Wigner rotation and Euler angle parametrization

Analogous to the famous Euler angle parametrization in three-dimensional Euclidean space, a reflection-free Lorentz transformation in (2+1)-dimensional Minkowski space can be decomposed into three simple parts. Applying this decomposition to the Wigner rotation problem, we are able to show the related mathematics becomes much simpler and the physical meanings more comprehensible and enlightening.