GroupTheory`

GTEulerAnglesQ

gives True if A is a list of Euler angles, and gives False otherwise.

Details and Options

Any arbitrary rotation can be seen as a superposition of three rotations. First, a rotation by an angle ψ about the z-axis, second a rotation by an angle θ about the y-axis and third a rotation by an angle ϕ about the z-axis. Thus, it can be written
(α)=R(ϕ,θ,ψ)=(ϕ)(θ)(ψ)
Within GTPack, the calculation with Euler angles is implemented. Usually Euler angles are only defined for proper rotations. To represent all proper and improper rotations, a fourth parameter is needed, given by the determinant of the rotation matrix. Euler angles are implemented in the form {{ϕ,θ,ψ}, Det(R)}.
See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 2.1.2

First, load the package:

Then run the example: