  This article discusses and explains the Hamiltonian formulation for a class
of simple gauge invariant mechanical systems consisting of point masses and
idealized rods. The study of these models may be helpful to advanced
undergraduate or graduate students in theoretical physics to understand, in a
familiar context, some concepts relevant to the study of classical and quantum
field theories. We use a geometric approach to derive the Hamiltonian
formulation for the model considered in the paper: four equal masses connected
by six ideal rods. We obtain and discuss the meaning of several important
elements, in particular, the constraints and the Hamiltonian vector fields that
define the dynamics of the system, the constraint manifold, gauge symmetries,
gauge orbits, gauge fixing, and the reduced phase space.
