Editing Euler angles (section)

===Geometrical definition===
The axes of the original frame are denoted as ''x'', ''y'', ''z'' and the axes of the rotated frame as ''X'', ''Y'', ''Z''. The '''geometrical definition''' (sometimes referred to as static) begins by defining the [[line of nodes]] (N) as the intersection of the planes ''xy'' and ''XY'' (it can also be defined as the common perpendicular to the axes ''z'' and ''Z'' and then written as the vector product ''N'' = ''z'' &times; ''Z''). Using it, the three '''Euler angles''' can be defined as follows:

* <math>\alpha</math> (or <math>\varphi</math>) is the signed angle between the ''x'' axis and the ''N'' axis (''x''-convention – it could also be defined between ''y'' and ''N'', called ''y''-convention).
* <math>\beta</math> (or <math>\theta</math>) is the angle between the ''z'' axis and the ''Z'' axis.
* <math>\gamma</math> (or <math>\psi</math>) is the signed angle between the ''N'' axis and the ''X'' axis (''x''-convention).

Euler angles between two reference frames are defined only if both frames have the same [[Orientation (mathematics)|handedness]].