FindOrientation[A1,A2]

A1, A2: names of defined observers

The function FindOrientation returns the rotation matrix between the reference triads of the observers labeled by A1 and A2.

Restart;
DeclareObservers[A,B];
DeclarePoints[A,B];
DeclareTriads[a,b];
DefineObservers[{A,A,a},{B,B,b}];
DefineTriads[a,b,q,1,2,3];
FindOrientation[A,B] //MatrixForm

$\left(\begin{array}{ccc}\frac{1}{14}\left(1+13\mathrm{Cos}\left[q\right]\right)& \frac{1}{14}\left(2-2\mathrm{Cos}\left[q\right]-3\sqrt{14}\mathrm{Sin}\left[q\right]\right)& \frac{1}{14}\left(3-3\mathrm{Cos}\left[q\right]+2\sqrt{14}\mathrm{Sin}\left[q\right]\right)\\ \frac{1}{14}\left(2-2\mathrm{Cos}\left[q\right]+3\sqrt{14}\mathrm{Sin}\left[q\right]\right)& \frac{1}{7}\left(2+5\mathrm{Cos}\left[q\right]\right)& \frac{1}{14}\left(6-6\mathrm{Cos}\left[q\right]-\sqrt{14}\mathrm{Sin}\left[q\right]\right)\\ \frac{1}{14}\left(3-3\mathrm{Cos}\left[q\right]-2\sqrt{14}\mathrm{Sin}\left[q\right]\right)& \frac{1}{14}\left(6-6\mathrm{Cos}\left[q\right]+\sqrt{14}\mathrm{Sin}\left[q\right]\right)& \frac{1}{14}\left(9+5\mathrm{Cos}\left[q\right]\right)\end{array}\right)$

DeclareTriads, DefineTriads, DeclareObservers, DeclarePoints, DefineObservers, FindRotation