Re: Interesting Yaw, Pitch, Roll Problem

• To: mathgroup at smc.vnet.net
• Subject: [mg19178] Re: [mg19142] Interesting Yaw, Pitch, Roll Problem
• From: "Dr. Christopher Purcell" <purcell at drea.dnd.ca>
• Date: Tue, 10 Aug 1999 02:52:42 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Robert Milhar=E8i=E8 <robert.m at ib-caddy.si> wrote:

>Does anyone know how to calculate all three angles (Roll, Yaw, Pitch) if
>we know only base coordinate system vectors (U, V, N), new coordinate
>system vectors (Unew, Vnew, Nnew) and order in which 3D rotations are
>applied (Roll, Yaw, Pitch).
>
>
I don't know how to solve this with Mathematica, (an attempt recently on my small
mac ran out of memory) but 20 years ago when I was at the peak of my
powers, I was able to do it by hand in many pages of algebra and trig
substitutions.

You have the problem overspecified.

Only 2 non-collinear vectors (U,V) and their rotated images (Unew,Vnew) are
needed to determine the 3 Euler angles Roll, Yaw, Pitch, given the order of
rotations that compose your Euler matrix.

You will need to use Mathematica's four quadrant form of the inverse trig functions.
Dr. Christopher J. Purcell
DREA, 9 Grove St. Dartmouth NS B2Y3Z7

```

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