  We demonstrate how a classical Snyder-like phase space can be constructed in
the Hamiltonian formalism for the free massless relativistic particle, for the
two-time physics model and for the relativistic Newtonian gravitodynamic
theory. In all these theories the Snyder-like phase space emerges as a
consequence of a new local scale invariance of the Hamiltonian. The
implications and consequences of this Snyder-like phase space in each of these
theories are also considered.
