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For perfect fluids with equation of state $\rho = \rho (n,s)$, Brown gave anaction principle depending only on their Lagrange coordinates $\alpha^i(x)$without Clebsch potentials. After a reformulation on arbitrary spacelikehypersurfaces in Minkowski spacetime, the Wigner-covariant rest-frame instantform of these perfect fluids is given. Their Hamiltonian invariant mass can begiven in closed form for the dust and the photon gas. The action for thecoupling to tetrad gravity is given. Dixon's multipoles for the perfect fluidsare studied on the rest-frame Wigner hyperplane. It is also shown that the sameformalism can be applied to non-dissipative relativistic elastic materialsdescribed in terms of Lagrangian coordinates.Comment: revtex file, 70 page

THE REST-FRAME INSTANT FORM OF RELATIVISTIC PERFECT FLUIDS WITH EQUATION OF STATE ρ=ρ(n, s) AND OF NONDISSIPATIVE ELASTIC MATERIALS