Do Quaternions Have Units?

Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space.

How do you find the unit quaternion?

The unit quaternion can now be written in terms of the angle θ and the unit vector u = q/q: q = cos θ + usinθ. 0 − q2)v + 2(q · v)q + 2q0(q × v).

Is quaternion a unit vector?

|pq| = √ pq(pq) = √ pq¯q¯p = √p(q¯q)¯p = √ p¯p √ q¯q = |p||q|. 5.6 Unit quaternions. quaternions {q ∈ H | |q| = 1} is a sphere of radius one in the 4-space H ¯ . ... The unit vectors are very special quaternions.