GroupTheory`
GroupTheory`

GTGetEulerAngles

GTGetEulerAngles[symmetry element]

gives the Euler angles corresponding to a symmetry element.

Details and Options

  • Any arbitrary rotation can be seen as a superposition of three rotations. First, a rotation by an angle about the z-axis, second a rotation by an angle about the y-axis and third a rotation by an angle about the z-axis. Thus, it can be written
  • .
  • The input of GTGetEulerAngles can be of type symbol, matrix, quaternion, and Euler angles.
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 2.1.2

Examples

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Basic Examples  (1)

First, load the package:

Get the Euler angles for the symmetry element :

Quaternion to Euler angles:

Matrix to Euler angles:

Generalizations & Extensions  (1)

GTGetEulerAngles can be applied to lists.