       Eulers PSI and PHI interchanged in Guide Std MMa Pkg

• To: mathgroup at smc.vnet.net
• Subject: [mg3917] Eulers PSI and PHI interchanged in Guide Std MMa Pkg
• From: adbened at alumnae.caltech.edu ( Alto D. Benedicto)
• Date: Sun, 5 May 1996 23:14:08 -0400
• Organization: California Institute of Technology, Pasadena
• Sender: owner-wri-mathgroup at wolfram.com

```Half a day ago, I posted the question:
> Why is it that: Rotate3D[object3D, Pi/2, Pi/2, 0] doesn't show the
> same picture as Rotate3D[Rotate3D[object3D, 0,Pi/2,0], Pi/2, 0, 0]?

> It seems that the angle PHI doesn't behave according to the
> definition on p.113 of Guide to Std Mma Pkg.   As far as I
> understand it, the definition of Rotate3D[obj, phi, theta psi] is
> Rotate3D[Rotate3D[Rotate3D[obj,0,0,psi],0,theta,0],phi,0,0].
> (THETA and PSI are clockwise rotation wrt X and Z axis).

For what it's worth, the parameters PHI and PSI are misprinted in
p.113 of Guide to Std MMa Pkg for the commands Rotate3D and
RotationMatrix3D.  The correct form should be:

RotationMatrix3D[psi, theta, phi]  instead of RotationMatrix3D[phi,
theta, psi].  Also, Rotate3D[psi, theta, phi] instead of
Rotate3D[phi, theta, psi].

The standard definition of Euler angles follows, i.e., first rotate
by angle psi about z, then angle theta about x, and finally angle phi
about z again.  (all rotations clockwise).