用各种类型的四元数表示物理运动
The representation of physical motions by various types of quaternions
摘要：
证明了欧氏旋转群、刚体运动群、固有正交洛伦兹变换群和复刚体运动群可以分别用实、对偶、复和复对偶四元数代数中的单位范数元群表示.它显示了如何一些物理上有用的张量和旋量可以表示的各种四元数。运动状态的基本概念，在每种情况下，除了复杂的对偶四元数，在那里他们可能的作用，描述的对称性的麦克斯韦方程组进行了讨论。
英文摘要：
It is shown that the groups of Euclidian rotations, rigid motions, proper, orthochronous Lorentz transformations, and the complex rigid motions can be represented by the groups of unit-norm elements in the algebras of real, dual, complex, and complex dual quaternions, respectively. It is shown how someof the physically-useful tensors and spinors can be represented by the various kinds of quaternions. The basic notions of kinematical states are described in each case, except complex dual quaternions, where their possible role in describing the symmetries of the Maxwell equations is discussed.
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