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Euler angles

Euler angles one way of representing rotations in 3-dimensional Euclidean space as a product of three successive 2D coordinate rotations θ, φ, ψ about the x-, y- and z-axes. Most often, the rotations are carried out first around Z axis, then around the X axis and finally around the Z axis again, but other definitions are possible.

As a representation of rotations, they have several flaws:

Quaternions are a far better representation of 3D rotations for many purposes, alleviating all of the above issues.

The Euler angles form a chart on SO(3), the mathematical group of rotations in 3D space. See Charts on SO(3) for a fuller treatment.

Some naming systems for Euler angles include:

References: See also: