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Euler angles are defined as follows. Beginning with a body-fixed axis system x,y,z and a space-fixed axis system X,Y,Z, in coincidence, the body-fixed system is moved to its final orientation in three steps. First, the body is rotated by an angle φ about the z axis. We call the new position of the body-fixed axis system x′, y′, z′. The second step is rotation of the body about the x′ axis by an angle θ. The new position of the body-fixed axis system is called x″, y″, z″. Finally, the body is rotated about z″ axis by an angle ψ. Then the final position x‴, y‴, z‴ is obtained.
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