If you code a system with 3D rotations coded as Euler angles, you can align two axises and lose a degree of freedom. This is gimbal lock. Using unit quaternio

If you code a system with 3D rotations coded as Euler angles, you can align two axises and lose a degree of freedom. This is gimbal lock. Using unit quaternions (aka versors) to code the rotation instead, you cannot lose a degree of freedom. 4x4 matrices also solve this problem, but quaternions are more mathematically efficient. They also give very smooth interpolation for computer-assisted animations. Also related to spinors in quantum physics and exists as a subalgebra of some conformal geometric algebras.