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

Akyar, Bedia

Turk. J. Math. 32, No. 4, 373-391 (2008).

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.

Reviewer: Hans-Peter Schröcker (Innsbruck)

MSC:

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

Keywords:

dual quaternion; Hamilton operator; Lie algebra