Editing Euler angles (section)

===Conventions===
[[File:Plane with ENU embedded axes.svg|thumb|right|250px|Heading, elevation and bank angles (''Z''-''Y''′-''X''″) for an aircraft using onboard ENU axes both onboard and for the ground tracking station. The fixed reference frame ''x''-''y''-''z'' represents such a tracking station. Onboard axes ''Y'' and ''Z'' are not shown. ''X'' shown in green color. According to RHS rules the shown ''y''-axis is negative.]]

The three elemental rotations may occur either about the axes of the original coordinate system, which remains motionless ([[#Extrinsic rotations|extrinsic rotations]]), or about the axes of the rotating coordinate system, which changes its orientation after each elemental rotation ([[#Intrinsic rotations|intrinsic rotations]]).

There are six possibilities of choosing the rotation axes for Tait–Bryan angles. The six possible sequences are:

* ''x''-''y''′-''z''″ (intrinsic rotations) or ''z''-''y''-''x'' (extrinsic rotations)
* ''y''-''z''′-''x''″ (intrinsic rotations) or ''x''-''z''-''y'' (extrinsic rotations)
* ''z''-''x''′-''y''″ (intrinsic rotations) or ''y''-''x''-''z'' (extrinsic rotations)
* ''x''-''z''′-''y''″ (intrinsic rotations) or ''y''-''z''-''x'' (extrinsic rotations)
* ''z''-''y''′-''x''″ (intrinsic rotations) or ''x''-''y''-''z'' (extrinsic rotations): the intrinsic rotations are known as: yaw, pitch and roll
* ''y''-''x''′-''z''″ (intrinsic rotations) or ''z''-''x''-''y'' (extrinsic rotations)