  We examine Hamiltonian formalism on Euclidean Snyder space. The latter
corresponds to a lattice in the quantum theory. For any given dynamical system,
it may not be possible to identify time with a real number parametrizing the
evolution in the quantum theory. The alternative requires the introduction of a
dynamical time operator. We obtain the dynamical time operator for the
relativistic (nonrelativistic) particle, and use it to construct the generators
of Poincar\'e (Galilei) group on Snyder space.
