四元数与三维空间中的转动

Quaternion and rotation in three dimensions

由SU(2)群引入四元数,并详细和严格地讨论了四元数的各种特性;讨论得出了诸如SU(2)群与SO(3)群的2-1对应;给出了单位四元数的转轴和转角;自然地导出了表征无穷小转动的角位移等.

The quaternion was introduced via the special unitary group in two dimensions and its properties were discussed systematically and rigorously.Some important results were educed such as the homomorphism of SU(2)onto SO(3).Besides,the axis and the angle of the rotation were given by a quaternion,and the angular displacement of an infinitesimal rotation was derived smoothly.