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Dual quaternions in spatial kinematics in an algebraic sense. (English) Zbl 1159.53006

Hamilton operators for dual quaternions are maps \(H^+\), \(H^-\) from the space of dual quaternions to the space of \(4 \times 4\) matrices such that the dual quaternion multiplication obeys \(\hat{\mathbf p}\hat{\mathbf q} = H^+(\hat{\mathbf p})\hat{\mathbf q} = H^-(\hat{\mathbf q})\hat{\mathbf p}\). The author considers one-parameter motions and relative motions in dual quaternion form. He provides explicit formulas for transformation and transition matrices and time derivatives in terms of Hamilton operators.

MSC:

53A17 Differential geometric aspects in kinematics
53A25 Differential line geometry
70B10 Kinematics of a rigid body
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