  In the quadri-dimensional space-time, the variation of Hamilton's action is a
powerful tool to study the process equations for conservative fluid media. In
this framework, Hamilton's principle allows to obtain equation of motions,
equation of energy but also Rankine-Hugoniot conditions. The varia-tional
method may be a versatile key to obtain the shock-wave conditions for complex
media when the equations of processes are not expressed by linear or
quasi-linear differential equations.
