Euler axis/angle representation

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Parents: rotations-so3-group-index , orientation-parametrisations
See also: Rotation vector representation

Source: Markley 2014

3 parameters:

  • there appears to be 4 parameters: 1 angle, 3-component unit vector (Euler axis, Euler angle of the rotation)
  • however, the vector $\mathbf{e}$ is a unit vector (constrained by $\left\lVert \mathbf{e} \right\rVert = 1$

To rotation matrix

unknown_filename.png unknown_filename.4.png

The matrix is periodic (period 2*pi) unknown_filename.1.png

From rotation matrix

unknown_filename.2.png

If -1 < cos theta < 1:  unknown_filename.5.png

If cos theta = 1: axis undefined

If cos theta = -1, e = any column of the following (apply normalisation to the column), whichever sign unknown_filename.3.png