Versor

Also known as unit quaternion

In mathematics, a versor is a quaternion whose norm is one, also known as a unit quaternion. Each versor has the form \ u = \exp(a\mathbf{r}) = \cos a + \mathbf{r} \sin a, \qquad \mathbf{r}^2 = -1, \qquad a \in [0,\pi]\ , where the condition \ \mathbf{r}^2 = -1\ means that \ \mathbf{r}\ is an algebraic imaginary unit. There is a sphere of imaginary units in the quaternions. Note that the expression for a versor is just Euler's formula for the imaginary unit \ \mathbf{r} ~. If \ a = \tfrac{\pi}{2}\ (when \ a\ is a right angle), then \ u = \mathbf{r}\ , and it is called a right versor.