Re: Euler rotation angles

• To: mathgroup at smc.vnet.net
• Subject: [mg46745] Re: Euler rotation angles
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Fri, 5 Mar 2004 01:46:49 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <c26gc5\$e28\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

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}

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)]

Regards
Jens

"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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