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MathGroup Archive 2004

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Re: Euler rotation angles

  • To: mathgroup at
  • Subject: [mg46745] Re: Euler rotation angles
  • From: Jens-Peer Kuska <kuska at>
  • Date: Fri, 5 Mar 2004 01:46:49 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <c26gc5$e28$>
  • Reply-to: kuska at
  • Sender: owner-wri-mathgroup at


suppose you have build from the angle alpha and the rotation
axes n={nx,ny,nz} (with |n|=1) the quaternion

q={q[0],q[1],q[2],q[3]}={Cos[alpha/2],Sin[alpha/2] nx,Sin[alpha/2]
ny,Sin[alpha/2] nz}

than your Euler angels are:

phi=ArcTan[2 (q[2] q[3]+q[0] q[1]),(q[0]^2-q[1]^2-q[2]^2+q[3]^2)]
theta=ArcSin[-2 (q[1] q[3] - q[0] q[])]
psi=ArcTan[2 (q[1] q[2]+q[0] q[3]),(q[0]^2+q[1]^2-q[2]^2-q[3]^2)]


"S. Campbell" wrote:
> Hi,
> 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?
> Cheers,
> Sam

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