exchange product between two vectors parallel or vertical to each other, names it as the Glassman product, and promises this non-exchange product meet the commutative law. Furthermore, this paper derives the specific expression of the Glassman product between any two vectors, and then leads to the conception of the quaternion and its operation rules. In theory, this paper proves that any quaternion can be represented as the Glassman product between two vectors, and the Eulerian equation of the rotating vector can be represented by the orthogonal transformation of the unit quaternion either. |
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| Keywords: | Glassman product quaternion vector rotation orthogonal transformation |
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