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Quaternions and Vector Mapping in Three-Dimensional Space

On the basis of analyzing the relations between vector operation and properties of multiplication operation of quaternions, the geometric representation and mapping of quaternions and vectors defined in three-dimensional space are established. The mathmatic operation of space vector, in addition to any space unit vector, rotating around three coordinate axises is carried based on the utilization of quaternions.The main purpose of this paper is to solve the issues of mathmatic tools introduced in spatial mechanism analysises and integrations by making use of quatnions.