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In previous papers, we have presented hyperbolic governing equations and jumpconditions for barotropic fluid mixtures. Now we extend our results to the mostgeneral case of two-fluid conservative mixtures taking into account theentropies of components. We obtain governing equations for each component ofthe medium. This is not a system of conservation laws. Nevertheless, usingHamilton's principle we are able to obtain a complete set of Rankine-Hugoniotconditions. In particular, for the gas dynamics they coincide with classicaljump conditions of conservation of momentum and energy. For the two-fluid case,the jump relations do not involve the conservation of the total momentum andthe total energy.

Hamilton's Principle and Rankine-Hugoniot Conditions for General Motions of Mixtures