  By considering the nonrelativistic limit of de-Sitter geometry one obtains
the nonrelativistic space-time with a cosmological constant and Newton-Hooke
(NH) symmetries. We show that the NH symmetry algebra can be enlarged by the
addition of the constant acceleration generators and endowed with central
extensions (one in any dimension (D) and three in D=(2+1)). We present a
classical Lagrangian and Hamiltonian framework for constructing models
quasi-invariant under enlarged NH symmetries which depend on three parameters
described by three nonvanishing central charges. The Hamiltonian dynamics then
splits into external and internal sectors with new non-commutative structures
of external and internal phase spaces. We show that in the limit of vanishing
cosmological constant the system reduces to the one presented in [1] which
possesses accelaration-enlarged Galilean symmetries.
