Euler angles are 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. Commonly, the rotations are carried out first around z-axis, then around the x-axis and finally around the z-axis again, but numerous other definitions are in use.
The Euler angles form a chart on SO(3), the mathematical group of rotations in 3D space. See Charts on SO(3) for a more complete treatment.
As a representation of rotations, Euler angles have several drawbacks:
- a single rotation can be represented by several different sets of Euler angles, allowing a phenomenon known as gimbal lock
- it is difficult to compute the combination of sets of rotations within the Euler angle framework
- they are difficult to interpolate smoothly, or in a coordinate-independent way
Quaternions provide another mechanism for representing 3D rotations which alleviate the above issues.
Some naming systems for Euler angles include:
- "NASA standard aerospace" convention: precession, nutation and spin
- heading, attitude and bank
See also
References
- G. J. Minkler, Aerospace Coordinate Systems and Transformations, Magellan Book Company, Balitmore, MD, 1990.
