In this paper we consider the conservation laws for classical particles in $AdS_4$. At first we parameterize a geodesic line and construct conserved quantities with analog of five dimensional Minkowski space-time $M^{ (2,3)}$. Consequently we change $AdS_4$ space to AdS-Beltrami space-time and write conserved quantities in the Beltrami coordinates. Finally we take a limit for small velocity $\dot{ x}\ll c$ and we get the conserved quantities in Lorentz-Fock space-time. And finally we give out the energy of the nonrelativistic noncosmological particle under the cosmological limit.
Categories: gr-qc physics.class-ph physics.ed-ph