Eulerangles

Euler angles are a set of three angles used to describe the orientation of a rigid body in three-dimensional space. They represent a sequence of rotations about the principal axes of the body. There are several conventions for defining Euler angles, often denoted by a sequence of three Greek letters like \( \alpha, \beta, \gamma \). The specific order of rotations and the axes about which these rotations are performed are crucial in defining a particular Euler angle representation.

Common conventions include Z-X-Z, Z-Y-Z, X-Y-Z, and others. Each convention implies a different sequence of rotations. For example, a Z-Y-Z convention would involve a rotation about the z-axis, followed by a rotation about the new y-axis, and finally another rotation about the newest z-axis. The choice of convention depends on the application.

Euler angles are widely used in various fields, including robotics, aerospace engineering, computer graphics, and physics. They provide a way to parameterize rotational transformations. However, they suffer from the "gimbal lock" problem, a singularity that occurs when the middle rotation angle is 0 or \(\pi\), causing two of the rotational degrees of freedom to become dependent. This can lead to difficulties in interpolation and numerical stability. Due to gimbal lock, other representations like quaternions are often preferred in certain applications.