Editing Euler angles (section)

{{Short description|Description of the orientation of a rigid body}}
[[Image:Eulerangles.svg|right|thumb|300px|Classic Euler angles geometrical definition. 
{{Legend-line|solid #0f52ba 2px|Fixed coordinate system ({{math|x, y, z}})}}
{{Legend-line|solid red 2px|Rotated coordinate system ({{math|X, Y, Z}})}}
{{Legend-line|solid green 2px|[[Line of nodes]] ({{math|N}})}}
]]

The '''Euler angles''' are three angles introduced by [[Leonhard Euler]] to describe the [[Orientation (geometry)|orientation]] of a [[rigid body]] with respect to a fixed [[coordinate system]].<ref name="Euler">Novi Commentarii academiae scientiarum Petropolitanae 20, 1776, pp. 189–207 (E478) [https://math.dartmouth.edu/~euler/docs/originals/E478.pdf PDF]</ref>

They can also represent the orientation of a mobile [[frame of reference]] in physics or the orientation of a general [[Basis (linear algebra)|basis]] in  three dimensional [[linear algebra]].

Classic Euler angles usually take the inclination angle in such a way that zero degrees represent the vertical orientation. Alternative forms were later introduced by [[Peter Guthrie Tait]] and [[George H. Bryan]] intended for use in aeronautics and engineering in which zero degrees represent the horizontal position.