Dual quaternion: Difference between revisions

A dual quaternion can be written as <math>\mathbf{q} = \mathbf{q}_r + \mathbf{q}_d \epsilon</math>.   

Here, <math>\epsilon^2=0</math>.

<math>s\mathbf{q} = s\mathbf{q}_r + s \mathbf{q}_d \epsilon</math>

<math>\mathbf{q}_1 + \mathbf{q}_2 = \mathbf{q}_{r1} +\mathbf{q}_{r2}  +  (\mathbf{q}_{d1} + \mathbf{q}_{d2}) \epsilon</math>

<math>\mathbf{q}_1 \mathbf{q}_2 = \mathbf{q}_{r1} \mathbf{q}_{r2} + (\mathbf{q}_{r1}\mathbf{q}_{d2} + \mathbf{q}_{d1} \mathbf{q}_{r2})\epsilon</math>.

<math>\mathbf{q}^* = \mathbf{q}_{r}^* + \mathbf{q}_{d}^*\epsilon</math>