Mechanical models for Lorentz group representations

Simple classical mechanical models are constructed to help understand the natures of certain unitary representations of the Lorentz groupSO(3, 1) associated with its action on spacetime. In particular, different kinds of Principal Series unitary irreducible representations ofSO(3, 1) with positive or negative quadratic Casimir invariant are seen to correspond to bounded and unbounded motions, respectively, in the mechanical models.