In the sections below, an axis designation with a prime mark superscript (e.g., z″) denotes the new axis after an elemental rotation.Įuler angles are typically denoted as α, β, γ, or ψ, θ, φ. The three elemental rotations may be extrinsic (rotations about the axes xyz of the original coordinate system, which is assumed to remain motionless), or intrinsic (rotations about the axes of the rotating coordinate system XYZ, solidary with the moving body, which changes its orientation with respect to the extrinsic frame after each elemental rotation).
The geometrical definition demonstrates that three composed elemental rotations (rotations about the axes of a coordinate system) are always sufficient to reach any target frame.
Euler angles can be defined by elemental geometry or by composition of rotations.
