Euler angles [SEP] named after
Euler angles
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system. They can also represent the orientation of a mobile frame of reference in physics or the orientation of a general basis in 3-dimensional linear algebra.
Any orientation can be achieved by composing three "elemental rotations", i.e., rotations about the axes of a coordinate system. Euler angles can be defined by three of these rotations. They can also be defined by elemental geometry and
associated with both proper Euler angles and Tait–Bryan angles are commonly named using this notation (see above for details).
Proper Euler angles Conventions.
There are six possibilities of choosing the rotation axes for proper Euler angles. In all of them, the first and third rotation axes are the same. The six possible sequences are:
1. "z"-"x"′-"z"″ (intrinsic rotations) or "z"-"x"-"z" (extrinsic rotations)
2. "x"-"y"′-"x"″ (intrinsic rotations) or "x"-"y"-"x" (extrinsic rotations)