Note on finite rotation and vector

When we study the rotation movement of rigid bodies we need a rotation kinematics that describes this type of displacement that the bodies can have. It is said in the textbooks that: “… we cannot identify finite rotations with vectors.” This note uses a simple algebraic demonstration to show the validity of this statement in the case of finite angular movement of a particle and to understand why despite this impossibility we can associate a vector with an infinitesimal angular variation, without any conflict.

Keywords:
Finite rotation; infinitesimal rotation; vector; angular displacement vector