I'm reading a paper where the orientation of a coordinate system is specified by y-convention Euler angles (eqns 30-47)$(\phi_0, \theta_0, \psi_0)$ and rotation matrix $\xi$. It then goes on to say let $d\xi = (d\psi_0\sin\theta_0\cos\phi_0 - d\theta_0\sin\phi_0,~d\psi_0\sin\theta_0\sin\phi_0 + d\theta_0\cos\phi_0,~d\phi_0 + d\psi_0\cos\theta_0)$ What sort of infinitesimal change is it describing?
This is equation 3.22 of http://148.216.10.84/archivoshistoricosMQ/ModernaHist/Thomas1927.pdf