Euler angles

Euler angles represent a rigid body's orientation using three successive rotations about specified axes. Their values depend on the chosen rotation sequence and coordinate-frame convention.

Rotation matrix: A matrix that represents a rotation by transforming vector coordinates while preserving lengths and angles. Successive Euler rotations can be composed by multiplying their rotation matrices.
Rigid body: An idealized object whose internal distances remain fixed during motion. Euler angles describe the orientation of such an object's body frame.
Inertial measurement unit: A sensor unit combining accelerometers and gyroscopes to measure motion and orientation. Its attitude estimates are often displayed as Euler angles.
Rotation vector: A three-component representation whose direction is the rotation axis and whose magnitude is the rotation angle. It encodes a rotation without choosing three successive axes.
Intrinsic and extrinsic rotations: Intrinsic rotations use moving axes, while extrinsic rotations use fixed axes. These conventions can describe equivalent orientations but produce different angle-order interpretations.
Three-dimensional rotation: A transformation in three-dimensional space that changes directions while preserving lengths and angles. Euler angles parameterize this class of transformations.
Flight dynamics: The study of aircraft motion and the forces and moments that produce it. Aircraft attitude is commonly expressed through heading, pitch, and roll.
Modified Rodrigues parameters: A three-parameter representation of a rotation derived from quaternion components. It offers compact rotation coordinates with a different singularity structure.
Yaw, pitch, and roll: A three-angle convention that describes heading, elevation, and tilt using a specified rotation order. This familiar Euler-angle convention names rotations by their physical effects.
Axis-angle representation: A rotation description using one axis and one angle of rotation. It represents the same orientation with a different parameterization.

Linked from 12 pages