we know that the rotation matrix of a 3 rotations around XYZ in order, will be :
and we also know that the trace of the matrix is :
TR = $$\arccos \left ( -1 + \sum_{i=j} R_{ij} \right )$$
if we have the intention of decomposing these 3 rotations into a rotation around a single axis in space, then :
what does
value 1 = $\frac{1}{2} * \frac{(R(3,2) - R(2,3)) }{\sin (TR)}$
value 2 = $\frac{1}{2} * \frac{(R(1,3) - R(3,1)) }{\sin (TR)}$
value 3 = $\frac{1}{2} * \frac{(R(2,1) - R(1,2)) }{\sin (TR)}$
mean ?
and then what will be the
$a1 = value 1 * TR$
$a2= value 2 * TR$
$a3= value 3 * TR$