Are there specific Euler angles and initial spherical vectors for which the D-matrix loses a degree of freedom, akin to gimbal lock in the conventional Euler rotation matrices?

(Of course the specifics will depend on the rotation convention, so let's assume the common ZYZ convention used in the Wikipedia page.)

  • $\begingroup$ Hint: these matrices are expressed in the spherical basis. Transform the Cartesian basis in WP to it, to display the Gimbal block in the spherical language: you cannot prevent Gimbal block by a change of basis! See, e.g., this. $\endgroup$ Jan 31 at 21:11
  • $\begingroup$ ... of course this is for XYZ, not ZYZ... But see here. $\endgroup$ Jan 31 at 22:59


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