# Quaternions and Spatial Rotation

Quaternions And Spatial Rotation

Unit quaternions provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions. Compared to Euler angles they are simpler to compose and avoid the problem of gimbal lock. Compared to rotation matrices they are more numerically stable and may be more efficient. Quaternions have found their way into applications in computer graphics, computer vision, robotics, navigation, molecular dynamics, flight dynamics, and orbital mechanics of satellites.

When used to represent rotation, unit quaternions are known as versors, or rotation quaternions. When used to represent an orientation (rotation relative to a reference position), they are called orientation quaternions or attitude quaternions.

Read more about Quaternions And Spatial Rotation:  Using Quaternion Rotations, Pairs of Unit Quaternions As Rotations in 4D Space

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Quaternions And Spatial Rotation - Pairs of Unit Quaternions As Rotations in 4D Space
... A pair of unit quaternions zl and zr can represent any rotation in 4D space ... Given a four dimensional vector, and pretending that it is a quaternion, we can rotate the vector like this It is straightforward to check that for each matrix M MT = I, that is, that each matrix (and hence ... Therefore, there are two commuting subgroups of the set of four dimensional rotations ...

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The lazy manage to keep up with the earth’s rotation just as well as the industrious.
Mason Cooley (b. 1927)