Eulervinklarna

Eulervinklarna, or Euler angles, are a way to describe the orientation of a rigid body in three-dimensional space using three angles. They express orientation as a sequence of three rotations about coordinate axes, often interpreted as yaw, pitch, and roll. Because there are multiple conventions for which axes and in which order the rotations occur, Euler angles are not unique and different notations can describe the same orientation.

Common conventions include the ZYX (yaw-pitch-roll) and ZXZ schemes. In the prevalent ZYX convention, yaw is a rotation about the z axis, pitch about the y axis, and roll about the x axis, with the overall orientation obtained by the combined rotation R = Rz(ψ) Ry(θ) Rx(φ), where φ, θ, ψ are roll, pitch, and yaw angles, respectively. The same three angles can have different numerical values under other conventions, and the order of rotations matters because rotation in three dimensions is not commutative.

Euler angles connect with other representations of attitude such as rotation matrices and quaternions. A sequence of three angle-valued rotations corresponds to a 3×3 rotation matrix, while quaternions offer a related but non-redundant representation that avoids some numerical issues. However, Euler angles can be sensitive to small changes near singular configurations, a problem known as gimbal lock, where the loss of one degree of freedom complicates interpolation and control.

Applications of Euler angles span aerospace, robotics, computer graphics, and motion analysis, where intuitive, human-readable descriptions of orientation are useful. They are often used for visualization and interfacing with human operators, even as more robust representations like quaternions become preferred for computation.