Euler anglesEuler 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:
- 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
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:
- "NASA standard aerospace" convention: "precession, nutation and spin";
- "heading, attitude and bank"
- G. J. Minkler, Aerospace Coordinate Systems and Transformations. Magellan Book Company, Balitmore, MD, 1990.