Table A1.

The table used to convert an arbitrary set of Euler angles (α, β,γ) to a unique set ($\stackrel{.}{\mathit{\alpha }}$, $\stackrel{.}{\mathit{\beta }}$, $\stackrel{.}{\mathit{\gamma }}$) in the region of $\dot{\alpha }$ ∈ [0, 2π), $\dot{\beta }$ ∈ [0,π] and $\dot{\gamma }$ ∈ [0, 2π). *The conversion is made based on the relation:

$${\mathbf{R}}_Z(\mathbf{a}){\mathbf{R}}_Y(\beta ){\mathbf{R}}_Z(\gamma )={\mathbf{R}}_Z(\alpha -\pi ){\mathbf{R}}_Y(2\pi -\beta ){\mathbf{R}}_Z(\gamma -\pi ).$$

	β mod 2π
	0	(0, π)	π	(π, 2π)
$\stackrel{.}{\mathit{\alpha }}$,	(α + γ) mod 2 π	α mod 2π	(α − γ) mod 2π	(α − π) mod 2π
$\stackrel{.}{\mathit{\beta }}$,	0	β mod 2π	π	2π − (β mod 2π)
$\stackrel{.}{\mathit{\gamma }}$,	0	γ mod 2π	0	(γ − π) mod 2π