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RE: Euler rotation angles

  • To: mathgroup at
  • Subject: [mg46761] RE: [mg46739] Euler rotation angles
  • From: "Wolf, Hartmut" <Hartmut.Wolf at>
  • Date: Sun, 7 Mar 2004 01:33:39 -0500 (EST)
  • Sender: owner-wri-mathgroup at


stated such, your problem is not well determined. Take for example

 vector1 = {1,-1,0}/Sqrt[2]; 
 vector2 = {1,1,0}/Sqrt[2];

Then a rotation about the "z-axis" viz. {0,0,1} with angle Pi/2 will do, but
also a rotation about the "x-axis" viz. {1,0,0} with angle +(-)Pi; and there
is an infinity of rotations between those which also will do.

Euler angles have been introduced to this world to describe rotations of
rigid bodies (or, if you prefer, between orthonormal triples of vectors of
same orientation). Such you have to specify two sets of at least two (say
normalized) vectors, not collinear, making up the same angle (in the plane
between them), which are to be rotated to each other.

In effect your problem spezfies only "cannoneers angles": azimuth and
elevation, not a triple like Euler's.


>-----Original Message-----
>From: sam_campbell at [mailto:sam_campbell at]
To: mathgroup at
>Sent: Thursday, March 04, 2004 6:48 AM
>To: mathgroup at
>Subject: [mg46761] [mg46739] Euler rotation angles
>Can anyone help me with the following? I have two vectors, one rotated
>with respect to the other, and I wish to find the Euler rotation
>angles that connect the vectors. Can mathematica tell me what the
>required angles are?

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