对偶四元数和四元分裂四元数的代数性质OACSTPCD

Dual quaternion and split quaternion are powerful tools to deal with rigid body spiral motion and attitude control.By using Clifford's concept of dual numbers and with the help of 4×4 primitive complex matrix,the definitions of dual quaternion and split quaternion in matrix form are given,and the algebraic properties such as adjoint matrix,inverse matrix,determinant of dual quaterni-on matrix and split quaternion matrix are obtained.At the same time,their important differences in the definition of inner product,expressions of conjugation and norm,and determinant operations of product are pointed out.